{
  "protocol_version": "heat-inverse-v1",
  "data_kind": "constructed simulation; not physical measurements",
  "config": {
    "L_m": 1.0,
    "assumed_kappa_m2_per_s": 0.01,
    "N": 16,
    "M": 8,
    "time_s": 1.0,
    "future_time_s": 1.5,
    "noise_sigma_K": 0.02,
    "manual_lambda": 0.001,
    "lambda_candidates": [
      1e-06,
      1e-05,
      0.0001,
      0.001,
      0.01,
      0.1
    ],
    "split_seeds": {
      "train": 101,
      "validation": 202,
      "test": 303
    },
    "split_counts": {
      "train": 128,
      "validation": 32,
      "test": 32
    },
    "test_scenarios": [
      "smooth",
      "high-frequency",
      "wrong-diffusivity"
    ]
  },
  "fitted": {
    "learned_weights": [
      1.103667722036627,
      1.4875059427833095,
      2.3852023153421498,
      3.7201957517355746,
      1.5403195228515336,
      0.2617685121257251,
      0.12301144397794432,
      -0.04874553326738988
    ],
    "validation_selected_lambda": 0.01,
    "validation_scores": [
      {
        "lambda": 1e-06,
        "initial_field_mse_K2": 4.1242804752439985
      },
      {
        "lambda": 1e-05,
        "initial_field_mse_K2": 0.652696130258817
      },
      {
        "lambda": 0.0001,
        "initial_field_mse_K2": 0.07391091908191762
      },
      {
        "lambda": 0.001,
        "initial_field_mse_K2": 0.007877252590200433
      },
      {
        "lambda": 0.01,
        "initial_field_mse_K2": 0.0018293230951237779
      },
      {
        "lambda": 0.1,
        "initial_field_mse_K2": 0.032886621436539656
      }
    ],
    "learned_fit_split": "train",
    "lambda_selection_split": "validation"
  },
  "metric_aggregation": "sqrt(mean squared error over all trajectories and all 16 sensors)",
  "tikhonov_table_lambda": "validation_selected_lambda",
  "splits": {
    "train": [
      {
        "split": "train",
        "index": 0,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.104647695846184,
          -0.2805735040325878,
          0.20209722847646489,
          0.04017927940437796,
          -0.03410261618256248,
          0.04798415515573114,
          0.06632116540520665,
          -0.059885407164685135
        ],
        "initial_K": [
          0.33956014288965036,
          0.6535156932796986,
          0.9127748735240991,
          1.1189690790556177,
          1.3088079068505347,
          1.4901962487090623,
          1.6131910747547449,
          1.6479547012222193,
          1.6482735070826608,
          1.6736277817414165,
          1.6800381024865387,
          1.5673923693568925,
          1.322375312335472,
          1.0296086889104739,
          0.737018352977622,
          0.4019599215457906
        ],
        "observed_K": [
          0.3060662882807371,
          0.5628028807823423,
          0.7843742337429129,
          0.9839103175601062,
          1.2210989921672655,
          1.3809801991988122,
          1.437086196348851,
          1.5320549749831125,
          1.5508059884602476,
          1.560638666087851,
          1.4839428169984374,
          1.3308727240505536,
          1.1890852938445653,
          0.9598714177245478,
          0.6783926201914061,
          0.30233577290603075
        ],
        "future_observed_K": [
          0.2632560321584337,
          0.5484926613350678,
          0.764770415057605,
          1.0060652358452753,
          1.1507950419029507,
          1.299125385005007,
          1.4068818779850267,
          1.5015243292164033,
          1.497542969327583,
          1.4860976796553993,
          1.4139429149304619,
          1.2700580822127554,
          1.0758864459974515,
          0.8870568869407418,
          0.5925738306750659,
          0.2887895499637475
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.1094277469266505,
              -0.35334789457897114,
              0.26095205376239305,
              -0.026854065942651523,
              0.01945936717593193,
              0.5335952010450165,
              2.707439386806379,
              34.9709736641184
            ],
            "initial_K": [
              13.325287439160103,
              3.4677912037389063,
              -11.298023503284696,
              -4.214191610703197,
              12.097277419510524,
              8.765311869504028,
              -7.483479145395528,
              -7.079681161877546,
              8.927391476921757,
              11.407498437474047,
              -3.8202512950917518,
              -8.907546118660761,
              5.048771680358561,
              12.075011832123476,
              -1.0508049921978553,
              -10.789960758137166
            ],
            "metrics": {
              "initial_rmse_K": 8.78346655664109,
              "observation_residual_rms_K": 0.012270404366129237,
              "future_predictive_rmse_K": 0.01863368205195333
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.047932740076233,
              -0.34573330678333664,
              0.24639199127608785,
              -0.021738913815595326,
              0.008140440230480602,
              0.040442226006591316,
              0.016952837138860012,
              0.01140468291846677
            ],
            "initial_K": [
              0.3389105312639926,
              0.6313353057068769,
              0.8743060783076473,
              1.0930164609322435,
              1.2945488066567254,
              1.4578981999229004,
              1.5659471101914657,
              1.6261848639725214,
              1.6550436331179355,
              1.6560707702981967,
              1.6186807859014694,
              1.5265025602285003,
              1.3614262905005254,
              1.1111362595856105,
              0.7823885182911845,
              0.4020084681355233
            ],
            "metrics": {
              "initial_rmse_K": 0.037599152297532544,
              "observation_residual_rms_K": 0.02527356570611031,
              "future_predictive_rmse_K": 0.025472213499703182
            }
          },
          "learned": {
            "coefficients_K": [
              5.1091359156078955,
              -0.3541674366490293,
              0.25604577606998924,
              -0.020595175007145316,
              0.0025419139833331834,
              0.003999963393072808,
              0.002643687036320026,
              -0.0030789392699408394
            ],
            "initial_K": [
              0.32134140956891893,
              0.6250060335428514,
              0.896065572481247,
              1.1262143578878776,
              1.3144925162470624,
              1.4626716175352985,
              1.5714257445294124,
              1.6421940612326842,
              1.6788661408423233,
              1.6822612589569657,
              1.643087201338034,
              1.5444764210306146,
              1.3726070614928747,
              1.1232988526117689,
              0.8009512976086545,
              0.4182724779889945
            ],
            "metrics": {
              "initial_rmse_K": 0.03758275692824606,
              "observation_residual_rms_K": 0.021063141051115588,
              "future_predictive_rmse_K": 0.018463380856813497
            }
          }
        }
      },
      {
        "split": "train",
        "index": 1,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.00872881316169,
          0.8624644715481307,
          0.5455940910733243,
          0.048115539892920424,
          0.16281498135095263,
          -0.027350458943952684,
          0.0079783730592905,
          -0.0061754873602832055
        ],
        "initial_K": [
          0.6318911073883523,
          1.1750351342602807,
          1.5713744072044293,
          1.813343271717981,
          1.9374588578270617,
          1.991321196072407,
          2.0007836195541784,
          1.9648825087910906,
          1.8751144345453572,
          1.7341704574444563,
          1.5599325261459287,
          1.3769269189509343,
          1.198579994856696,
          1.0078925227226612,
          0.7593308201404192,
          0.41694091240864056
        ],
        "observed_K": [
          0.4621959865613294,
          0.8889869159877616,
          1.2712027721174746,
          1.5071560873723724,
          1.6977719335905195,
          1.8305574005622187,
          1.8752942715293848,
          1.8131828584766962,
          1.727599182349406,
          1.6294064812299076,
          1.4698063293370343,
          1.3613315957653311,
          1.1300759290548046,
          0.8901056306536612,
          0.6062955104988952,
          0.31097961909511573
        ],
        "future_observed_K": [
          0.39515574533314274,
          0.7935805185902532,
          1.1086285935106275,
          1.4343348399901443,
          1.5875004255055294,
          1.6914682411403568,
          1.7578670708186046,
          1.7766309624958438,
          1.6729427985364853,
          1.5905975722273362,
          1.4526049061845112,
          1.2772406085855608,
          1.0802298115588618,
          0.8231668969238876,
          0.59751292435892,
          0.27154935818953324
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.015154554857573,
              0.8746866661504826,
              0.6120970565931212,
              -0.03052917681585137,
              -0.03352961721197741,
              1.458815411357354,
              0.12272388349308419,
              -11.973461828255036
            ],
            "initial_K": [
              -3.019167476215131,
              0.7807037713119273,
              5.381013873807686,
              2.8249841989594118,
              -1.9778535732965388,
              0.12622652860949612,
              5.7989666095944035,
              4.89765733340089,
              -1.2805367258648905,
              -2.086821625557336,
              3.5897102378789816,
              5.460817625737027,
              0.22675805448888298,
              -2.8556862725973313,
              1.1079809395300493,
              4.061049570147125
            ],
            "metrics": {
              "initial_rmse_K": 3.015451328166425,
              "observation_residual_rms_K": 0.011536763150785565,
              "future_predictive_rmse_K": 0.01840463282069653
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.942758586291468,
              0.8558373153682746,
              0.5779445321612031,
              -0.02471399098662279,
              -0.014026450212758479,
              0.110566478957211,
              0.0007684449077771633,
              -0.0039047679054965362
            ],
            "initial_K": [
              0.6082625067049333,
              1.1286397481481383,
              1.5188548794689671,
              1.7884649433743287,
              1.9631450410065927,
              2.0471395528471668,
              2.0271521610035896,
              1.9123397525847312,
              1.7566027153454105,
              1.625245747788334,
              1.536328207607687,
              1.4430289641739262,
              1.2789699697538992,
              1.018194857300278,
              0.6899588789824629,
              0.34237018649595324
            ],
            "metrics": {
              "initial_rmse_K": 0.06179492017319459,
              "observation_residual_rms_K": 0.02339040301173234,
              "future_predictive_rmse_K": 0.021532449696231106
            }
          },
          "learned": {
            "coefficients_K": [
              6.014810991826015,
              0.8767153821327396,
              0.6005887427436993,
              -0.023413725902412093,
              -0.004379865083811629,
              0.010935646031395964,
              0.00011983409173204819,
              0.0010541760196393273
            ],
            "initial_K": [
              0.5933093606367639,
              1.125895682970415,
              1.552353500470995,
              1.8492365791097787,
              2.0135350839310133,
              2.059221033932727,
              2.014203532010671,
              1.9146361401650167,
              1.7948610315821796,
              1.6763252318379955,
              1.5607368916530864,
              1.4310233756787716,
              1.2608083249119568,
              1.0288742943483604,
              0.7305941711506885,
              0.37943603506033113
            ],
            "metrics": {
              "initial_rmse_K": 0.04867936941301467,
              "observation_residual_rms_K": 0.016488778937134053,
              "future_predictive_rmse_K": 0.017977687750276562
            }
          }
        }
      },
      {
        "split": "train",
        "index": 2,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.687190854207929,
          0.2885105445854004,
          0.2676302378115174,
          -0.031256087141210115,
          -0.12443156151213455,
          -0.03359398429718672,
          0.01856084105563407,
          0.0123875727837357
        ],
        "initial_K": [
          0.46429420638930763,
          0.9206275446712173,
          1.357228155637682,
          1.7413856048609535,
          2.01962087081128,
          2.1588058302826174,
          2.1855695264678623,
          2.165453186694298,
          2.139197256268402,
          2.091914590167203,
          1.9840933885312644,
          1.7948396845674166,
          1.5291573634181757,
          1.2011100122910263,
          0.8254710915398252,
          0.4194112649396484
        ],
        "observed_K": [
          0.4111449917289168,
          0.7965802991520778,
          1.1457123501430897,
          1.4845221090772336,
          1.7416219809389368,
          1.9322541275586338,
          1.9847579344456392,
          2.018211877622779,
          1.9900013880767116,
          1.9676174855888253,
          1.8270998430544578,
          1.5924765251106396,
          1.358859741727581,
          1.0795420448820543,
          0.7205974294170661,
          0.3876709123489753
        ],
        "future_observed_K": [
          0.3919207141945127,
          0.7507955787274103,
          1.1074695834391028,
          1.425168119883125,
          1.6569761732866173,
          1.8018080134596515,
          1.9329087739249216,
          1.9339155248318707,
          1.9441609921878693,
          1.8187839378568045,
          1.6963320209988204,
          1.5389731368128612,
          1.303910868257501,
          1.0193670050543437,
          0.6584932797284608,
          0.3553248227544602
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.663092267497911,
              0.24718609090272134,
              0.21612709184373524,
              -0.06292619584949306,
              -0.5441829338777016,
              -0.981545698528181,
              4.652563920874571,
              16.042907366317376
            ],
            "initial_K": [
              7.0388275631076365,
              2.330584249868649,
              -5.037663858342754,
              -1.3149418862426623,
              7.575183594131473,
              6.610544311301421,
              -1.9720908385668352,
              -3.0971851381314197,
              4.624780224164711,
              7.352917748496217,
              0.8833764948928429,
              -2.915838381092563,
              1.8521031297275785,
              5.306489681394984,
              0.7744358981915371,
              -3.3489983411843536
            ],
            "metrics": {
              "initial_rmse_K": 4.179804848045729,
              "observation_residual_rms_K": 0.010657475576655136,
              "future_predictive_rmse_K": 0.02077528804847165
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.582897982554511,
              0.2418592721501115,
              0.20406807978823516,
              -0.05094003832554576,
              -0.2276481350923918,
              -0.07439327208702785,
              0.029132381989079498,
              0.005231889548185874
            ],
            "initial_K": [
              0.3961797317281953,
              0.8269252730224351,
              1.2866765419398432,
              1.7124522389401236,
              2.0145111218006724,
              2.1456285621264093,
              2.1462996465336475,
              2.11000323075597,
              2.0961766878546135,
              2.0813558141492865,
              1.996161655057233,
              1.7989410063186586,
              1.505878272041045,
              1.1601173937028495,
              0.7900112004294813,
              0.40189611606436126
            ],
            "metrics": {
              "initial_rmse_K": 0.04327394885380943,
              "observation_residual_rms_K": 0.025886108040958238,
              "future_predictive_rmse_K": 0.02769146196565376
            }
          },
          "learned": {
            "coefficients_K": [
              6.662711696698259,
              0.24775940520212977,
              0.2120635885520442,
              -0.04825995507800739,
              -0.07108485063306075,
              -0.007357912618126367,
              0.004543009525238172,
              -0.0014124610303561293
            ],
            "initial_K": [
              0.45705927839796157,
              0.9066890214999331,
              1.3294119894305958,
              1.6932559142354182,
              1.9662590139725167,
              2.1328915182936963,
              2.202559644885647,
              2.203105433786119,
              2.16192018246197,
              2.0877038162137778,
              1.9677504636482674,
              1.7828244344888893,
              1.5248977888238986,
              1.2018284273820055,
              0.8293575206999999,
              0.42344862220573276
            ],
            "metrics": {
              "initial_rmse_K": 0.02444101586090008,
              "observation_residual_rms_K": 0.020028959487562455,
              "future_predictive_rmse_K": 0.021168945256996908
            }
          }
        }
      },
      {
        "split": "train",
        "index": 3,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          4.863723601647442,
          -1.953248730135774,
          0.135013077587365,
          -0.34643781745348595,
          0.09532429542595888,
          0.08975539953780483,
          -0.0028814371106856695,
          -0.0262169386520144
        ],
        "initial_K": [
          0.05259286940675706,
          0.12826746505893416,
          0.24524904563318983,
          0.42921878857296936,
          0.7046586966180565,
          1.0478694312181698,
          1.370524360411885,
          1.5887281296732936,
          1.7045571569113238,
          1.7874994685351253,
          1.875790107378922,
          1.9258966704205358,
          1.8598138126498065,
          1.6283620141353496,
          1.221774088855751,
          0.6595248784968348
        ],
        "observed_K": [
          0.08226169952500711,
          0.2428351019062918,
          0.40000509837995374,
          0.5639606584538165,
          0.794665801858761,
          1.0326633382360082,
          1.2476288133210653,
          1.4464023860357906,
          1.5629139312752185,
          1.6467243981861197,
          1.6706791855251495,
          1.64975951145856,
          1.4702943524927081,
          1.2294163264407716,
          0.910655295675755,
          0.42619545368362494
        ],
        "future_observed_K": [
          0.16164378585328903,
          0.2880192655077123,
          0.4161032554514385,
          0.601299478128338,
          0.8162059364749846,
          0.9757828263907472,
          1.1837887836819785,
          1.3462688912153387,
          1.5026030370930992,
          1.5605115083767689,
          1.5850869415947635,
          1.535162579427114,
          1.3314068739760605,
          1.116882714974086,
          0.8007106006825068,
          0.4233038187187182
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              4.879599652853202,
              -1.9252425089399916,
              0.07338325950798692,
              -0.43582804773958705,
              0.013627899130240118,
              0.8407737117439925,
              -1.615871157148847,
              -8.42520876230661
            ],
            "initial_K": [
              -3.1671629623175015,
              -0.5547316185058035,
              3.2973216989825413,
              1.7228632242331956,
              -2.0993651296243097,
              -0.8617355661537663,
              3.772950615302467,
              4.120153382612934,
              0.05747974867889605,
              -0.9859818347041593,
              2.7388871562213275,
              4.57582415748143,
              1.5597709661826304,
              -0.7348743934281705,
              1.2344599658224402,
              2.7500402445687206
            ],
            "metrics": {
              "initial_rmse_K": 2.1466300266693743,
              "observation_residual_rms_K": 0.015000683273447597,
              "future_predictive_rmse_K": 0.020414599087004392
            }
          },
          "tikhonov": {
            "coefficients_K": [
              4.820870764033902,
              -1.8837538561501421,
              0.0692887723082122,
              -0.35281168924151973,
              0.005700961256024265,
              0.06372388732911895,
              -0.010117899849583861,
              -0.002747616791538854
            ],
            "initial_K": [
              0.01826653224584085,
              0.08013976552611868,
              0.21912265096390882,
              0.4487443922397506,
              0.75223762278393,
              1.0792295862769987,
              1.3642198896383129,
              1.565284184880962,
              1.6910209237803693,
              1.7828135305136845,
              1.8628761883800156,
              1.8988781334511897,
              1.8213132786963264,
              1.5752536216239474,
              1.1571752582288157,
              0.6108769372389966
            ],
            "metrics": {
              "initial_rmse_K": 0.035654041552972665,
              "observation_residual_rms_K": 0.02291062536341594,
              "future_predictive_rmse_K": 0.025345910651444606
            }
          },
          "learned": {
            "coefficients_K": [
              4.879320948451805,
              -1.9297078453841796,
              0.07200354762632553,
              -0.33424938090894585,
              0.0017801682372002667,
              0.006302650515311131,
              -0.0015778220747378626,
              0.000741778206259429
            ],
            "initial_K": [
              0.006341385264094279,
              0.06868764651150572,
              0.2215837026977805,
              0.46506587837720503,
              0.7662781230697632,
              1.0756407714067797,
              1.349123109898485,
              1.564439090581063,
              1.7229174329198667,
              1.8368436048768384,
              1.909661167738489,
              1.9212627299936385,
              1.8296624399269326,
              1.5908366114442143,
              1.1852760905251494,
              0.6346386035277803
            ],
            "metrics": {
              "initial_rmse_K": 0.03653726369343647,
              "observation_residual_rms_K": 0.017706202758063068,
              "future_predictive_rmse_K": 0.019198267398096748
            }
          }
        }
      },
      {
        "split": "train",
        "index": 4,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.814437577008524,
          1.462019531145553,
          0.332194803877343,
          -0.10436119369504314,
          -0.06253688108170846,
          -0.028202104219291396,
          -0.05521446994465889,
          -0.011630670136537388
        ],
        "initial_K": [
          0.5355125895681354,
          1.0855746394134516,
          1.5942935419443134,
          1.9662447648434926,
          2.1546683283506276,
          2.1889276259651806,
          2.120241868668736,
          1.9748186041212203,
          1.7694771519109762,
          1.5410746212399005,
          1.3308972162996717,
          1.1464382643118316,
          0.9592507023210598,
          0.7424031423465487,
          0.49809094740570536,
          0.24670338429308458
        ],
        "observed_K": [
          0.4641084791262178,
          0.9317719420990964,
          1.2813140366285707,
          1.5837494458885757,
          1.776401175008519,
          1.907884884865377,
          1.8726718012207477,
          1.8427893396947732,
          1.7012344195649056,
          1.5350610273967757,
          1.3318986443335767,
          1.1408664935985173,
          0.9059930668591237,
          0.6593156953979391,
          0.4691398786071819,
          0.2514177556431073
        ],
        "future_observed_K": [
          0.4473516246080543,
          0.8488402751134383,
          1.181202949982689,
          1.4386869361749008,
          1.6336113445597693,
          1.7455692017921094,
          1.7982551855670703,
          1.7517751898327023,
          1.6022685097325604,
          1.5031686180407458,
          1.295301800984743,
          1.0840198054202148,
          0.9056124267913332,
          0.6783994262797277,
          0.4709622943731628,
          0.256715893465349
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.819175327785794,
              1.473550154846363,
              0.25343332978648053,
              -0.02839501140408398,
              0.08084642624497282,
              -0.191532898984138,
              2.3510330097041945,
              -7.397693549090128
            ],
            "initial_K": [
              -1.1990922456997841,
              1.0621571503519944,
              3.5013053096499474,
              2.1588590734031667,
              0.008914502368650323,
              1.608223831724966,
              4.391857567851863,
              3.056374182743278,
              -0.4860912833206894,
              -0.076650164931511,
              3.501804207453862,
              3.4806375038580346,
              -0.803691916735284,
              -2.2932159859007046,
              1.4378891054320166,
              3.6196142172300183
            ],
            "metrics": {
              "initial_rmse_K": 1.9429892745896928,
              "observation_residual_rms_K": 0.0129510620252724,
              "future_predictive_rmse_K": 0.01820191661351058
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.749138085971147,
              1.4417953964411425,
              0.2392927814957074,
              -0.022986340579652244,
              0.03382049861873996,
              -0.014516653772830021,
              0.014721171567431818,
              -0.0024125250290621815
            ],
            "initial_K": [
              0.5877171014381867,
              1.120821666087099,
              1.5587127924765114,
              1.879419453392717,
              2.0750846121569206,
              2.1473315395689876,
              2.1084189854434277,
              1.982591753308721,
              1.7992830161868318,
              1.582223935753447,
              1.3473438967615703,
              1.11024953107965,
              0.8872965595956168,
              0.6825013632845789,
              0.478446170976078,
              0.25161159177740205
            ],
            "metrics": {
              "initial_rmse_K": 0.046350361356480546,
              "observation_residual_rms_K": 0.022032765082465957,
              "future_predictive_rmse_K": 0.020976272912379173
            }
          },
          "learned": {
            "coefficients_K": [
              5.8188429583514685,
              1.4769678527094738,
              0.2486684150271769,
              -0.021776971518796175,
              0.010560706292072388,
              -0.0014357786258295648,
              0.002295672996412652,
              0.0006513129829911419
            ],
            "initial_K": [
              0.5930375996061369,
              1.1347341333076864,
              1.5837854843792758,
              1.913501596879044,
              2.1117898285588366,
              2.1806761075337726,
              2.135851362391911,
              2.003285594088491,
              1.812535089889671,
              1.59043927310513,
              1.3578837601379565,
              1.128348367728552,
              0.9065911822508823,
              0.6889838098317194,
              0.4677304239427964,
              0.23753162747969256
            ],
            "metrics": {
              "initial_rmse_K": 0.03837123613891473,
              "observation_residual_rms_K": 0.014331134653536942,
              "future_predictive_rmse_K": 0.01863237114595625
            }
          }
        }
      },
      {
        "split": "train",
        "index": 5,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          7.048471588816824,
          2.0820196898024346,
          0.15954576123540715,
          0.23002896253787325,
          0.2559850517756565,
          -0.028607566440521124,
          -0.0274857661186438,
          0.0549966969419974
        ],
        "initial_K": [
          0.8551683178436045,
          1.5571167066486833,
          2.0511473914335916,
          2.3628199109651646,
          2.5287266993814708,
          2.5859412957406187,
          2.581663679840722,
          2.525623468182826,
          2.35593378826262,
          2.0206885136708372,
          1.5851732313681073,
          1.1910726523104822,
          0.9064167008919498,
          0.6793822990364411,
          0.44651136506209854,
          0.21291611886622713
        ],
        "observed_K": [
          0.5878254183617536,
          1.1408373799571798,
          1.6386978278836406,
          1.9769601818568594,
          2.222207062420728,
          2.3409136606452234,
          2.3454137085200877,
          2.242575774859905,
          2.1109080088083276,
          1.8536032897335888,
          1.5925123131305727,
          1.285674396843303,
          1.0019065630774566,
          0.7210025918819756,
          0.4528293492592704,
          0.24141132779181415
        ],
        "future_observed_K": [
          0.5318792096199391,
          1.014890632387662,
          1.4883041911977497,
          1.7933412690063986,
          2.0396984621660854,
          2.1681379500602516,
          2.1724514419510474,
          2.137317909558472,
          2.0022299254129177,
          1.7962069611912008,
          1.5459620084764765,
          1.291955606891899,
          1.0433398717754223,
          0.7643445211924593,
          0.48477606179947075,
          0.25956022810825535
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              7.068472631565942,
              2.1186557084009023,
              0.09857631824237714,
              0.2151058897598081,
              0.01869551162422498,
              -0.5854071086528849,
              -0.6840334628148139,
              -2.3510559392789894
            ],
            "initial_K": [
              -0.42774439218362137,
              1.0433632273307876,
              2.9922683128228087,
              3.0885684336970503,
              1.9710031245298523,
              1.9380361512183386,
              2.9856561147267437,
              3.119020186939188,
              2.0301305529105393,
              1.4654604915248775,
              1.9142427868766778,
              1.8239629975932115,
              0.6453979201958084,
              -0.05154015467234774,
              0.5341173494017103,
              0.9132367165649554
            ],
            "metrics": {
              "initial_rmse_K": 0.6418799748115881,
              "observation_residual_rms_K": 0.009554822770966547,
              "future_predictive_rmse_K": 0.01801679018348989
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.983399352437648,
              2.072999033639719,
              0.0930761609047162,
              0.17413260281335632,
              0.0078208964135017,
              -0.04436915202317906,
              -0.004283127426283284,
              -0.0007667229333842136
            ],
            "initial_K": [
              0.7408742476772497,
              1.4219608692198493,
              1.9819061178236752,
              2.3727803901294493,
              2.5825357997500813,
              2.6393695411389726,
              2.5882037017700097,
              2.4591776067717497,
              2.256694159234372,
              1.9764008646311235,
              1.6307025853611337,
              1.2576066127926238,
              0.9053663787962727,
              0.6075001854784685,
              0.36936294208695397,
              0.1744590706353898
            ],
            "metrics": {
              "initial_rmse_K": 0.06952525440835564,
              "observation_residual_rms_K": 0.023335447650701183,
              "future_predictive_rmse_K": 0.019042525180392976
            }
          },
          "learned": {
            "coefficients_K": [
              7.068068906962751,
              2.1235696402840176,
              0.0967229402588789,
              0.1649710496031325,
              0.0024421340115295728,
              -0.004388358441137081,
              -0.0006679264573253197,
              0.00020699333472379064
            ],
            "initial_K": [
              0.7633466103167428,
              1.4520113205653788,
              2.007116512018384,
              2.396588582458356,
              2.617626136197247,
              2.6896082568451933,
              2.640735236424309,
              2.495567543922111,
              2.270451053163611,
              1.9782674090746402,
              1.6369530416465587,
              1.2739008475940596,
              0.9224071333852788,
              0.6123537822817269,
              0.36029044492218043,
              0.16341717080891088
            ],
            "metrics": {
              "initial_rmse_K": 0.07021457356932095,
              "observation_residual_rms_K": 0.010912772266400542,
              "future_predictive_rmse_K": 0.018522101229576104
            }
          }
        }
      },
      {
        "split": "train",
        "index": 6,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.814331777165797,
          -0.8385446658784401,
          0.0698578970617889,
          0.16998235346960403,
          -0.15408633461287627,
          0.15036531509331977,
          -0.04928461273287668,
          -0.0073370482296300325
        ],
        "initial_K": [
          0.2996712117247152,
          0.5871230786241434,
          0.848023948162891,
          1.0812517251573825,
          1.3053303564014853,
          1.5312979076222768,
          1.735968231312076,
          1.883859984968991,
          1.9739905938343494,
          2.036447383929738,
          2.0678900325327665,
          1.9939906455999552,
          1.7300021810730803,
          1.284013241936844,
          0.7771577226609159,
          0.3415889923257348
        ],
        "observed_K": [
          0.2584073073013436,
          0.5622736788336284,
          0.7744131497644089,
          1.0396862721445386,
          1.234212310326869,
          1.4756913315302744,
          1.6087047808724655,
          1.7271029401961056,
          1.8525333574466438,
          1.8317468204359797,
          1.7777089376474196,
          1.6729826833882824,
          1.4241503469527645,
          1.1088997275277384,
          0.8065482586683528,
          0.39198884824179636
        ],
        "future_observed_K": [
          0.26167749438905635,
          0.5102675888413102,
          0.783488379171261,
          1.0037302049555294,
          1.239706994998632,
          1.3898937409487813,
          1.5971796580225932,
          1.6683980167830166,
          1.7422938415347495,
          1.7000029318685779,
          1.7107951841991265,
          1.5566606020292995,
          1.3179008492215352,
          1.0431298688534145,
          0.7544785069087783,
          0.3672041729424285
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.819135753975309,
              -0.864620647860721,
              0.08401115285020594,
              0.15913217886462072,
              -0.12607258086883885,
              0.18099937473408723,
              1.3734040371434164,
              -1.2466050419398738
            ],
            "initial_K": [
              0.35996287203200006,
              0.7787414412419772,
              0.9243793340822101,
              0.7782127355988002,
              0.9942719121220643,
              1.7877738079764187,
              2.2606213554498895,
              1.791614888806835,
              1.298551326760896,
              1.864510277813355,
              2.7714266186834124,
              2.4713824829429694,
              1.1592524252252328,
              0.5685048813305252,
              1.127679508438795,
              1.241049610205533
            ],
            "metrics": {
              "initial_rmse_K": 0.471869450079829,
              "observation_residual_rms_K": 0.018002889772597435,
              "future_predictive_rmse_K": 0.02023758359389231
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.749098988455048,
              -0.845988218082418,
              0.07932367245904062,
              0.12882074278858044,
              -0.052739963226274084,
              0.013718297326722247,
              0.008599673581246555,
              -0.0004065410178291254
            ],
            "initial_K": [
              0.29408295298522363,
              0.5730891416086514,
              0.8314334883661068,
              1.0717818205374767,
              1.2963632235839622,
              1.5028852153365682,
              1.688547503989947,
              1.8520871463182724,
              1.9855059860395292,
              2.0635715571171787,
              2.047753138036067,
              1.9076626738531555,
              1.6423619918097356,
              1.281875300649629,
              0.8686118163124459,
              0.4360459906350451
            ],
            "metrics": {
              "initial_rmse_K": 0.049013212045430965,
              "observation_residual_rms_K": 0.02449055968578604,
              "future_predictive_rmse_K": 0.027356745132535682
            }
          },
          "learned": {
            "coefficients_K": [
              5.8188033868012905,
              -0.8666260170915383,
              0.08243162113470774,
              0.1220431602418868,
              -0.016468452099602134,
              0.0013568166874205773,
              0.0013410643526570282,
              0.00010975448537977344
            ],
            "initial_K": [
              0.29882843429714934,
              0.582900880044194,
              0.8436696395831769,
              1.080957282570877,
              1.300412476549571,
              1.5083793359513593,
              1.7062030457562531,
              1.8851795201690653,
              2.0242229286217097,
              2.093244429729961,
              2.062950068078624,
              1.9168513843645711,
              1.6584605483122137,
              1.3092774132843663,
              0.8992929234994497,
              0.4562762241872313
            ],
            "metrics": {
              "initial_rmse_K": 0.054213380842933444,
              "observation_residual_rms_K": 0.018511850079783457,
              "future_predictive_rmse_K": 0.02040072290988045
            }
          }
        }
      },
      {
        "split": "train",
        "index": 7,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.4839125002452125,
          0.2928290884896556,
          0.14565818627829524,
          -0.12200063611054023,
          0.10889405611104484,
          0.0060110519233369415,
          -0.053907989521738,
          -0.06179123653170855
        ],
        "initial_K": [
          0.372782590260043,
          0.7741459982548837,
          1.1424201639556326,
          1.4019526333192698,
          1.5767758525557434,
          1.741006168522199,
          1.884987193174665,
          1.9220157186931641,
          1.8241436611751827,
          1.666387535208258,
          1.5210293609895715,
          1.3802297488538533,
          1.2059624322856555,
          0.9893754376385869,
          0.7266475502051982,
          0.39511582353568964
        ],
        "observed_K": [
          0.3451727091522244,
          0.6839216562116848,
          0.9984644069780672,
          1.2411606255301635,
          1.454788759536841,
          1.584033424612426,
          1.6753600031441798,
          1.6895698786436526,
          1.6644205490258457,
          1.6143931150164106,
          1.4921458115767499,
          1.2855920433532722,
          1.1242906960700698,
          0.8647458370586325,
          0.5862329808332272,
          0.33566105456913137
        ],
        "future_observed_K": [
          0.32427753241745455,
          0.6659571099653725,
          0.9432258220148337,
          1.1638919577760232,
          1.3646894839162116,
          1.4890068990706133,
          1.5803594864866872,
          1.6147662831925258,
          1.556620963140118,
          1.5100388276007,
          1.3851187940290621,
          1.2202526250415522,
          1.0273661485421393,
          0.8618918512061396,
          0.561534133828255,
          0.2678977699267683
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.528273289253687,
              0.294270848717339,
              0.1840922094343259,
              -0.015384041135584742,
              -0.005807239526940956,
              -0.6869623860693598,
              1.263721757606441,
              -1.742407607366205
            ],
            "initial_K": [
              0.023871142679680712,
              0.7326658508089099,
              1.4726141608724848,
              1.4829342622697252,
              1.3412389743360136,
              1.8046229632286899,
              2.23763773609882,
              1.7787142744842996,
              1.1806350457341024,
              1.6373074668562593,
              2.4328489454037663,
              1.8940131175609234,
              0.39881830618346603,
              0.06408595245149584,
              1.2028764204220672,
              1.5700883810885937
            ],
            "metrics": {
              "initial_rmse_K": 0.5628500211064473,
              "observation_residual_rms_K": 0.01255526094238938,
              "future_predictive_rmse_K": 0.02364773687863447
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.461737226776216,
              0.2879293613400786,
              0.17382061343053906,
              -0.012453694911461467,
              -0.0024293434542731122,
              -0.05206622552270752,
              0.007912889666130882,
              -0.0005682314272286038
            ],
            "initial_K": [
              0.3941781812979233,
              0.778725653658709,
              1.1318989015584013,
              1.422461613844385,
              1.62693388642915,
              1.7456382187464639,
              1.8006945025898313,
              1.815533128576824,
              1.79469320076973,
              1.7243208968631811,
              1.5929062104135217,
              1.4087451557763673,
              1.1928616097527764,
              0.9549677796861016,
              0.6827399332382708,
              0.3609427838261047
            ],
            "metrics": {
              "initial_rmse_K": 0.047857439085170844,
              "observation_residual_rms_K": 0.0203601528710172,
              "future_predictive_rmse_K": 0.02008240420199722
            }
          },
          "learned": {
            "coefficients_K": [
              5.527957535050995,
              0.2949533696668495,
              0.1806310084685908,
              -0.011798474770305357,
              -0.0007585808533565249,
              -0.005149642259364267,
              0.0012339647729068914,
              0.0001534062865417994
            ],
            "initial_K": [
              0.4135087618556745,
              0.8031011738212236,
              1.147073259994391,
              1.428249524409622,
              1.6364910528417176,
              1.770523950777499,
              1.8371380390314813,
              1.846910205663085,
              1.8087378079598921,
              1.7269780451963583,
              1.6024920802401132,
              1.4351438754999795,
              1.2249037701506196,
              0.9718601957449216,
              0.6776469810524381,
              0.3489266157378585
            ],
            "metrics": {
              "initial_rmse_K": 0.0463263748465544,
              "observation_residual_rms_K": 0.0137312758985835,
              "future_predictive_rmse_K": 0.023516088726022764
            }
          }
        }
      },
      {
        "split": "train",
        "index": 8,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.118950371267791,
          1.4940629140990473,
          0.053716601919326534,
          -0.18305933372855465,
          -0.07075900767594394,
          -0.06857597717306048,
          -0.004066546179123079,
          0.03263580609992108
        ],
        "initial_K": [
          0.5075519500973263,
          1.0165899724232061,
          1.5175686400949082,
          1.9599846773146963,
          2.257248077465314,
          2.35706877972969,
          2.2949142110186886,
          2.1484180358865155,
          1.9545733233967537,
          1.707659572093236,
          1.4235902206389999,
          1.153613483332897,
          0.9253534964195022,
          0.7132014338896869,
          0.48457581203377265,
          0.24172818898630238
        ],
        "observed_K": [
          0.47718331650864576,
          0.9045129967351963,
          1.2734209124912035,
          1.6521460039984017,
          1.8459018246050325,
          1.9922896191830872,
          1.9746843246593675,
          1.957537197493432,
          1.8030242020538199,
          1.6160208852656726,
          1.4077792536585951,
          1.1811037920306962,
          0.9763209513555962,
          0.7097329865508307,
          0.4661446787652637,
          0.2310805522270193
        ],
        "future_observed_K": [
          0.45522891020909645,
          0.8518895732558232,
          1.2160385910064182,
          1.5077202104542,
          1.7047836308190345,
          1.829501401923044,
          1.9049112329127684,
          1.8845984024971352,
          1.7452021286259751,
          1.6007017550511335,
          1.3878064334976894,
          1.1706914163859565,
          0.9699186184000399,
          0.6855726277034742,
          0.47514343437956075,
          0.21341353039497618
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.094111388163314,
              1.4684677432720583,
              0.08733496704988018,
              -0.18756859801196168,
              -0.25225363238416537,
              0.21890433307673934,
              -2.085726793411501,
              9.835221155281928
            ],
            "initial_K": [
              3.2076019217713827,
              1.2771317027193039,
              -1.2780200962067076,
              1.3169136220130089,
              5.121114891924554,
              3.478407954981644,
              -0.5786086847020344,
              0.42862029503316856,
              4.663345357965419,
              4.0105234756224375,
              -1.0552771616931724,
              -1.8539425619892982,
              2.919191700247361,
              4.439849770385358,
              -0.6329773032034012,
              -3.922162640455305
            ],
            "metrics": {
              "initial_rmse_K": 2.5067658042320478,
              "observation_residual_rms_K": 0.014298585546594692,
              "future_predictive_rmse_K": 0.020344119285566124
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.020765127070233,
              1.4368225099828493,
              0.08246203135479076,
              -0.151840603780519,
              -0.10552530299570659,
              0.016591188404193984,
              -0.013059936564847864,
              0.0032074479763220093
            ],
            "initial_K": [
              0.5102914180601055,
              1.0190492936476967,
              1.5027387489787474,
              1.9121708754922677,
              2.1920052896544835,
              2.3093445586615493,
              2.269796291521579,
              2.111890882842461,
              1.8886409617741489,
              1.6480984643640513,
              1.4173219471428573,
              1.1948437168610282,
              0.9616048811843957,
              0.7077497030535085,
              0.44925031516106134,
              0.2120269833983952
            ],
            "metrics": {
              "initial_rmse_K": 0.038831982284035664,
              "observation_residual_rms_K": 0.023683591389595412,
              "future_predictive_rmse_K": 0.031485742383981906
            }
          },
          "learned": {
            "coefficients_K": [
              6.093763315414048,
              1.4718736531772771,
              0.08569294279896625,
              -0.14385188857996128,
              -0.03295107336773865,
              0.0016409617574842173,
              -0.0020366139725667125,
              -0.0008659195175518096
            ],
            "initial_K": [
              0.5391845558018584,
              1.0614980707531803,
              1.5387029591267158,
              1.9313459015462247,
              2.2006196589146425,
              2.322919579021879,
              2.2989570369679124,
              2.154483210233102,
              1.9323111895630263,
              1.6774890108156653,
              1.4221555690110088,
              1.1788081518504203,
              0.9449569225008696,
              0.7132443801922381,
              0.47874105602358297,
              0.24050508723738456
            ],
            "metrics": {
              "initial_rmse_K": 0.02642537353982181,
              "observation_residual_rms_K": 0.0164545311148471,
              "future_predictive_rmse_K": 0.019722900005133638
            }
          }
        }
      },
      {
        "split": "train",
        "index": 9,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.914943210353943,
          -2.000522124652649,
          0.010718406953229244,
          0.029295866525175115,
          0.029074257091992736,
          0.02905220053167752,
          0.016235936653490577,
          0.0019380334148034054
        ],
        "initial_K": [
          0.1565196095249593,
          0.30451229603329183,
          0.46285274439796364,
          0.6682741153565308,
          0.9400586486679318,
          1.2609730098860739,
          1.591900803310906,
          1.8961850900577963,
          2.146017022748419,
          2.3135545623019476,
          2.3675597595852045,
          2.2828330604412743,
          2.050723111559955,
          1.680230471695759,
          1.1928968335894523,
          0.6195652531981132
        ],
        "observed_K": [
          0.1998011823018306,
          0.3749621720979429,
          0.5615207659489297,
          0.8101758190240812,
          1.0271684956663387,
          1.2752985823043852,
          1.5524462928770342,
          1.7843551816179535,
          1.8874343773835804,
          2.0371543135548222,
          2.001158791903502,
          1.9257552879590227,
          1.7181529922857912,
          1.3971899283207054,
          0.985314768309576,
          0.49942030484228495
        ],
        "future_observed_K": [
          0.19184889262102842,
          0.34039185381094816,
          0.5909045440308496,
          0.8278805615342124,
          1.012588876942605,
          1.2500533697103065,
          1.4656754045779063,
          1.6644659263643475,
          1.825366885146993,
          1.8875383683599063,
          1.8873280538341364,
          1.7804701368231313,
          1.5703515865607203,
          1.2686044471533675,
          0.9106842418134632,
          0.45900523607265803
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.963514428310475,
              -1.9797338378161613,
              0.057131402780255004,
              -0.0016546711780234908,
              0.16861998799474442,
              0.9324208115035605,
              -0.9756149178818211,
              -1.70428382788999
            ],
            "initial_K": [
              -0.4309975354135514,
              0.32568975407017253,
              1.2378219336073386,
              0.8900751209103815,
              0.12875708253659068,
              0.7217136855065058,
              2.2719102761014667,
              2.774323044610961,
              1.8990988850045027,
              1.4159424816341442,
              2.1888022950801034,
              2.9118826733071232,
              2.4354561461890984,
              1.4474710649944882,
              0.9461436024384865,
              0.6519281305128921
            ],
            "metrics": {
              "initial_rmse_K": 0.5440825094820413,
              "observation_residual_rms_K": 0.015130917386328546,
              "future_predictive_rmse_K": 0.02026437638451728
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.891739979431713,
              -1.9370709060389621,
              0.05394370303841583,
              -0.0013394900499991312,
              0.07053882695801675,
              0.07067000062636425,
              -0.006108886830002968,
              -0.0005557985558777586
            ],
            "initial_K": [
              0.1795494929945652,
              0.33998712012315374,
              0.4930232413962915,
              0.6804366994734822,
              0.9395753618242956,
              1.2660922340134055,
              1.6098621426843773,
              1.9087335033080126,
              2.1267936559074885,
              2.2599963298958046,
              2.3083174256887746,
              2.25018601744651,
              2.050247537168725,
              1.6918084364888426,
              1.1975049176714374,
              0.6171764046842235
            ],
            "metrics": {
              "initial_rmse_K": 0.026608575375518674,
              "observation_residual_rms_K": 0.024324490520095512,
              "future_predictive_rmse_K": 0.02374164886622338
            }
          },
          "learned": {
            "coefficients_K": [
              5.963173814768954,
              -1.984325559438109,
              0.05605724941393689,
              -0.001269016117091886,
              0.022026281814726455,
              0.00698966014995857,
              -0.0009526420142269464,
              0.00015004976570611218
            ],
            "initial_K": [
              0.1477055656260929,
              0.30613235950828743,
              0.48873201877924033,
              0.7094846056790198,
              0.9756131035597372,
              1.2801425304725802,
              1.600025009825552,
              1.9014782358063727,
              2.1488354122722058,
              2.3111519317856235,
              2.363808792659536,
              2.287564754413668,
              2.0697228871009465,
              1.7089353722638334,
              1.2202127161522072,
              0.6356325579530985
            ],
            "metrics": {
              "initial_rmse_K": 0.020020952117950422,
              "observation_residual_rms_K": 0.016954352932626753,
              "future_predictive_rmse_K": 0.019419279554706324
            }
          }
        }
      },
      {
        "split": "train",
        "index": 10,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.00596419914444,
          -0.5291340860991677,
          -0.021306349070397596,
          0.15400605705986878,
          -0.13318177443846788,
          0.009581581399783528,
          0.05438873733990911,
          -0.04484987455224401
        ],
        "initial_K": [
          0.25079430026484917,
          0.5097292648086147,
          0.7614359042076428,
          0.9896584084917714,
          1.1981388409234366,
          1.385165563965268,
          1.5274734252451512,
          1.6206196900503917,
          1.7012942160852937,
          1.7820336386846929,
          1.7902687113194666,
          1.6348507307494127,
          1.3268880964001903,
          0.9736721088929242,
          0.6494807934196092,
          0.3354964513655052
        ],
        "observed_K": [
          0.292942122306567,
          0.4881135531512333,
          0.7032455214454423,
          0.969845457583246,
          1.1261102122878512,
          1.2878896344687232,
          1.3994114998094442,
          1.5185259865560412,
          1.5462284976928258,
          1.5678184459709492,
          1.5262804122909046,
          1.3206567765913808,
          1.1697752452416559,
          0.9366906470996952,
          0.5936890327584515,
          0.35391170354486967
        ],
        "future_observed_K": [
          0.2011989930063166,
          0.46522760454554607,
          0.6866105182691834,
          0.8892670396831766,
          1.0964890900329691,
          1.2116001356026358,
          1.383211372869716,
          1.4340600332588953,
          1.4453391373715705,
          1.4478521395069868,
          1.4086111069411698,
          1.2654492535611137,
          1.0560217791814837,
          0.8678700054798274,
          0.5784680557221663,
          0.31799390435296365
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              4.994091500377497,
              -0.4949315674051297,
              0.05779173105748428,
              0.20503772201309864,
              -0.08407284189334903,
              -0.4905874955213745,
              2.1365757574568445,
              13.303607302549738
            ],
            "initial_K": [
              5.3861019772517675,
              1.6544364694842588,
              -4.036460387590221,
              -1.1136471169626563,
              5.535284229791817,
              4.417138432867684,
              -2.0676588385925245,
              -2.143367396910012,
              4.295275963774628,
              5.854953382553545,
              0.1406142711049876,
              -2.460275633490745,
              2.1716499770726188,
              4.871194215075146,
              0.3347452662521041,
              -3.3720177179562674
            ],
            "metrics": {
              "initial_rmse_K": 3.3798998145174504,
              "observation_residual_rms_K": 0.022882760038435097,
              "future_predictive_rmse_K": 0.022834462215532616
            }
          },
          "tikhonov": {
            "coefficients_K": [
              4.933984633965293,
              -0.48426587523416625,
              0.054567187685409926,
              0.16598221577721492,
              -0.035170205600824074,
              -0.037182587720104326,
              0.013378331211221567,
              0.004338553007263078
            ],
            "initial_K": [
              0.2840237645532165,
              0.5537942334753625,
              0.7997472024947198,
              1.0140997453669263,
              1.1903273860008468,
              1.3330461878068558,
              1.462279612136208,
              1.5938576017745212,
              1.7114646688067467,
              1.7668614643572997,
              1.715314070384577,
              1.549942256754085,
              1.3005058331320802,
              1.0044348908900764,
              0.68402942495799,
              0.3471900946587939
            ],
            "metrics": {
              "initial_rmse_K": 0.04256535127246234,
              "observation_residual_rms_K": 0.027960531281497576,
              "future_predictive_rmse_K": 0.019552030077144133
            }
          },
          "learned": {
            "coefficients_K": [
              4.993806256631871,
              -0.4960794934222682,
              0.05670516256030391,
              0.15724947488191157,
              -0.010982162497636777,
              -0.003677566850941782,
              0.002086265590886244,
              -0.0011712856310237571
            ],
            "initial_K": [
              0.295999345900355,
              0.5709149217433432,
              0.8105739091741881,
              1.012651995775089,
              1.1862393403197158,
              1.3446370055882402,
              1.4951456709688842,
              1.631761376799066,
              1.734047474960583,
              1.7727287060309425,
              1.7212970514092563,
              1.5693631253927776,
              1.328969813938673,
              1.0278845947644015,
              0.6949275395170359,
              0.34931798748934006
            ],
            "metrics": {
              "initial_rmse_K": 0.04114657885329051,
              "observation_residual_rms_K": 0.024460745315905322,
              "future_predictive_rmse_K": 0.022569822266792022
            }
          }
        }
      },
      {
        "split": "train",
        "index": 11,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.375004517970917,
          0.6183588090148,
          -0.04500579810201123,
          0.03322557193829472,
          0.08219374178050376,
          -0.10666002030289157,
          0.007689586026656845,
          0.014594755375423962
        ],
        "initial_K": [
          0.47522766298895763,
          0.9305405283713426,
          1.3449991845656422,
          1.6902512266587333,
          1.9389145482646741,
          2.091555556807463,
          2.180698371052899,
          2.227484329293458,
          2.203036188151022,
          2.0586395631863192,
          1.7961273741775523,
          1.484660463015226,
          1.1969236849330314,
          0.9432755460277777,
          0.6786195895116589,
          0.36216533326550654
        ],
        "observed_K": [
          0.4271674119778796,
          0.7768967591315141,
          1.1822559044811323,
          1.4798652295974308,
          1.6951255124626818,
          1.8824135436624674,
          2.0018996600580747,
          1.9791361928585331,
          1.9560660514073214,
          1.837129429730502,
          1.6439749877702532,
          1.4591443128305621,
          1.1755091733673892,
          0.9200731105867049,
          0.6101575468746578,
          0.2923404567470552
        ],
        "future_observed_K": [
          0.363484473382978,
          0.7975688873542847,
          1.0684759117210354,
          1.3566418469001655,
          1.6403841155768293,
          1.764942948568559,
          1.8667178451956077,
          1.9120711346164614,
          1.8533583821441584,
          1.7390768472871267,
          1.6070877302479372,
          1.3893311339038212,
          1.1468943473112945,
          0.8702754451279151,
          0.6275404581838705,
          0.3278480461692043
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.365259313985532,
              0.6144095708836574,
              -0.03921047089923905,
              0.020992753683226235,
              -0.0752288631482782,
              0.19410790550883478,
              -1.4558870597556666,
              -1.4239824520607145
            ],
            "initial_K": [
              -0.4525602138616927,
              0.6014756875030085,
              2.1149850589412136,
              2.2442875028007117,
              1.3881948476587787,
              1.4051784567660812,
              2.484407614200336,
              2.962511196858266,
              2.1620728154571554,
              1.3632902050518878,
              1.5488203521890498,
              1.954526289855379,
              1.5971548452905597,
              0.8111121333159688,
              0.3764190428011739,
              0.23896094889541936
            ],
            "metrics": {
              "initial_rmse_K": 0.5200419451061272,
              "observation_residual_rms_K": 0.015311578267021604,
              "future_predictive_rmse_K": 0.020712044570432978
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.288649626070154,
              0.6011691477999248,
              -0.03702268621550475,
              0.016994062055491338,
              -0.031470502536331074,
              0.014711818563735721,
              -0.009116147285470754,
              -0.000464387080073673
            ],
            "initial_K": [
              0.4608124109345065,
              0.9045158854092727,
              1.3095306797867092,
              1.6530966458516934,
              1.918617941035156,
              2.098032587096457,
              2.1885732383010326,
              2.1913813220660665,
              2.1142870775666402,
              1.9716056012211556,
              1.7766661455335644,
              1.5351836742939557,
              1.2499069923497863,
              0.9326114480517624,
              0.6070813903725445,
              0.29526603128407053
            ],
            "metrics": {
              "initial_rmse_K": 0.047591844066223514,
              "observation_residual_rms_K": 0.023490126085920326,
              "future_predictive_rmse_K": 0.026150210228877906
            }
          },
          "learned": {
            "coefficients_K": [
              6.364895754285341,
              0.6158346097739712,
              -0.038473257085789817,
              0.01609996180508557,
              -0.009826902255248121,
              0.0014550815202625338,
              -0.0014216051391503924,
              0.00012537127314401616
            ],
            "initial_K": [
              0.47156024737413305,
              0.9215394660064169,
              1.3286054288304021,
              1.6733004072656597,
              1.940645064842182,
              2.121934220737782,
              2.214613318692568,
              2.2209449062653204,
              2.1468404532345757,
              2.001178612063479,
              1.7950216234300358,
              1.5407227618547987,
              1.251605208845286,
              0.9418880369343493,
              0.6251209046177618,
              0.31053064471649183
            ],
            "metrics": {
              "initial_rmse_K": 0.036136520958171894,
              "observation_residual_rms_K": 0.015720931742722922,
              "future_predictive_rmse_K": 0.020520806542127845
            }
          }
        }
      },
      {
        "split": "train",
        "index": 12,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.194051981414222,
          -0.7020790364158003,
          -0.03873931002569517,
          -0.097671744340929,
          -0.04786077144288546,
          0.0106767581833559,
          0.0309605630017005,
          0.028375518138356984
        ],
        "initial_K": [
          0.283911131484047,
          0.5544988675885791,
          0.8397783427891123,
          1.1668492982689438,
          1.5011817527630709,
          1.77238473676453,
          1.9523085509200073,
          2.068314091777269,
          2.1418660309680067,
          2.1541128326990218,
          2.079390049392988,
          1.9166557592864653,
          1.6728049909279015,
          1.3444460396254438,
          0.9362605199060594,
          0.47709352741624567
        ],
        "observed_K": [
          0.29594487028481103,
          0.5868366312462034,
          0.8374949338851579,
          1.1397136988089014,
          1.412585681974786,
          1.5977209995247865,
          1.7599120606491265,
          1.8812460650115126,
          1.9616717568263213,
          1.9584893391299718,
          1.8543011706560995,
          1.6858434436190206,
          1.4459292057762163,
          1.1558073823528376,
          0.826980044664345,
          0.41316217406275646
        ],
        "future_observed_K": [
          0.2916326921550844,
          0.5645481161137725,
          0.822869679141107,
          1.075305837036772,
          1.334828201881249,
          1.5319193604123826,
          1.6969749700650782,
          1.8143842620309587,
          1.8720572476684296,
          1.8467863552185073,
          1.7477160185560299,
          1.6001509725665943,
          1.4046445765901707,
          1.0983728486814754,
          0.746367206806108,
          0.39738927422864473
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.207899487417103,
              -0.7029066871495585,
              -0.024374367086483106,
              -0.051451817636047184,
              -0.011759933848904737,
              -1.1045023403050291,
              2.247890964702081,
              16.883050404864136
            ],
            "initial_K": [
              6.453251633290844,
              1.7454601148292532,
              -5.138354758252337,
              -1.2310648753077824,
              7.0582513174513135,
              5.414255436066498,
              -2.778113089574972,
              -2.629271045249353,
              5.6479745964451595,
              7.440959870040171,
              -0.05815774848210431,
              -3.3744861655801968,
              2.7105797454458695,
              6.321780769273021,
              0.5819705163259167,
              -4.202804921366183
            ],
            "metrics": {
              "initial_rmse_K": 4.259124827260782,
              "observation_residual_rms_K": 0.007441796323886938,
              "future_predictive_rmse_K": 0.015167316006794912
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.13318371876081,
              -0.6877591660703217,
              -0.02301437661035343,
              -0.041651295250201434,
              -0.004919535036566781,
              -0.08371239693300124,
              0.014075339827075725,
              0.005505875770382887
            ],
            "initial_K": [
              0.26702492722245497,
              0.5580672526074197,
              0.8766049143077963,
              1.1969134669693982,
              1.4801373744764996,
              1.706628744732816,
              1.8886164329485626,
              2.042346772140673,
              2.1514935580594665,
              2.171604816697178,
              2.07440699036246,
              1.8768153071551685,
              1.6180803329785585,
              1.3148241288442164,
              0.94949987999923,
              0.5043525166650139
            ],
            "metrics": {
              "initial_rmse_K": 0.034330163508002394,
              "observation_residual_rms_K": 0.02190269989312447,
              "future_predictive_rmse_K": 0.02474948300820695
            }
          },
          "learned": {
            "coefficients_K": [
              6.207544915519066,
              -0.7045369829862739,
              -0.023916093576929656,
              -0.039459916085448056,
              -0.0015361619945471108,
              -0.008279626428669178,
              0.002194959647629888,
              -0.0014864294997099909
            ],
            "initial_K": [
              0.28775564969916057,
              0.583053185376109,
              0.885889417845553,
              1.1872752981508201,
              1.4729669819721476,
              1.727446550897537,
              1.9360724706779355,
              2.086239121145906,
              2.167571313749509,
              2.1711119470816915,
              2.089687605446773,
              1.9206615803599236,
              1.6676646330804705,
              1.3381066790469578,
              0.9403296698249234,
              0.48668289088926636
            ],
            "metrics": {
              "initial_rmse_K": 0.0223899465134411,
              "observation_residual_rms_K": 0.01398118957643908,
              "future_predictive_rmse_K": 0.01467078180312855
            }
          }
        }
      },
      {
        "split": "train",
        "index": 13,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.757563041483361,
          -0.8690994642202763,
          -0.1680392328900327,
          -0.05170749444050791,
          0.02130223174325793,
          0.0484797688316709,
          0.02457537121077229,
          -0.031231356106392008
        ],
        "initial_K": [
          0.2310545813551475,
          0.4660744723386541,
          0.7054300926210133,
          0.960835744405277,
          1.251225084475999,
          1.5613932614599775,
          1.8267109578798038,
          1.9892560524542273,
          2.054052311882581,
          2.0586038926879096,
          2.002316829369689,
          1.847573297453439,
          1.5852554277984379,
          1.2529348140558865,
          0.8804469515784978,
          0.46188541485860574
        ],
        "observed_K": [
          0.23479634664340987,
          0.49409488489892,
          0.7592788689200095,
          0.9906455865136039,
          1.189545153156967,
          1.4413360759397262,
          1.6475438027044378,
          1.7797506497951823,
          1.8684523257517194,
          1.8226691948743807,
          1.764459042656788,
          1.598706585170705,
          1.336311414947324,
          1.086072749805041,
          0.7488986066697623,
          0.423382562836512
        ],
        "future_observed_K": [
          0.25519623884680964,
          0.4512452536283603,
          0.6999584708134805,
          0.96588988028641,
          1.1635109926261569,
          1.3770077403045284,
          1.5685042732126095,
          1.6766784706442965,
          1.7336649222041252,
          1.7415912412601235,
          1.6303302646017466,
          1.5022069478929843,
          1.292411391892228,
          1.0162724626556838,
          0.707445677373277,
          0.35739728342832855
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.744610192700764,
              -0.8329765656325895,
              -0.2293209295979274,
              0.016509370095162505,
              0.5246319602350435,
              -0.5004615656050578,
              0.3417762211649801,
              -25.11881416037837
            ],
            "initial_K": [
              -8.254980874323257,
              -1.0307892732871888,
              9.012070413961538,
              4.0590002315929095,
              -6.488232570450035,
              -3.0572607721390797,
              8.572633265915787,
              7.764602936696416,
              -3.554271917293637,
              -4.525492632719873,
              6.604796659300947,
              9.26092899397291,
              -1.9289959370735914,
              -7.122107537556803,
              2.7831202089339775,
              9.408989308158104
            ],
            "metrics": {
              "initial_rmse_K": 6.27520909199299,
              "observation_residual_rms_K": 0.011204246250550866,
              "future_predictive_rmse_K": 0.017706281311356615
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.675470386708673,
              -0.815026060512775,
              -0.2165257550966237,
              0.013364671644694254,
              0.2194693731138108,
              -0.03793096284257016,
              0.0021400577400107344,
              -0.008191711032653924
            ],
            "initial_K": [
              0.2670400028069863,
              0.5148599177902258,
              0.7360446290667275,
              0.947922607975672,
              1.186783086551309,
              1.4725762635935955,
              1.7745076450454023,
              2.0186189847492404,
              2.1345780142189184,
              2.0984695183917705,
              1.9399263344101114,
              1.7168698143268835,
              1.475899106398852,
              1.219030866299424,
              0.9041936945713754,
              0.49172292189558353
            ],
            "metrics": {
              "initial_rmse_K": 0.06325526934290254,
              "observation_residual_rms_K": 0.02373872962626193,
              "future_predictive_rmse_K": 0.01898685390974681
            }
          },
          "learned": {
            "coefficients_K": [
              5.744282082146841,
              -0.8349085407465826,
              -0.22500936298994026,
              0.012661522731556636,
              0.06853097039426666,
              -0.0037515853556022776,
              0.0003337283817393622,
              0.0022115284542988914
            ],
            "initial_K": [
              0.23935606623050507,
              0.4758366267463423,
              0.7154041601868493,
              0.9699102049382705,
              1.244867489923076,
              1.5294032949805205,
              1.7948841152368968,
              2.0016714911676727,
              2.112427173286946,
              2.1079426120729905,
              1.9949468957097116,
              1.7972265460160302,
              1.5366862370723804,
              1.2221571776368014,
              0.8548170801993584,
              0.4411961307716177
            ],
            "metrics": {
              "initial_rmse_K": 0.03102329881896426,
              "observation_residual_rms_K": 0.019004282434265534,
              "future_predictive_rmse_K": 0.017427426922033827
            }
          }
        }
      },
      {
        "split": "train",
        "index": 14,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.39077519432663,
          2.1417168186717737,
          -0.1324093971226842,
          0.029582579992007824,
          -0.05388837875366194,
          -0.02153412741895186,
          -0.012800745886790556,
          0.02486975176638076
        ],
        "initial_K": [
          0.6339875536518134,
          1.2317793870992126,
          1.7638465977214715,
          2.1915270025567684,
          2.4642899754093763,
          2.5569281746089287,
          2.4974267396045784,
          2.334989737224145,
          2.0916249638934987,
          1.7704794832479804,
          1.4003507397220294,
          1.0366295115579205,
          0.7168144401730951,
          0.4461679475145435,
          0.2304287307059093,
          0.0858135174599865
        ],
        "observed_K": [
          0.5250460807327503,
          1.0132163995310786,
          1.441762518365984,
          1.813946231265211,
          2.0949364941730795,
          2.163789221842912,
          2.171387273503431,
          2.0948704299915333,
          1.9334174152331591,
          1.697767802066624,
          1.3486130105016716,
          1.116656541444556,
          0.8182419754994371,
          0.5552531775215584,
          0.36477637526442164,
          0.1467232915369198
        ],
        "future_observed_K": [
          0.49307591881943186,
          0.9521290441222715,
          1.3382916310410202,
          1.680710898347271,
          1.8904055490693357,
          2.0075661193182004,
          2.025301589099693,
          1.9408904164718048,
          1.7957855824170867,
          1.5856820912707208,
          1.3806655692924505,
          1.1135559335751926,
          0.8302391554719871,
          0.6275137229466932,
          0.46063780955295663,
          0.16903004015420142
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.392434771954722,
              2.1526863103623004,
              -0.2419558993874018,
              0.01599322805819033,
              -0.20240167341825266,
              -0.8678459557586289,
              -2.569691357236121,
              19.299996119680554
            ],
            "initial_K": [
              6.051613920780401,
              1.6687394745794113,
              -4.006777288317144,
              0.8676149172724277,
              8.460583903065402,
              5.108426467197469,
              -3.361716975525034,
              -1.5784891314930833,
              7.38705057198095,
              7.029002605991572,
              -2.814214538091334,
              -5.206756863283427,
              3.605284001196953,
              7.287430976608083,
              -1.2947487713425154,
              -7.139519740387128
            ],
            "metrics": {
              "initial_rmse_K": 4.865816954771936,
              "observation_residual_rms_K": 0.01633233064471727,
              "future_predictive_rmse_K": 0.026815270936613716
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.315498011213042,
              2.1062962818431106,
              -0.22845574499805,
              0.012946844143923768,
              -0.08467072490663524,
              -0.06577574575813272,
              -0.01609031740051122,
              0.006294086581250601
            ],
            "initial_K": [
              0.5742286784205097,
              1.1550661213014584,
              1.7078847234545567,
              2.1581622100405067,
              2.437928750547872,
              2.5328152087619595,
              2.481125424946737,
              2.32854785012043,
              2.092917561277956,
              1.7768050061432077,
              1.4023235763078485,
              1.0185919103347252,
              0.6759470786425753,
              0.4032309387004537,
              0.2080093617774652,
              0.08237662556944253
            ],
            "metrics": {
              "initial_rmse_K": 0.035074623679302995,
              "observation_residual_rms_K": 0.02782501555556093,
              "future_predictive_rmse_K": 0.026682061380839558
            }
          },
          "learned": {
            "coefficients_K": [
              6.39206966009446,
              2.15767917156806,
              -0.23740677699271545,
              0.012265678184116873,
              -0.026439073750981486,
              -0.006505590843137925,
              -0.0025091825736058768,
              -0.0016992239487904552
            ],
            "initial_K": [
              0.6195353233659653,
              1.2108287088418814,
              1.7372222595199218,
              2.1576645412214317,
              2.4396707976051406,
              2.56826196845029,
              2.545725661275623,
              2.3876866051499555,
              2.1203123253433036,
              1.7775697105708745,
              1.3973909887454024,
              1.0184854734061957,
              0.6775633031665788,
              0.4035853489009663,
              0.20905154832102235,
              0.08432843049968225
            ],
            "metrics": {
              "initial_rmse_K": 0.028909281837898555,
              "observation_residual_rms_K": 0.020532253223953273,
              "future_predictive_rmse_K": 0.026671665863964467
            }
          }
        }
      },
      {
        "split": "train",
        "index": 15,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.704818904463256,
          -0.6857193021999042,
          -0.07536211342824581,
          0.37801386609203014,
          0.015310078351850661,
          -0.04472966171161964,
          -0.019054654959611228,
          0.030460017957364877
        ],
        "initial_K": [
          0.40592696131967493,
          0.7695588748280876,
          1.0769123380570425,
          1.3323892330791307,
          1.54467088310731,
          1.7408977358201827,
          1.9644656880331208,
          2.219531478934002,
          2.429873028278379,
          2.491457038824664,
          2.365785299246463,
          2.094248524823596,
          1.7311684248138213,
          1.3055181292292228,
          0.8489029065848057,
          0.40781643583232857
        ],
        "observed_K": [
          0.31511476270370997,
          0.6693747593242614,
          1.0059486120957997,
          1.2230596440594472,
          1.4559355243253826,
          1.6986781466482768,
          1.9104704678812914,
          2.0485755771166283,
          2.124415179540748,
          2.108670099531285,
          2.0555293349533383,
          1.7914935413086874,
          1.5601600205141193,
          1.1813530567189507,
          0.8586890726009506,
          0.42704202927471224
        ],
        "future_observed_K": [
          0.2968409676121517,
          0.6685589389449649,
          0.931626905667108,
          1.218083706444958,
          1.4886808728392056,
          1.6347981628444255,
          1.8587020469070619,
          1.9821767938865755,
          2.037120176454997,
          1.967713938936425,
          1.8906744727317206,
          1.7729783423390406,
          1.471795701194302,
          1.1008736239077532,
          0.7652144275887658,
          0.37644516779044335
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.696229542945335,
              -0.7057426346279164,
              -0.0671237825919923,
              0.4306996481044627,
              0.3972021573491975,
              -0.4183848968480743,
              0.42797142520417797,
              -25.585763841126756
            ],
            "initial_K": [
              -8.19496541791261,
              -0.7256571574597532,
              9.5049006632478,
              4.420175897152768,
              -6.3538571156957335,
              -2.8923766486385323,
              8.903390599737795,
              8.052804575666627,
              -3.4249096276982343,
              -4.298027205511747,
              7.121603960198188,
              9.785605822455729,
              -1.7684987738318774,
              -7.231901879399313,
              2.760458725427468,
              9.514613339508118
            ],
            "metrics": {
              "initial_rmse_K": 6.406439803444348,
              "observation_residual_rms_K": 0.01788240415442489,
              "future_predictive_rmse_K": 0.03123762640695049
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.615636431150558,
              -0.6905339993567201,
              -0.06337854872712889,
              0.3486601451916174,
              0.16616164298077912,
              -0.03171021126677399,
              0.0026797755498897528,
              -0.008343991981390523
            ],
            "initial_K": [
              0.4342960821655046,
              0.8058592300141414,
              1.0810389579254727,
              1.278168089777281,
              1.4603828328338877,
              1.6882974946555738,
              1.967686761159606,
              2.2401384866595646,
              2.421177761215818,
              2.448255542613964,
              2.3072399297688575,
              2.0323823564650247,
              1.6829104290863228,
              1.3047085677754686,
              0.9052429510014999,
              0.46945538208891663
            ],
            "metrics": {
              "initial_rmse_K": 0.04602022578871423,
              "observation_residual_rms_K": 0.02904065860762663,
              "future_predictive_rmse_K": 0.040407127456533215
            }
          },
          "learned": {
            "coefficients_K": [
              6.695847079468994,
              -0.707379508056582,
              -0.06586175796941271,
              0.3303162600095809,
              0.051885228787131865,
              -0.003136318070944671,
              0.00041789393854622394,
              0.002252639969321354
            ],
            "initial_K": [
              0.41294367740728305,
              0.7752580663864101,
              1.0655473183557274,
              1.2997028504929793,
              1.5153226548025212,
              1.7456103693760783,
              1.9966887929057653,
              2.237806243360842,
              2.411001492881646,
              2.458359485190441,
              2.350763562495426,
              2.0985107615780727,
              1.7397432871949872,
              1.3201969600465573,
              0.877979008660079,
              0.43597032110529454
            ],
            "metrics": {
              "initial_rmse_K": 0.02115059210082573,
              "observation_residual_rms_K": 0.023308805606948542,
              "future_predictive_rmse_K": 0.03123170062493375
            }
          }
        }
      },
      {
        "split": "train",
        "index": 16,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.483121342064137,
          -0.25667256594986376,
          -0.2921752862746881,
          -0.09012761035614307,
          0.0044168210614506315,
          0.08600291159015656,
          -0.04819670391466927,
          -0.014551159740265775
        ],
        "initial_K": [
          0.24693617092690334,
          0.5149618612615393,
          0.7978571735833213,
          1.0811308337453984,
          1.3673347817670678,
          1.6519686520806263,
          1.8854044101127434,
          1.9974922847670697,
          1.9697286260550526,
          1.8560394971195262,
          1.7169559459035804,
          1.5528232843487246,
          1.3209557390772275,
          1.0060527238719463,
          0.6498998943453346,
          0.30932175952406626
        ],
        "observed_K": [
          0.23020400618760478,
          0.5332547933050009,
          0.7902903664531498,
          1.0469845297419138,
          1.3188947087239509,
          1.4707434392848597,
          1.637287498508287,
          1.6930907850540033,
          1.7306402504676481,
          1.7027111482517554,
          1.5534655542800793,
          1.4094447193695037,
          1.1998281398303445,
          0.9142792073303859,
          0.5934741695286831,
          0.316650652278437
        ],
        "future_observed_K": [
          0.25429956560942574,
          0.5167911035120757,
          0.7925376199709863,
          1.0287896947999362,
          1.251068663019574,
          1.406212855100068,
          1.5017983636645524,
          1.643722829891438,
          1.6440095364839191,
          1.6112299675440611,
          1.4820278162405378,
          1.2942219255217564,
          1.1327999816781926,
          0.8886694348530654,
          0.6243699550824321,
          0.3059364383123349
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.4607994609075945,
              -0.2694942381542012,
              -0.2722339871040224,
              -0.076317501320601,
              -0.49542553578729365,
              -0.11306109568554011,
              -2.3121907967935176,
              5.740285095560628
            ],
            "initial_K": [
              1.2713693024327402,
              0.2545898949259306,
              -0.6242926498685619,
              1.2159293033835352,
              3.1979508432872388,
              1.992518621009212,
              -0.08833310951315942,
              1.0812482218290156,
              3.790016536503046,
              3.1817875073002364,
              0.04472590647453978,
              -0.22902360309468994,
              2.7575321559359707,
              3.356204954559045,
              -0.23040870602288857,
              -2.478154062922563
            ],
            "metrics": {
              "initial_rmse_K": 1.5519046659425748,
              "observation_residual_rms_K": 0.014724013983675385,
              "future_predictive_rmse_K": 0.019593731841826344
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.395075486151466,
              -0.26368668257420275,
              -0.25704443865639953,
              -0.0617805730935922,
              -0.207251444832103,
              -0.00856912201480183,
              -0.014477958104261971,
              0.0018720134018927967
            ],
            "initial_K": [
              0.18317006177159023,
              0.43430712345894185,
              0.7660871385121223,
              1.1268241426237995,
              1.4414684014890142,
              1.6631243730126686,
              1.7923122849850543,
              1.8567863489790182,
              1.8786742416597697,
              1.8564773940509058,
              1.7681599928969012,
              1.5880301281840334,
              1.3095375279782169,
              0.9619869393717235,
              0.6028256962469886,
              0.2810495557799629
            ],
            "metrics": {
              "initial_rmse_K": 0.06373431194861022,
              "observation_residual_rms_K": 0.022533623306301986,
              "future_predictive_rmse_K": 0.02434999948768175
            }
          },
          "learned": {
            "coefficients_K": [
              5.460487560556505,
              -0.2701192931472946,
              -0.26711559267567747,
              -0.05853014210817966,
              -0.06471582995132756,
              -0.0008475343163453779,
              -0.0022577454050381816,
              -0.0005053902522454481
            ],
            "initial_K": [
              0.2300331278163926,
              0.4901367106317024,
              0.788507971520957,
              1.1054487470889929,
              1.4049911227517269,
              1.652774657603363,
              1.8278450980621317,
              1.9240037790152993,
              1.9436207845671412,
              1.8897533829922484,
              1.7624214384712202,
              1.5619994084063864,
              1.2966519358816873,
              0.9859831770069254,
              0.655480462695326,
              0.3248867734882343
            ],
            "metrics": {
              "initial_rmse_K": 0.03254754764214936,
              "observation_residual_rms_K": 0.018157477167063108,
              "future_predictive_rmse_K": 0.019001084106292043
            }
          }
        }
      },
      {
        "split": "train",
        "index": 17,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.230640368216733,
          0.8851664265605479,
          -0.20509853518626642,
          -0.3016628504181871,
          -0.013252302340067182,
          -0.02012899117541351,
          -0.07281355306638441,
          -0.004525804193580415
        ],
        "initial_K": [
          0.3602506154857272,
          0.7872314259117152,
          1.2621406890415665,
          1.6988633089109633,
          2.0297114125725284,
          2.2426607704948402,
          2.339862009018978,
          2.302076491978303,
          2.1209228376520532,
          1.8462299950743675,
          1.5656727375794026,
          1.3302096553130789,
          1.1178565960907536,
          0.878197842399651,
          0.5957965696038062,
          0.29576384461250516
        ],
        "observed_K": [
          0.3917412081373627,
          0.7776984430172623,
          1.1692808994385586,
          1.465847776917605,
          1.742991608342817,
          1.8944666442444025,
          2.010837442844218,
          1.980885888231173,
          1.8816651181613266,
          1.7555202360765452,
          1.5553086920687447,
          1.3306455121947292,
          1.101939711167754,
          0.8366973016727677,
          0.5645323077053215,
          0.2533584369559486
        ],
        "future_observed_K": [
          0.38757151065403306,
          0.7251601339591013,
          1.1338793553718274,
          1.3915277423170382,
          1.6243646797304747,
          1.7959579410741864,
          1.8955481264377216,
          1.8654076927939114,
          1.8126360642156465,
          1.6989966030471257,
          1.5432808035152845,
          1.2915784330384772,
          1.0456283195282086,
          0.8105150361035824,
          0.5448241782575082,
          0.29387744266863075
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.208240967642323,
              0.8518963036367458,
              -0.15706308282246395,
              -0.2827065625089535,
              -0.2276036653600583,
              0.4077182314001887,
              -1.9409709976695866,
              0.5097099486564971
            ],
            "initial_K": [
              -0.00021843015925249176,
              0.5394717718475548,
              1.4779884866566075,
              2.104103269681887,
              2.0296250285933386,
              1.774752763820142,
              2.0699303757645064,
              2.6780939161819415,
              2.5889780767678467,
              1.5892158573455735,
              0.8367550604682514,
              1.2408706728691543,
              1.953162049559099,
              1.4973256626250755,
              0.051425644833489575,
              -0.6792103259883775
            ],
            "metrics": {
              "initial_rmse_K": 0.4992322718303568,
              "observation_residual_rms_K": 0.01112787292142696,
              "future_predictive_rmse_K": 0.019395855360748296
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.133521089068084,
              0.8335380813398566,
              -0.14829960207105716,
              -0.22885672548097322,
              -0.0952134782878997,
              0.03090176378835731,
              -0.01215353716692322,
              0.00016622586493151542
            ],
            "initial_K": [
              0.3896608481489433,
              0.8037505632959768,
              1.239142968032581,
              1.6576818367925321,
              2.0014515531778807,
              2.2179379157486627,
              2.281515496382135,
              2.204255040666162,
              2.0313909823717617,
              1.8189476700656118,
              1.6029107002048777,
              1.3830096424347365,
              1.137596678135555,
              0.8565755736097456,
              0.5579168116770841,
              0.2697788454395383
            ],
            "metrics": {
              "initial_rmse_K": 0.045858420732930893,
              "observation_residual_rms_K": 0.02140568431224989,
              "future_predictive_rmse_K": 0.02937749931369726
            }
          },
          "learned": {
            "coefficients_K": [
              6.207886376240217,
              0.8538721604930297,
              -0.1541100687018942,
              -0.21681599885002262,
              -0.02973112817112519,
              0.0030563580727397824,
              -0.0018952667562633775,
              -4.4876244861556414e-05
            ],
            "initial_K": [
              0.4112866123086618,
              0.8358118296820622,
              1.267693109840872,
              1.675218038620426,
              2.0102725165614213,
              2.2276145163238774,
              2.303311913195567,
              2.243678483663062,
              2.0811933369212285,
              1.859699525177537,
              1.6163768610215115,
              1.3700231402538616,
              1.1213006684837359,
              0.8623982757851585,
              0.5876261874997121,
              0.2980444070650465
            ],
            "metrics": {
              "initial_rmse_K": 0.03274377931760957,
              "observation_residual_rms_K": 0.013282460567408382,
              "future_predictive_rmse_K": 0.01902376649753404
            }
          }
        }
      },
      {
        "split": "train",
        "index": 18,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.264298425261232,
          0.2103544989217369,
          -0.0964585246569604,
          -0.042326903822470986,
          0.006520460347848705,
          -0.02880447817005056,
          -0.012913581569521423,
          0.02396212857810112
        ],
        "initial_K": [
          0.3905414928827086,
          0.7741576527539344,
          1.1488710288671262,
          1.4996215507259751,
          1.7907092600528418,
          1.9958420791098754,
          2.122295960827433,
          2.184593720152631,
          2.169065556629539,
          2.053131905665748,
          1.851243614395347,
          1.6086037864487421,
          1.3482031298468085,
          1.0550479626589826,
          0.7186023156067356,
          0.35929543998078295
        ],
        "observed_K": [
          0.36072193222871257,
          0.7528703137672862,
          1.0354879297076125,
          1.3247329483703962,
          1.5933814697770226,
          1.7458158149663443,
          1.8955301099652184,
          1.9734463839888678,
          1.911456068805422,
          1.840770266299704,
          1.7164777241969464,
          1.483929994231329,
          1.2607296104413082,
          0.9984779602787183,
          0.6721909654218485,
          0.35439514333684313
        ],
        "future_observed_K": [
          0.3813330500294836,
          0.7001895798125028,
          1.0221811930182656,
          1.241547191209411,
          1.4935151982797967,
          1.6747950672125738,
          1.7894974216560424,
          1.858579570759964,
          1.8765640145886608,
          1.7492153083342836,
          1.6189105872707519,
          1.469024566246882,
          1.2082157846020922,
          0.9192680389948001,
          0.6172129188962808,
          0.3507395480046159
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.237358418348564,
              0.1641125375872074,
              -0.03136195810692472,
              -0.052171252649603116,
              0.33354517382186855,
              0.30790998693304195,
              0.6826190397287452,
              -1.8294624740315149
            ],
            "initial_K": [
              0.18194116784076408,
              0.985586049614641,
              1.6193755343789848,
              1.340761453488145,
              1.0631903253002064,
              1.8430961598894051,
              2.8221443140017812,
              2.5513323066654987,
              1.561033175216807,
              1.5190054709705112,
              2.30320195506349,
              2.2017989257752615,
              0.9850402056424545,
              0.378878543394946,
              1.0074227388274515,
              1.2259503648689036
            ],
            "metrics": {
              "initial_rmse_K": 0.5090719949220117,
              "observation_residual_rms_K": 0.014990949253668555,
              "future_predictive_rmse_K": 0.02152872015857598
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.1622880939085,
              0.16057593995922048,
              -0.02961208849238821,
              -0.042233692559756474,
              0.13953200672529836,
              0.02333710133982653,
              0.004274270908815002,
              -0.0005966216333567777
            ],
            "initial_K": [
              0.4397358397130395,
              0.8302804562732049,
              1.1553483191822118,
              1.4338980285362564,
              1.6906970553353875,
              1.923812578300738,
              2.0992220113513,
              2.175776885642798,
              2.1363667418618695,
              1.9990311286468192,
              1.8024738530778446,
              1.580647748498392,
              1.3447874784276814,
              1.0824105625502063,
              0.7722181970435025,
              0.4055386752004765
            ],
            "metrics": {
              "initial_rmse_K": 0.04915653416611675,
              "observation_residual_rms_K": 0.023196346620127394,
              "future_predictive_rmse_K": 0.029016973603499734
            }
          },
          "learned": {
            "coefficients_K": [
              6.237002163867058,
              0.16449317415202117,
              -0.030772307735403934,
              -0.04001167201105331,
              0.04356992361291938,
              0.002308170451461367,
              0.0006665453398034524,
              0.00016107083286497778
            ],
            "initial_K": [
              0.4115794305141136,
              0.802827846418894,
              1.1602726227109874,
              1.4776016897295214,
              1.7495338001013718,
              1.9656385299044514,
              2.110279041609819,
              2.169199886887666,
              2.1377909452472,
              2.0248169993169487,
              1.848559025772509,
              1.6275184807572987,
              1.3718480429243975,
              1.0815621806243172,
              0.7528539119059131,
              0.38778045360928015
            ],
            "metrics": {
              "initial_rmse_K": 0.02532286049289213,
              "observation_residual_rms_K": 0.01643874310610024,
              "future_predictive_rmse_K": 0.022067337557277945
            }
          }
        }
      },
      {
        "split": "train",
        "index": 19,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.338521974647269,
          -1.9232063326923363,
          -0.3913426380830449,
          0.2258498611237075,
          -0.07711520937778052,
          0.12348019945707588,
          -0.004560400938407643,
          -0.03920820020108196
        ],
        "initial_K": [
          0.08160441718750361,
          0.17910434754076926,
          0.29826413799950724,
          0.4633253122536741,
          0.7229838080013151,
          1.0873541664826587,
          1.482498243982087,
          1.8121241816057325,
          2.047801841436719,
          2.2099046226526933,
          2.2727621539556693,
          2.1546331512988504,
          1.8202943237045432,
          1.3453176092213108,
          0.8509908469567142,
          0.40477236928174726
        ],
        "observed_K": [
          0.13526807202579283,
          0.2624625363815504,
          0.45367305168073313,
          0.6035997976758452,
          0.8779023647027145,
          1.1213450362076978,
          1.3927320545382158,
          1.6352684630909953,
          1.7897643946349178,
          1.916276354587631,
          1.850879932512255,
          1.7481109798001053,
          1.5131985770087717,
          1.2413194508125387,
          0.8200696120113493,
          0.41932964552085
        ],
        "future_observed_K": [
          0.13913508839319874,
          0.3189851031206045,
          0.5110092162481225,
          0.6418435354070119,
          0.9023614621509791,
          1.1139278208305636,
          1.370542344155871,
          1.5493501577449145,
          1.677912088839414,
          1.7120819862777608,
          1.7046821054120114,
          1.5790403199398162,
          1.4110664371236972,
          1.1355655492652945,
          0.78646619233844,
          0.3984669855718707
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.36090152148383,
              -1.9405396109464605,
              -0.40277578842586625,
              0.2362028769683248,
              0.15588881396915436,
              0.48410762027583015,
              -1.265711553189318,
              11.338124290801504
            ],
            "initial_K": [
              3.7253867208847447,
              0.8428197718396971,
              -3.159946436566661,
              -0.7234296905010185,
              3.970988197026872,
              2.701247239475933,
              -1.6463730487019157,
              -0.32600376938708253,
              5.042241278764656,
              5.075670825175623,
              -0.2950821363765801,
              -1.4020802511856187,
              3.7014323876847923,
              5.444383913985226,
              -0.11590073372351095,
              -3.944879479680205
            ],
            "metrics": {
              "initial_rmse_K": 2.863777870223446,
              "observation_residual_rms_K": 0.015064026131206044,
              "future_predictive_rmse_K": 0.019852818651159957
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.296379877942367,
              -1.89872130817699,
              -0.3803025387890144,
              0.19121104403242847,
              0.06521299286062916,
              0.03669146527623379,
              -0.007925348922142491,
              0.0036975725545620682
            ],
            "initial_K": [
              0.10182539816877359,
              0.19639556156753152,
              0.30218977996332574,
              0.4614378893927238,
              0.7115554299445601,
              1.054804452323434,
              1.4482689135499909,
              1.8189599691210445,
              2.094138361477471,
              2.22833287129484,
              2.2099660947699418,
              2.048083304742698,
              1.7594168844180005,
              1.370539782260072,
              0.9227298362625538,
              0.45892150104426394
            ],
            "metrics": {
              "initial_rmse_K": 0.04564744922085617,
              "observation_residual_rms_K": 0.02339297003454059,
              "future_predictive_rmse_K": 0.020669631932790866
            }
          },
          "learned": {
            "coefficients_K": [
              5.360595326927762,
              -1.945040426924662,
              -0.3952030184962856,
              0.181150951172258,
              0.02036324986783346,
              0.003628992081672691,
              -0.0012359077145708906,
              -0.0009982391814911719
            ],
            "initial_K": [
              0.07329377731104345,
              0.16270411376869176,
              0.2882505056360607,
              0.47327802287104725,
              0.7357592070735486,
              1.073804534187398,
              1.4556177295011063,
              1.8236482106481027,
              2.1119418491855813,
              2.266244480205695,
              2.25757417712047,
              2.086819483612919,
              1.781185694808984,
              1.3832853698573948,
              0.9360080389483725,
              0.47002795641529105
            ],
            "metrics": {
              "initial_rmse_K": 0.04206711225989247,
              "observation_residual_rms_K": 0.016992994206880756,
              "future_predictive_rmse_K": 0.02011503872711147
            }
          }
        }
      },
      {
        "split": "train",
        "index": 20,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.825297636892962,
          1.5647713618636887,
          -0.2606272287423345,
          0.11924922460788749,
          0.07120385797563172,
          0.016558198948015336,
          0.029936901554523127,
          -0.014909372532692547
        ],
        "initial_K": [
          0.5708789605148274,
          1.076557006008522,
          1.481695814793933,
          1.7910208820801907,
          2.026049407237504,
          2.1871120170298637,
          2.245872121227949,
          2.1794671847056564,
          1.9989070653949343,
          1.7345429535691947,
          1.4104633326090568,
          1.0534746987558994,
          0.7143746499429635,
          0.44777442356017083,
          0.26475520241293266,
          0.12801828951519362
        ],
        "observed_K": [
          0.45732629999231017,
          0.8394910582130838,
          1.2209943886928385,
          1.514813599971862,
          1.7596022298971157,
          1.8969062117190227,
          1.9455232477511428,
          1.9056562972349123,
          1.790533512331037,
          1.567120201384034,
          1.3541767266956422,
          1.0640746493316477,
          0.8248640895949751,
          0.5910574129695014,
          0.39507993061663016,
          0.1622839444462995
        ],
        "future_observed_K": [
          0.3990636775809204,
          0.7906163201635165,
          1.158572855068818,
          1.431530488557599,
          1.682823194941752,
          1.755952810391594,
          1.7954766660873156,
          1.7914877173606552,
          1.671635676505714,
          1.525099896392657,
          1.3314303989257166,
          1.0768089945740535,
          0.8242271459586732,
          0.5954320637938811,
          0.37607011242412064,
          0.18257417683408522
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.796972224792824,
              1.5165640223736427,
              -0.3303054911910419,
              0.003799549225850022,
              0.23084904679803867,
              0.05117789906343662,
              0.2620083356651135,
              9.32560494266011
            ],
            "initial_K": [
              3.844853278852444,
              1.693822540249308,
              -1.7111136735227153,
              0.4728251542009424,
              4.834604818405734,
              3.94092585827945,
              -0.22665195272708694,
              0.03742706300245002,
              4.1385635413002415,
              4.298212648036085,
              -0.26722114242316297,
              -1.8676496499605952,
              1.7811731048013,
              3.515069272972533,
              -0.21317461768002044,
              -2.9341715972895197
            ],
            "metrics": {
              "initial_rmse_K": 2.336491224801051,
              "observation_residual_rms_K": 0.010907485723912366,
              "future_predictive_rmse_K": 0.02046723171751617
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.727202210550086,
              1.483882322345899,
              -0.31187578917501435,
              0.0030758125542425766,
              0.09657111923182854,
              0.0038788732664996528,
              0.0016405850728181378,
              0.0030412526804493886
            ],
            "initial_K": [
              0.5184214816029751,
              0.9912187866613862,
              1.3944042188523469,
              1.725443933370728,
              1.985134501468497,
              2.1625524785314445,
              2.2352653057807412,
              2.1812642471153363,
              1.994986164610946,
              1.7002957881942629,
              1.3501928457823658,
              1.0070944655523468,
              0.7147766388069742,
              0.4839980532132027,
              0.3008327210715934,
              0.14482019105384664
            ],
            "metrics": {
              "initial_rmse_K": 0.04624364531577751,
              "observation_residual_rms_K": 0.02070809377270844,
              "future_predictive_rmse_K": 0.027269207133784543
            }
          },
          "learned": {
            "coefficients_K": [
              5.796641123516332,
              1.520081485014117,
              -0.32409526812613865,
              0.002913986337181021,
              0.0301550618162365,
              0.0003836423610767283,
              0.0002558387987487686,
              -0.0008210515254647098
            ],
            "initial_K": [
              0.5040110012367209,
              0.9810191788633587,
              1.407424496507505,
              1.764547153273722,
              2.0368164088707625,
              2.2083484997799134,
              2.263089002687117,
              2.1915608830628757,
              2.000157014755174,
              1.715220645149489,
              1.3783263376193795,
              1.0355898998435202,
              0.725910472861315,
              0.47188889583238736,
              0.2764144185144756,
              0.12629855104913845
            ],
            "metrics": {
              "initial_rmse_K": 0.03824797932611568,
              "observation_residual_rms_K": 0.01248925838247731,
              "future_predictive_rmse_K": 0.01971866204648079
            }
          }
        }
      },
      {
        "split": "train",
        "index": 21,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.558986336075044,
          1.8946005557045609,
          -0.09935503242862614,
          -0.13755895947911193,
          -0.05973503489321003,
          -0.0670546700975339,
          0.005427381812016335,
          0.004586385073940817
        ],
        "initial_K": [
          0.5648255244502051,
          1.1362078241041158,
          1.6885090029577534,
          2.157500832460694,
          2.470519873245957,
          2.5922665565736525,
          2.543875685608095,
          2.376352900382424,
          2.12978293368467,
          1.8235214263435346,
          1.4792934941554936,
          1.1369668641631967,
          0.8375926776523461,
          0.5949569112315491,
          0.390707626293386,
          0.19694203605524258
        ],
        "observed_K": [
          0.5362581740021164,
          1.0298944017733525,
          1.4762604338491385,
          1.792265906353653,
          2.0656567709959806,
          2.1739082339950566,
          2.2094389371852765,
          2.1188818404154657,
          1.9872076591592933,
          1.7556657410564405,
          1.4528142007688536,
          1.1994281893702383,
          0.887509058901911,
          0.6670830346286216,
          0.4499654779237959,
          0.23753472777381884
        ],
        "future_observed_K": [
          0.46101655281119197,
          0.9197778024291247,
          1.3112246739092606,
          1.6738488324868825,
          1.885708489034256,
          2.0169262131101036,
          2.0697245705187903,
          1.9652874977530221,
          1.906695883648206,
          1.6918989951977046,
          1.4117811977500327,
          1.2219989741469524,
          0.9359725833419845,
          0.709945592653364,
          0.47350806972465337,
          0.19657130853488747
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.5739301653250894,
              1.932038715078804,
              -0.08568656665296881,
              -0.02105496846633068,
              0.4617059958201354,
              -1.0855744641442606,
              2.0456710175799326,
              0.5855339830928679
            ],
            "initial_K": [
              1.3012950937358962,
              1.4889462844076566,
              1.2049542436560632,
              1.7282682433950771,
              2.8318444207776867,
              3.122825158228007,
              2.2954215406504184,
              1.6483717289625344,
              2.0622567367157028,
              2.6468391859012224,
              2.108829085813717,
              0.6882056025802388,
              -0.15996014427861638,
              0.27956153492556957,
              1.1309084294497824,
              1.0989143933810086
            ],
            "metrics": {
              "initial_rmse_K": 0.603363616787194,
              "observation_residual_rms_K": 0.011599669214987085,
              "future_predictive_rmse_K": 0.024848274376408803
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.494808999399218,
              1.8904036051878508,
              -0.08090560499079247,
              -0.01704442619069722,
              0.19314554420233043,
              -0.08227781610465157,
              0.012809124285373617,
              0.00019095348843583263
            ],
            "initial_K": [
              0.6569178447674288,
              1.2544258172267009,
              1.7469571845095295,
              2.111522027224646,
              2.3483601671826797,
              2.4718985942298204,
              2.4935361853425086,
              2.407041243063429,
              2.194331153720847,
              1.8566949955262833,
              1.446099180836669,
              1.056761421491292,
              0.7681561137782097,
              0.5851894024417758,
              0.4374333602214281,
              0.24672900324774205
            ],
            "metrics": {
              "initial_rmse_K": 0.07213469191457311,
              "observation_residual_rms_K": 0.02460810554199897,
              "future_predictive_rmse_K": 0.02537992834576776
            }
          },
          "learned": {
            "coefficients_K": [
              6.573554687129766,
              1.936519814392767,
              -0.08407553472412672,
              -0.01614767615675224,
              0.06031115587435687,
              -0.008137738323972184,
              0.0019975013941608225,
              -5.155199828706155e-05
            ],
            "initial_K": [
              0.6499848226151309,
              1.2486755467141168,
              1.755944906353539,
              2.1475331178608714,
              2.4120530814356984,
              2.5447481073087235,
              2.543974940338051,
              2.4133939174567174,
              2.1682068089418034,
              1.8402550297659679,
              1.4760096775121576,
              1.1247632410648294,
              0.821411704036926,
              0.5745527442113819,
              0.36920155010678873,
              0.18259143583905119
            ],
            "metrics": {
              "initial_rmse_K": 0.04667654066611441,
              "observation_residual_rms_K": 0.016842210676796438,
              "future_predictive_rmse_K": 0.024814889157608763
            }
          }
        }
      },
      {
        "split": "train",
        "index": 22,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.318286867286365,
          -0.8376517789752561,
          -0.46382743199452003,
          -0.14638343306444984,
          0.03657467638517335,
          0.022577294683629453,
          0.03587104549573651,
          -0.012892631353535541
        ],
        "initial_K": [
          0.13819630689284568,
          0.29690327810704603,
          0.5036964325640629,
          0.7831878808873632,
          1.1289196644323587,
          1.4854331507700689,
          1.7733851211686003,
          1.9432053692847386,
          1.9984054073048725,
          1.9635154746001422,
          1.8464695346589513,
          1.6470959504334874,
          1.3855145476716484,
          1.0925537882061356,
          0.7732805823613755,
          0.40836823135654277
        ],
        "observed_K": [
          0.22242746135475147,
          0.39655191048115346,
          0.6225568344437902,
          0.8615192481301049,
          1.0978486790888322,
          1.330118345390224,
          1.5422193249224776,
          1.6446954458365843,
          1.7726989792504027,
          1.72258546613962,
          1.6189478252182594,
          1.4894383642119648,
          1.2337617008705242,
          0.9600605181437434,
          0.6562052306821166,
          0.3358115543404481
        ],
        "future_observed_K": [
          0.23431790194044833,
          0.43527661579467314,
          0.621943657954897,
          0.8893257984070736,
          1.0861205495928568,
          1.261543344585483,
          1.4565631061916746,
          1.5917508792886161,
          1.6476724941179386,
          1.617918447475039,
          1.539975794336372,
          1.373331365002182,
          1.2139634522207925,
          0.9226986501823146,
          0.6493969276508261,
          0.30361292150363794
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.290676272465016,
              -0.8217087526284353,
              -0.5081766795965842,
              0.0315808773884542,
              0.09199872689027035,
              0.2855000159045566,
              0.5814098820307684,
              4.9493417312231704
            ],
            "initial_K": [
              2.1421917337661993,
              0.8458340536219936,
              -1.235651414058191,
              -0.09776320318214793,
              2.5672881687082523,
              2.5274985019425706,
              0.5253951490561029,
              0.6958770614015939,
              2.991523157316693,
              3.3559599518562755,
              1.1400652511169675,
              0.21352964695933818,
              1.8744089283985943,
              2.55325016572474,
              0.4238531141550518,
              -1.2248319666345964
            ],
            "metrics": {
              "initial_rmse_K": 1.2507057345406778,
              "observation_residual_rms_K": 0.01418783540860934,
              "future_predictive_rmse_K": 0.01857216298957093
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.226999831631838,
              -0.8040010669868214,
              -0.4798224892296959,
              0.02556536403964389,
              0.038485842358575474,
              0.021638605717376753,
              0.0036405420889654492,
              0.0016140721056803501
            ],
            "initial_K": [
              0.16801390588221166,
              0.3426516601921209,
              0.5421056790931825,
              0.7881087092520194,
              1.08399147305499,
              1.4019505584387713,
              1.6920821165731972,
              1.9040073476354364,
              2.0046195434256533,
              1.9842326689046061,
              1.8530121835884361,
              1.6327185172738092,
              1.3487508600076303,
              1.0256213674202552,
              0.6847098033542207,
              0.3410478413004574
            ],
            "metrics": {
              "initial_rmse_K": 0.05033742858505084,
              "observation_residual_rms_K": 0.020927888878289596,
              "future_predictive_rmse_K": 0.026718006952725634
            }
          },
          "learned": {
            "coefficients_K": [
              5.2903740889113635,
              -0.8236145935926681,
              -0.4986222197984837,
              0.024220306082639784,
              0.012017495133164795,
              0.0021401796907157484,
              0.000567719364430972,
              -0.0004357534555080327
            ],
            "initial_K": [
              0.15092707321235171,
              0.32498710830574595,
              0.5400734562718595,
              0.8032329896124317,
              1.1055034585568726,
              1.4199495705481306,
              1.7060579159470763,
              1.9204516350239633,
              2.029296946319538,
              2.0166621261223465,
              1.886433006269791,
              1.6589334295846383,
              1.3640688953227562,
              1.0325594036711403,
              0.6879609458451883,
              0.34281675623247654
            ],
            "metrics": {
              "initial_rmse_K": 0.04590391343784413,
              "observation_residual_rms_K": 0.01469103987029583,
              "future_predictive_rmse_K": 0.01860171222912559
            }
          }
        }
      },
      {
        "split": "train",
        "index": 23,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.819508217172656,
          0.35939278689102944,
          -0.29758325276262326,
          0.05368504632067539,
          -0.17102366114030657,
          0.004880493615793203,
          0.045863925649199645,
          -0.013664861618803708
        ],
        "initial_K": [
          0.3351305320224246,
          0.6834128546814303,
          1.046616945627678,
          1.406303435330417,
          1.7208790002607717,
          1.9395503789823496,
          2.0373615959602844,
          2.040707043355591,
          2.0006311289436733,
          1.9297266770209274,
          1.781953197441942,
          1.5137831990892023,
          1.1538805568015285,
          0.7881320501417484,
          0.4796991545042573,
          0.22759591138780377
        ],
        "observed_K": [
          0.34080494090030455,
          0.651591277368336,
          0.9957334420139264,
          1.2733202431748485,
          1.5226802778155313,
          1.673254154786733,
          1.8050661819238278,
          1.8626095527278772,
          1.8228014443279923,
          1.7224868673735145,
          1.5963310688017753,
          1.3397786104495955,
          1.1042208973550947,
          0.7791271333722171,
          0.5638527986900117,
          0.2794444661499656
        ],
        "future_observed_K": [
          0.3422272225314487,
          0.6447877561804162,
          0.9355173495241804,
          1.218660196197236,
          1.4333906073322102,
          1.5826183555060993,
          1.7091832216929932,
          1.7751112919078182,
          1.7060228812878027,
          1.608031013005514,
          1.5328325605811333,
          1.295642349598376,
          1.0709765329406802,
          0.8195432075993481,
          0.516759845420887,
          0.2803776252983111
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.8159982219089175,
              0.37242832268008713,
              -0.34086918507330594,
              0.12321387609334267,
              -0.2109963972316188,
              -0.8354243064754562,
              1.1799849345726259,
              -15.325030083287215
            ],
            "initial_K": [
              -4.7793735826193755,
              -0.30697241368365047,
              5.891445864953892,
              3.2358494694210367,
              -2.7155726281287,
              -0.5504019030655192,
              6.069213762059848,
              5.109647953068291,
              -1.6875511998594384,
              -1.8084291319579053,
              5.068361549115339,
              6.107847987817773,
              -1.3829861124250793,
              -4.621572911566706,
              1.8258239647278298,
              6.052444195276388
            ],
            "metrics": {
              "initial_rmse_K": 3.8441411229155844,
              "observation_residual_rms_K": 0.013848599728858288,
              "future_predictive_rmse_K": 0.018313300382362667
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.745999218456244,
              0.3644025548627707,
              -0.3218500719344519,
              0.09974414448072007,
              -0.08826615711507473,
              -0.0633184454202575,
              0.007388565195438925,
              -0.004997776455826373
            ],
            "initial_K": [
              0.32935916741156795,
              0.6859759576071635,
              1.0597850016398431,
              1.405584443594173,
              1.678818416491913,
              1.865536820770305,
              1.9802648292436864,
              2.0398397720650996,
              2.0391804170414547,
              1.9504337479060736,
              1.7493576496239696,
              1.4482099416670806,
              1.1010834057879624,
              0.7701313965416496,
              0.48472750053452135,
              0.2352559888274795
            ],
            "metrics": {
              "initial_rmse_K": 0.036395708185215,
              "observation_residual_rms_K": 0.023256805653796734,
              "future_predictive_rmse_K": 0.023661376058563787
            }
          },
          "learned": {
            "coefficients_K": [
              5.815666033938944,
              0.37329211919111827,
              -0.33446034921767476,
              0.09449635473713115,
              -0.02756177463054058,
              -0.006262550032385216,
              0.0011521997093579533,
              0.0013492571693784793
            ],
            "initial_K": [
              0.36560635524956037,
              0.7259157885679426,
              1.072623311945963,
              1.3922808063394236,
              1.6678441340437449,
              1.8839447934240778,
              2.0301809428367767,
              2.098185251552583,
              2.0774336278850054,
              1.958418564352684,
              1.743005525313681,
              1.4519460261098882,
              1.121587814279433,
              0.7917634325747138,
              0.4921091421459447,
              0.23235336347877716
            ],
            "metrics": {
              "initial_rmse_K": 0.040437822216798994,
              "observation_residual_rms_K": 0.017267435060586988,
              "future_predictive_rmse_K": 0.01831723103525573
            }
          }
        }
      },
      {
        "split": "train",
        "index": 24,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.825653243628734,
          1.432688284980496,
          -0.07915008182625453,
          0.1293544120951745,
          0.12874802745202124,
          -0.09790145176385723,
          0.031439265862395586,
          0.044964460998458515
        ],
        "initial_K": [
          0.6542165621589119,
          1.220855729983716,
          1.6807609067330616,
          2.0468685199168988,
          2.302224800696068,
          2.427179816777708,
          2.4553382403690587,
          2.434430292862032,
          2.3420290889918287,
          2.1088743048095258,
          1.73624755378618,
          1.3307838763119866,
          0.9984862881693917,
          0.7474941554956156,
          0.5183058638996296,
          0.2688063704882895
        ],
        "observed_K": [
          0.5140243539327687,
          1.0058016036088353,
          1.3958310913762226,
          1.7643491803338613,
          1.9943236504150361,
          2.130907922579488,
          2.2167851186161998,
          2.2101610380138466,
          2.054537524756328,
          1.916602348639485,
          1.6181941605038503,
          1.4087682886680057,
          1.100716334338518,
          0.7934027078644981,
          0.5302398781983874,
          0.2796925555790724
        ],
        "future_observed_K": [
          0.4622633274436247,
          0.8955314081933998,
          1.2794691736142323,
          1.6220235907567027,
          1.8798594717713175,
          2.014950414348923,
          2.093477681001519,
          2.053253774730878,
          1.9739772571326915,
          1.8055876215252853,
          1.5713835112003016,
          1.3661141850527898,
          1.0548379387927918,
          0.8049491763682356,
          0.5515112096073196,
          0.29090861271227236
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.843634378550352,
              1.4070019506062657,
              -0.07252846808012853,
              0.17929948872222695,
              0.22715981158262827,
              0.14171225818544655,
              -0.8324589633369086,
              -9.260377705805332
            ],
            "initial_K": [
              -2.697682237825801,
              0.5918281105538593,
              4.958635832283832,
              3.3686191425644383,
              -0.7100509524209255,
              0.4404569307292021,
              4.967800967479432,
              4.890764269774012,
              0.4269692594284229,
              -0.596462010418005,
              3.097595190810952,
              4.178426748912073,
              0.18363117164524545,
              -2.0957250659979936,
              0.9088092208677021,
              3.109231003674788
            ],
            "metrics": {
              "initial_rmse_K": 2.337283867900896,
              "observation_residual_rms_K": 0.01735671360404681,
              "future_predictive_rmse_K": 0.017375044066726426
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.761267161743372,
              1.3766812948279532,
              -0.0684816747629002,
              0.14514659124010246,
              0.0950278008651153,
              0.010740649770118047,
              -0.005212504959116229,
              -0.0030199808691146147
            ],
            "initial_K": [
              0.6444422001563086,
              1.2175758809594281,
              1.6731792091073647,
              2.004223898855514,
              2.2339636358147406,
              2.3862695192994807,
              2.460242735843531,
              2.433817912989153,
              2.290979966217924,
              2.0432238675284937,
              1.7268232753465884,
              1.3848547731601752,
              1.0518994298065465,
              0.7476938547631431,
              0.47669656280846656,
              0.23167473505048877
            ],
            "metrics": {
              "initial_rmse_K": 0.038916237927114544,
              "observation_residual_rms_K": 0.02660032613965715,
              "future_predictive_rmse_K": 0.01964733460409059
            }
          },
          "learned": {
            "coefficients_K": [
              6.843243495863543,
              1.4102652990197313,
              -0.07116482751905533,
              0.13751006483755326,
              0.029673148992603902,
              0.0010623106129540455,
              -0.000812856967497304,
              0.0008153087428087049
            ],
            "initial_K": [
              0.6334219247810958,
              1.2088879142547841,
              1.685516482322019,
              2.046588585694683,
              2.2945400535453166,
              2.439418192544855,
              2.4883866747127463,
              2.441859190671112,
              2.2981631547223733,
              2.06326075421383,
              1.7575615964871436,
              1.4136864358128207,
              1.066851137220098,
              0.7448990543425942,
              0.4625187904080591,
              0.21918472910097125
            ],
            "metrics": {
              "initial_rmse_K": 0.038358091640271236,
              "observation_residual_rms_K": 0.01857363354790935,
              "future_predictive_rmse_K": 0.016801177082152372
            }
          }
        }
      },
      {
        "split": "train",
        "index": 25,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.95380165311864,
          -2.0558799597571458,
          -0.5088740315120195,
          0.006649613321287238,
          -0.0974333022732776,
          0.0015290925500910024,
          -0.006443360867632703,
          0.0014788387734191197
        ],
        "initial_K": [
          0.002339691286560086,
          0.07587299362303707,
          0.2606669394260651,
          0.5536409467289067,
          0.9201374187870577,
          1.315964224768304,
          1.7016854491638367,
          2.0426903839843056,
          2.303615460568785,
          2.447972787700465,
          2.4448999753350336,
          2.2788212230279283,
          1.95848396419038,
          1.5206636971553662,
          1.0204351661315145,
          0.5067845106232991
        ],
        "observed_K": [
          0.11689822298686707,
          0.2664199101763301,
          0.49583632935410477,
          0.7497518578529919,
          0.9919821581840917,
          1.2660297392778357,
          1.573073983941527,
          1.828085386943774,
          1.966429437795142,
          2.059339303532655,
          2.062314044503981,
          1.8991293148611526,
          1.681206758285572,
          1.3260305605565021,
          0.8797612465690988,
          0.454372349108747
        ],
        "future_observed_K": [
          0.11517115509806453,
          0.33992979437688253,
          0.5274254764627481,
          0.7521804015171746,
          1.0191952989480464,
          1.2524061435498235,
          1.4953993382711186,
          1.7122013349838883,
          1.8971078409751154,
          1.9439883104339204,
          1.900202310409362,
          1.7536308376889658,
          1.5434651413366485,
          1.2181114264245987,
          0.8380089374921948,
          0.4701407745336254
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.933989814071171,
              -2.033638991946224,
              -0.48626695885274107,
              0.09476523497243752,
              -0.4861336780980025,
              0.27983911708725007,
              -5.235440458738759,
              -12.104020838390767
            ],
            "initial_K": [
              -5.8521561385136405,
              -1.643590423982777,
              5.43199638054522,
              3.6522042443439497,
              -3.069028459649509,
              -2.561929070063889,
              4.403031565960964,
              6.178412223471767,
              0.7632901453670842,
              -1.6216857336077717,
              2.9156554116906035,
              5.869131456893948,
              2.2145182720041237,
              -1.3221136304339134,
              0.6040592647256824,
              2.7040301933963393
            ],
            "metrics": {
              "initial_rmse_K": 3.2988941342840543,
              "observation_residual_rms_K": 0.011147716999974609,
              "future_predictive_rmse_K": 0.020084256849091837
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.86257071151392,
              -1.9898144131490259,
              -0.45913524172754006,
              0.07671438955202958,
              -0.20336438049614866,
              0.02120955510200092,
              -0.03278210765482376,
              -0.003947345619432899
            ],
            "initial_K": [
              -0.00354802567934584,
              0.08437842586365246,
              0.2941545794860835,
              0.5945476847873883,
              0.9387781300496861,
              1.2967279412029193,
              1.6487780698885526,
              1.9700972871249085,
              2.230442546830864,
              2.3978187765794283,
              2.432808850384763,
              2.2916013322121707,
              1.9570723412448139,
              1.4741265861986608,
              0.9404595030655787,
              0.4437657080011087
            ],
            "metrics": {
              "initial_rmse_K": 0.04500183901193953,
              "observation_residual_rms_K": 0.024998583142990277,
              "future_predictive_rmse_K": 0.028649850803388666
            }
          },
          "learned": {
            "coefficients_K": [
              5.933650886864702,
              -2.0383557391938525,
              -0.47712443363259255,
              0.07267825300714557,
              -0.06350206473594255,
              0.0020977441740604834,
              -0.00511216101000855,
              0.0010656707886215232
            ],
            "initial_K": [
              0.03399171927239791,
              0.12128902171316225,
              0.2953229065177294,
              0.5611497078430197,
              0.9006515532373047,
              1.2833995594578846,
              1.6732027871000585,
              2.028509087451077,
              2.303191453152979,
              2.4530936682131905,
              2.4463163780070456,
              2.272134163682529,
              1.945972319486883,
              1.508211104093908,
              1.0123910800029445,
              0.5035116638774308
            ],
            "metrics": {
              "initial_rmse_K": 0.021264061461729156,
              "observation_residual_rms_K": 0.01867992533423294,
              "future_predictive_rmse_K": 0.019829509041734483
            }
          }
        }
      },
      {
        "split": "train",
        "index": 26,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.530399492207092,
          -0.3629033563434738,
          -0.31562016476478955,
          -0.07761850086316652,
          0.06329272355277446,
          0.04791962045673019,
          -0.03586292632288878,
          -0.06025300128866266
        ],
        "initial_K": [
          0.22829318477567473,
          0.5016922633704206,
          0.7911161333610327,
          1.0539539890198515,
          1.3155032203265928,
          1.6123952165431938,
          1.888138428451096,
          2.0315140125535387,
          2.0128725733835435,
          1.9058128183138294,
          1.7697322853941584,
          1.5860651460245803,
          1.3283119800382865,
          1.0227428010318842,
          0.7037893390129644,
          0.3658262325955287
        ],
        "observed_K": [
          0.21997755370405525,
          0.510609654697332,
          0.7575993344698787,
          1.045557508129319,
          1.2894220338232565,
          1.4550758966252215,
          1.6484863460711052,
          1.7296040989570864,
          1.736260209145172,
          1.7577556823024836,
          1.609541665660992,
          1.4236461443303574,
          1.2164863455206973,
          0.9618970614972517,
          0.6717909201233665,
          0.37492061261550713
        ],
        "future_observed_K": [
          0.26101711458357063,
          0.5311588636633173,
          0.7695603621929512,
          1.0061908886446462,
          1.2113282161788115,
          1.4057157585088715,
          1.5674723153825847,
          1.6553355925932178,
          1.6436768307457206,
          1.6402157789807157,
          1.530341874017228,
          1.3556339449243053,
          1.1669611226548018,
          0.9177258836860559,
          0.6145039104945561,
          0.3127523387658976
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.52769835842532,
              -0.4218588776778434,
              -0.2688568546284768,
              -0.23271885595325717,
              0.018762245330363945,
              -1.7135145992013878,
              1.1257377871883754,
              -6.729957188346435
            ],
            "initial_K": [
              -2.2543095772274775,
              -0.2583236536957527,
              2.783483073384565,
              2.0951157785846695,
              -0.22329785195172036,
              0.6281019208282319,
              3.2785654429102884,
              2.9221965446676395,
              0.4262438490046463,
              0.7742346999100347,
              3.560504419244313,
              3.3118143528439017,
              -0.385729212162608,
              -1.4865275576352617,
              1.881958907625301,
              3.607030789320028
            ],
            "metrics": {
              "initial_rmse_K": 1.7494397247958888,
              "observation_residual_rms_K": 0.015442291899822855,
              "future_predictive_rmse_K": 0.013554193101626083
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.4611692155828795,
              -0.41276788970047523,
              -0.2538557364275583,
              -0.1883906579970317,
              0.0078488131356269,
              -0.12987062955360038,
              0.007048892566262278,
              -0.002194763821137153
            ],
            "initial_K": [
              0.16752836958856138,
              0.40717545705787195,
              0.7293456815590464,
              1.0791462158339247,
              1.3883072897789737,
              1.6260632152054444,
              1.8012440179772091,
              1.9237880542307122,
              1.9750186734815525,
              1.9221292934179819,
              1.7607012650243299,
              1.5339488508164751,
              1.298608184342753,
              1.0681301657897944,
              0.7979927661766406,
              0.43813101182002234
            ],
            "metrics": {
              "initial_rmse_K": 0.06287895197897235,
              "observation_residual_rms_K": 0.024864474957375263,
              "future_predictive_rmse_K": 0.02006370954023387
            }
          },
          "learned": {
            "coefficients_K": [
              5.527382637060517,
              -0.42283732159441595,
              -0.2638019551965887,
              -0.17847895272378747,
              0.0024508512189937545,
              -0.012844934993564799,
              0.0010992299250680638,
              0.0005925236646608206
            ],
            "initial_K": [
              0.2043912865473805,
              0.44273669679485117,
              0.7299366670587765,
              1.0527586255834311,
              1.3753696589373232,
              1.6552127269782988,
              1.8586528485245901,
              1.9682785268350722,
              1.9822613465094276,
              1.9108503937789103,
              1.771896272817993,
              1.583606489548772,
              1.355754402580089,
              1.0860688325730066,
              0.7670219020246456,
              0.3991418348997896
            ],
            "metrics": {
              "initial_rmse_K": 0.04251586669082723,
              "observation_residual_rms_K": 0.020227727399055026,
              "future_predictive_rmse_K": 0.012304223155024777
            }
          }
        }
      },
      {
        "split": "train",
        "index": 27,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          7.069786011256706,
          0.6008164339971255,
          -1.1726056270936605,
          -0.02006253605165202,
          -0.2572724823081962,
          -0.015701293897427214,
          -0.07438577246346625,
          0.022971664894965653
        ],
        "initial_K": [
          0.2117186988723015,
          0.5467714538931786,
          1.0337742666364447,
          1.588254923751813,
          2.0855281554358904,
          2.4519197706500466,
          2.6808720865583964,
          2.774996494926929,
          2.710577800336734,
          2.4748801684014055,
          2.1053694322617735,
          1.6604973797192324,
          1.1757181228110323,
          0.688987381030584,
          0.28850721332188134,
          0.06605305780431647
        ],
        "observed_K": [
          0.34398123551560733,
          0.7803234965255296,
          1.1421973844098994,
          1.5077802655872452,
          1.812583420018008,
          2.082219032764933,
          2.2940747768955885,
          2.357130935321789,
          2.314119116899403,
          2.138152177222482,
          1.88056313951761,
          1.585365969367834,
          1.2151829703456318,
          0.8705566882070053,
          0.5447542378555816,
          0.26474514302838414
        ],
        "future_observed_K": [
          0.3866189505425184,
          0.718040086137806,
          1.1018543171324218,
          1.4293167996025227,
          1.723378153823419,
          1.9566923502784712,
          2.12570245057211,
          2.207081158035102,
          2.161974989041547,
          1.99151017978061,
          1.792023762953944,
          1.5331837516648592,
          1.2048732343681077,
          0.8686421718638947,
          0.5982030548784875,
          0.269300415955754
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              7.063429973381499,
              0.6064029065174356,
              -1.0804511941011228,
              0.14940534798449112,
              -0.013384175633669166,
              0.30240041608679474,
              -2.8869482758360285,
              -16.832328423597083
            ],
            "initial_K": [
              -6.252296235244382,
              -0.7691859667818047,
              7.332909385513933,
              4.427637442447764,
              -3.442840864201833,
              -1.631219751492592,
              6.995572820191612,
              7.518797123820984,
              -0.40890637964934573,
              -2.552841605523548,
              4.139104894412524,
              6.687104665787702,
              0.022901292384269745,
              -4.189227752713564,
              0.8046994116899546,
              4.840311276826208
            ],
            "metrics": {
              "initial_rmse_K": 4.273534855096959,
              "observation_residual_rms_K": 0.009723722068265777,
              "future_predictive_rmse_K": 0.01665058676415979
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.978417385648594,
              0.593335025706353,
              -1.0201664150671954,
              0.12094667490427664,
              -0.0055990043661284065,
              0.022919520167944032,
              -0.01807684566718648,
              -0.005489334391841267
            ],
            "initial_K": [
              0.35474376633490234,
              0.7306585979502791,
              1.130766347315661,
              1.543252139439633,
              1.951408373719783,
              2.3264133398952067,
              2.6146775426830544,
              2.750968425441243,
              2.695335821216108,
              2.4560166897552964,
              2.0777049377692745,
              1.6175623737544278,
              1.1364806475442504,
              0.6994696343369163,
              0.3619781637212052,
              0.14148913337147745
            ],
            "metrics": {
              "initial_rmse_K": 0.08672418155028647,
              "observation_residual_rms_K": 0.024595580441908713,
              "future_predictive_rmse_K": 0.02010651315098027
            }
          },
          "learned": {
            "coefficients_K": [
              7.063026536796002,
              0.607809375045821,
              -1.0601371420945571,
              0.1145833668285176,
              -0.0017483314277912324,
              0.002266869327213305,
              -0.002818969011290361,
              0.0014819637990557202
            ],
            "initial_K": [
              0.35530943895479195,
              0.7288526768422035,
              1.1310480289241769,
              1.556974548633871,
              1.9820982343626923,
              2.363993038121886,
              2.64956546297875,
              2.786418424689634,
              2.7380644990341505,
              2.499693434741761,
              2.105762698004785,
              1.6225784149551716,
              1.1292189869796645,
              0.6963428721201312,
              0.36825672413313776,
              0.14932917908767424
            ],
            "metrics": {
              "initial_rmse_K": 0.07987190220216607,
              "observation_residual_rms_K": 0.014050433907274843,
              "future_predictive_rmse_K": 0.01733425830885599
            }
          }
        }
      },
      {
        "split": "train",
        "index": 28,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.002767624928394,
          -0.7473453842891561,
          -0.5268076314387524,
          0.3197853361139353,
          0.15217626933939257,
          -0.054122723527804804,
          -0.018313214385831174,
          0.0035634154821746694
        ],
        "initial_K": [
          0.28471082984079377,
          0.5508531354731002,
          0.7873552234898253,
          1.0033669118532795,
          1.2339686070496563,
          1.5187415897220071,
          1.8567974842260422,
          2.178360655043191,
          2.373002453951405,
          2.3619789824271407,
          2.150986705719041,
          1.8153550938891976,
          1.4387178333088604,
          1.0667499529340547,
          0.7069842340921193,
          0.35292251571259586
        ],
        "observed_K": [
          0.23637619873837795,
          0.5037704961194658,
          0.7343229565001042,
          1.0509893074596586,
          1.3081960792493472,
          1.4854809718025779,
          1.7341222312063824,
          1.905607291778646,
          1.9879901217873184,
          1.9657672765560377,
          1.8449498381394125,
          1.6246842574253475,
          1.3402833932421476,
          1.0606200900323643,
          0.6918817173213558,
          0.33832034960753754
        ],
        "future_observed_K": [
          0.26201718317658124,
          0.5030021635344705,
          0.7957326305695438,
          1.0409131140016887,
          1.278119945241719,
          1.458956042274854,
          1.6828928820866147,
          1.7452998516909177,
          1.8499738681987232,
          1.8148397027822667,
          1.7452985879454015,
          1.5354227768522404,
          1.2908553791106712,
          1.0285552612039204,
          0.6385225815047598,
          0.3147595417861876
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.000752354199876,
              -0.7493209485668285,
              -0.6017009811238971,
              0.2993835119811458,
              -0.002489265802352515,
              -1.1238371513563756,
              -3.590825429134875,
              9.511204599700758
            ],
            "initial_K": [
              1.9639219754239374,
              0.13051416156591283,
              -1.507605756472057,
              1.280126356752303,
              4.221230053805948,
              1.9288399014124746,
              -1.5408065035005782,
              0.745017156542819,
              5.715127299314435,
              4.888066263454958,
              -0.6196986605398962,
              -1.5362410044861194,
              3.369679460658885,
              4.922539799385822,
              -0.31135536449586704,
              -3.7954266081617525
            ],
            "metrics": {
              "initial_rmse_K": 2.5535799381661115,
              "observation_residual_rms_K": 0.014570310532081967,
              "future_predictive_rmse_K": 0.024205081072117506
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.928529724698726,
              -0.7331732079477175,
              -0.5681285153895897,
              0.24235705604757163,
              -0.0010413349673001138,
              -0.08517782015420321,
              -0.02248422586701258,
              0.0031017801698654634
            ],
            "initial_K": [
              0.2034278896065816,
              0.4459684714421275,
              0.7270848779464445,
              1.0141111422785287,
              1.2862852723372236,
              1.558024093485487,
              1.847533403225779,
              2.1257219381119077,
              2.31039140197367,
              2.321010016064319,
              2.139285608205361,
              1.816290547159673,
              1.4289366593448818,
              1.0359446542061832,
              0.6654975059364642,
              0.3232967074908304
            ],
            "metrics": {
              "initial_rmse_K": 0.04865203885576885,
              "observation_residual_rms_K": 0.025134305912661196,
              "future_predictive_rmse_K": 0.029248001737274813
            }
          },
          "learned": {
            "coefficients_K": [
              6.000409613767917,
              -0.7510588959290397,
              -0.5903881285955409,
              0.22960604314717337,
              -0.0003251647134270142,
              -0.008424565019319735,
              -0.0035062718977025256,
              -0.0008373922221247039
            ],
            "initial_K": [
              0.22745404836071056,
              0.4639757981715388,
              0.7156451874759953,
              0.9869264184283827,
              1.2816100351774913,
              1.595922838195368,
              1.9067646765150188,
              2.167862014808201,
              2.3220878071787605,
              2.3242861002536017,
              2.160964750210559,
              1.8567022236806965,
              1.4652425220872454,
              1.0495442482587023,
              0.6589596331436262,
              0.3132063300510361
            ],
            "metrics": {
              "initial_rmse_K": 0.048591252181817764,
              "observation_residual_rms_K": 0.018962319801973125,
              "future_predictive_rmse_K": 0.024665904290777814
            }
          }
        }
      },
      {
        "split": "train",
        "index": 29,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.173262121647917,
          -0.7914841618083885,
          -0.31543724934403594,
          0.26894688022990665,
          -0.10625476874422457,
          0.08131566249339993,
          -0.023914742864648467,
          -0.04213737969568027
        ],
        "initial_K": [
          0.2067715941368456,
          0.433332566804449,
          0.6581125469836401,
          0.8606295116570271,
          1.0703077512170003,
          1.3217535109284138,
          1.5837217431394386,
          1.7860424616325132,
          1.9036182578969156,
          1.956092473927153,
          1.927559139065835,
          1.7531148893176713,
          1.41057655079123,
          0.9793611071398146,
          0.5762054692137637,
          0.257463522390076
        ],
        "observed_K": [
          0.19533857591944534,
          0.43043780832700634,
          0.6585121810927105,
          0.8955091157899802,
          1.05370522592031,
          1.2457572254462406,
          1.4423986077250832,
          1.6380020083058788,
          1.711415858578853,
          1.689820772866195,
          1.582424209224629,
          1.4806327171506979,
          1.1961678756718508,
          0.9588140089460715,
          0.6513717397835598,
          0.3308142489108974
        ],
        "future_observed_K": [
          0.18725443218993298,
          0.45694506388271156,
          0.6617730297187719,
          0.8911625388969969,
          1.0690680811045492,
          1.2028460452750656,
          1.3668740133699429,
          1.509670549914715,
          1.5552078471381412,
          1.5905290944227781,
          1.501974308172359,
          1.3402902280939213,
          1.1623489895546204,
          0.8881460130063721,
          0.634831322835737,
          0.3114444151190585
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.167550500645828,
              -0.8088551573231427,
              -0.34259424094181407,
              0.31681050018779633,
              0.3578207434271258,
              -0.8651706544253818,
              -6.309365987141838,
              -17.194240194656793
            ],
            "initial_K": [
              -7.884784834046851,
              -1.8853020693487847,
              7.883681143332064,
              5.1325180692516845,
              -4.551280938450144,
              -4.167104910069542,
              5.192306850834523,
              7.441485665450681,
              -0.011952026323586828,
              -3.1428093466595657,
              2.908469536421969,
              6.255563705073587,
              0.8133410537235921,
              -3.2469876801178166,
              0.9130867074469835,
              4.445359720657377
            ],
            "metrics": {
              "initial_rmse_K": 4.574495146671255,
              "observation_residual_rms_K": 0.013920268904397624,
              "future_predictive_rmse_K": 0.021851961460305828
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.1053559518280585,
              -0.7914244645020416,
              -0.32347887670673103,
              0.25646455825966924,
              0.14968720970008392,
              -0.06557297942713307,
              -0.039506573831611186,
              -0.005607360530691148
            ],
            "initial_K": [
              0.23045058745814856,
              0.4619173538446699,
              0.6722280052649474,
              0.8444766145467587,
              1.0097607429725046,
              1.2294735371039212,
              1.521053425588498,
              1.8149412240613352,
              1.999344473449178,
              2.006070246028101,
              1.8502189310352717,
              1.5977037237290803,
              1.3080906351443866,
              1.0058604516269294,
              0.6890963197052646,
              0.35214488669097643
            ],
            "metrics": {
              "initial_rmse_K": 0.0764410902853151,
              "observation_residual_rms_K": 0.026109015106743884,
              "future_predictive_rmse_K": 0.022670837409484806
            }
          },
          "learned": {
            "coefficients_K": [
              5.1672553495737255,
              -0.8107311861326525,
              -0.3361529715298886,
              0.24297131426588972,
              0.04674096248972839,
              -0.006485536113677335,
              -0.006160798704816302,
              0.0015138274919248983
            ],
            "initial_K": [
              0.2299501081880329,
              0.4453066797904554,
              0.6429207105083719,
              0.8358411403648067,
              1.0469944550590458,
              1.2922288530251207,
              1.5609343939624731,
              1.8090060521761757,
              1.974452027427876,
              2.008175198102925,
              1.8974263769590507,
              1.6657377237861257,
              1.3550948088930423,
              1.007942296024381,
              0.6573808912347765,
              0.3215162298412975
            ],
            "metrics": {
              "initial_rmse_K": 0.046668896965577855,
              "observation_residual_rms_K": 0.022513157160427927,
              "future_predictive_rmse_K": 0.022827033232098295
            }
          }
        }
      },
      {
        "split": "train",
        "index": 30,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.18299614955041,
          2.1486970324503263,
          -0.9515242903977499,
          -0.1316935992771241,
          0.06819000482727407,
          -0.012536703656165079,
          -0.0011237867114170146,
          0.006970123083774455
        ],
        "initial_K": [
          0.4705032702116187,
          0.9447835711544316,
          1.4223384220563715,
          1.8851488104347482,
          2.288815515112227,
          2.5735348851033,
          2.6860488922028716,
          2.594725170315141,
          2.298993151892207,
          1.8416001493189773,
          1.3109595256268713,
          0.8134577956389824,
          0.42749819225194785,
          0.17798549334519187,
          0.04770035899524955,
          0.001835034091560439
        ],
        "observed_K": [
          0.4570011937082425,
          0.9307737262713621,
          1.3033436253917903,
          1.7041049751145543,
          1.9909462853527085,
          2.09949380666733,
          2.2280020012308257,
          2.1517590866161695,
          1.9838306777973873,
          1.6534190788854535,
          1.3417363269887945,
          0.9970722445095223,
          0.6680359785895034,
          0.4294950522197891,
          0.23749318552357326,
          0.09405295953228417
        ],
        "future_observed_K": [
          0.41444354629673535,
          0.8630240826111374,
          1.2623485572476194,
          1.5845205776151638,
          1.8001183008641581,
          1.9622079099242506,
          2.0413147633465623,
          2.0085067332181508,
          1.8212133756957358,
          1.6337606844810917,
          1.3013331134455202,
          1.077728323324859,
          0.7505052399438719,
          0.5245165243035431,
          0.30346386632101086,
          0.1554632464548558
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.189634325655532,
              2.191897857710766,
              -0.9932173191973794,
              -0.007458724928004205,
              0.25175445243169486,
              -0.17055270365238825,
              -2.9543367676485204,
              -1.717401981005574
            ],
            "initial_K": [
              -1.0640252874790246,
              0.3605989190752822,
              2.740562728045516,
              3.0372480106395674,
              1.5355298545004972,
              1.1670604031541854,
              2.7312037834482776,
              3.8327126981019943,
              2.822465035242594,
              1.1113972335052782,
              0.6246859326934143,
              1.0624026564292897,
              1.002852089520754,
              0.2439998221645454,
              -0.3374478955824033,
              -0.3259170251310749
            ],
            "metrics": {
              "initial_rmse_K": 0.8577832628407756,
              "observation_residual_rms_K": 0.018189975638005115,
              "future_predictive_rmse_K": 0.021646504930622045
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.115138389102418,
              2.144662826930438,
              -0.9377998353282471,
              -0.006037989879461285,
              0.10531648096513375,
              -0.01292652365245536,
              -0.018498803821558368,
              -0.0005600766288360943
            ],
            "initial_K": [
              0.49897933367726255,
              0.9911025988910452,
              1.4590524761110757,
              1.8794595515066415,
              2.231925296552335,
              2.4933553201304184,
              2.623296530859151,
              2.5690228562190014,
              2.301598720837745,
              1.8536108485429112,
              1.3187128496152842,
              0.8090512855764076,
              0.4066022758265826,
              0.1433709282613157,
              0.01121506484816931,
              -0.021378084673734837
            ],
            "metrics": {
              "initial_rmse_K": 0.037362887355453324,
              "observation_residual_rms_K": 0.0275109813030343,
              "future_predictive_rmse_K": 0.027908841981483842
            }
          },
          "learned": {
            "coefficients_K": [
              6.189280796994919,
              2.196981664732751,
              -0.974543390762525,
              -0.005720316079898491,
              0.03288586711052008,
              -0.0012785058221346226,
              -0.0028847706994352576,
              0.00015120472344805547
            ],
            "initial_K": [
              0.4927184783484009,
              0.9833629571561231,
              1.4624903499285344,
              1.9087768377810648,
              2.2881179002373866,
              2.556292819540973,
              2.666749489253275,
              2.585150939009969,
              2.307332954699282,
              1.8707980003399791,
              1.350075416733132,
              0.8357846442014414,
              0.40800390009384513,
              0.11644465796923498,
              -0.027386987742693047,
              -0.04838950373300405
            ],
            "metrics": {
              "initial_rmse_K": 0.0355253232214776,
              "observation_residual_rms_K": 0.019829752575274952,
              "future_predictive_rmse_K": 0.022124347557554287
            }
          }
        }
      },
      {
        "split": "train",
        "index": 31,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.247051167655216,
          -0.8243380990702368,
          -0.5190461475495569,
          -0.2593135268903995,
          -0.027809440192226365,
          -0.027808629487270604,
          0.002325137154918983,
          0.03772522463903533
        ],
        "initial_K": [
          0.1354431984409979,
          0.321635377911099,
          0.6119670354433655,
          1.0123940741335333,
          1.4481401090611516,
          1.8212972112998507,
          2.0903474049057325,
          2.26207772543865,
          2.3292033378123533,
          2.268449042398257,
          2.094739678748572,
          1.8623803659518314,
          1.5991601727634568,
          1.2815174975105368,
          0.8902012764770082,
          0.45087206077770015
        ],
        "observed_K": [
          0.2485450651571572,
          0.4779711156934073,
          0.7806563970651014,
          1.0594350039224856,
          1.334532881367801,
          1.6114054004963247,
          1.8136491947449707,
          1.9573431394022538,
          2.031575239497696,
          2.0427536002551645,
          1.9021206491949825,
          1.6792081820170377,
          1.4337339432365181,
          1.1267840761223011,
          0.7617101826232822,
          0.3908326175078028
        ],
        "future_observed_K": [
          0.25900229784786494,
          0.48385154127916485,
          0.783320229864184,
          1.0451545727798779,
          1.2983762503403036,
          1.5373309714844863,
          1.7211385051470085,
          1.8601144704744723,
          1.9244993501457766,
          1.8573930782949997,
          1.7951827911413112,
          1.5796928341308318,
          1.3639507060607268,
          1.0703200409203255,
          0.733453818301677,
          0.40503782095542473
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.239081730328777,
              -0.8260831133739243,
              -0.54730585297592,
              -0.050601396437028136,
              -0.03814968098968366,
              -0.8408831493169004,
              0.5586852241733045,
              8.653108754896417
            ],
            "initial_K": [
              3.0513663973643426,
              0.8003344668381036,
              -2.2633741842597614,
              0.047166836986455074,
              4.275927924032937,
              3.3985947543305457,
              -0.5377404646864421,
              -0.05037035692335534,
              4.343932846885961,
              5.04090693295679,
              0.9009209897572814,
              -0.8995803255908716,
              2.2073202224527346,
              3.8749924128563804,
              0.5862691182645658,
              -2.1148314694997845
            ],
            "metrics": {
              "initial_rmse_K": 2.168524742431311,
              "observation_residual_rms_K": 0.009881056980638356,
              "future_predictive_rmse_K": 0.016146219687223278
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.163990664802375,
              -0.8082811609927675,
              -0.516768413996015,
              -0.040962861953287986,
              -0.015959162243083018,
              -0.06373218181724119,
              0.0034982499196296373,
              0.002821939204679855
            ],
            "initial_K": [
              0.1637446797561456,
              0.3824162352908798,
              0.6774197360444603,
              1.026745989128344,
              1.3851690853751468,
              1.7149202509724968,
              1.9964531445530982,
              2.2118117577723146,
              2.327865247910805,
              2.308271197815925,
              2.145148681056909,
              1.8724989091809685,
              1.542668775667599,
              1.1900195058383412,
              0.8184784626086833,
              0.4201845544569753
            ],
            "metrics": {
              "initial_rmse_K": 0.0599424826241567,
              "observation_residual_rms_K": 0.02129962015420489,
              "future_predictive_rmse_K": 0.021169943859825065
            }
          },
          "learned": {
            "coefficients_K": [
              6.238725377418164,
              -0.8279991000690798,
              -0.5370157078758443,
              -0.03880770299187082,
              -0.004983369021748923,
              -0.00630347088679236,
              0.0005455298064023248,
              -0.0007618431390675178
            ],
            "initial_K": [
              0.18129278207107596,
              0.40022043244873995,
              0.6781398712843597,
              1.0122976810649298,
              1.3779169526412798,
              1.7359585367337755,
              2.0424856634381006,
              2.25788201495783,
              2.354559592170422,
              2.3215582750788655,
              2.165466067226915,
              1.9077765783168352,
              1.578421267093722,
              1.206542512282476,
              0.8129364488734032,
              0.40880526369225856
            ],
            "metrics": {
              "initial_rmse_K": 0.05673202795977366,
              "observation_residual_rms_K": 0.012325823569020677,
              "future_predictive_rmse_K": 0.016341330392954607
            }
          }
        }
      },
      {
        "split": "train",
        "index": 32,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          4.686318542553408,
          -0.23242535164091493,
          -0.2987102702179465,
          0.00815395183714691,
          0.1238987219417818,
          0.1044968565207318,
          0.03230959529686678,
          -0.025456116968505485
        ],
        "initial_K": [
          0.2824696174754937,
          0.5117259819765919,
          0.6847303201675975,
          0.8586530388501246,
          1.0953242104452725,
          1.3821535817560977,
          1.6250551725532938,
          1.7373723484190393,
          1.7191889791606927,
          1.6286839369799082,
          1.4980690740028983,
          1.3155500878568434,
          1.0790270246181077,
          0.8193694344634337,
          0.5595754838305351,
          0.28951767088903047
        ],
        "observed_K": [
          0.2632885359101381,
          0.4471365320900698,
          0.6564810670425246,
          0.8892770326768807,
          1.0917977403430958,
          1.2573021224605971,
          1.4197866816087694,
          1.4670763590001716,
          1.488250114090019,
          1.4401953328571309,
          1.3300142444912897,
          1.214570395503604,
          1.00597016400334,
          0.7554591609813427,
          0.5509767391802798,
          0.27878197559031315
        ],
        "future_observed_K": [
          0.23150205749849032,
          0.4433497682921356,
          0.6545272214788457,
          0.8506830322926445,
          1.0731056689084406,
          1.18468403808369,
          1.3429887785895833,
          1.3809403512291243,
          1.3917444908164505,
          1.359093389510916,
          1.260234202496908,
          1.1249800566970514,
          0.973099851858682,
          0.7314004134752476,
          0.5324019030674475,
          0.2916374813793001
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              4.667996837412377,
              -0.23980201961273623,
              -0.2620892871884309,
              -0.08947555800349771,
              0.14702655197937384,
              0.7026779088848114,
              3.191457119077811,
              -2.8072034875849146
            ],
            "initial_K": [
              0.5466010444060736,
              1.052123641485921,
              0.8178123859359412,
              0.028944735234303853,
              0.3089211514522394,
              2.0498533197808406,
              2.9977965402344253,
              1.6238566482654302,
              0.08080031952763034,
              1.0127121535240176,
              2.96172633512534,
              2.4834144670827314,
              -0.02799627742332844,
              -0.7495876628882251,
              1.1932468484306666,
              2.133390165083059
            ],
            "metrics": {
              "initial_rmse_K": 1.0632482570104347,
              "observation_residual_rms_K": 0.013554693293043764,
              "future_predictive_rmse_K": 0.016091965618915884
            }
          },
          "tikhonov": {
            "coefficients_K": [
              4.611814714538232,
              -0.23463432635652648,
              -0.24746577170566184,
              -0.07243228821267582,
              0.06150564136340796,
              0.05325733579556888,
              0.019983550892787076,
              -0.000915481106445971
            ],
            "initial_K": [
              0.23963616179295705,
              0.4549074290794868,
              0.6562939794684468,
              0.8785440571768994,
              1.1350105560795172,
              1.3903194805674695,
              1.5833020959378519,
              1.6741608093504474,
              1.6661314196626231,
              1.5866769214529706,
              1.4581081875290092,
              1.2888416079931417,
              1.082858126251535,
              0.8461386094435208,
              0.5837806419015603,
              0.29917674961949664
            ],
            "metrics": {
              "initial_rmse_K": 0.03703748087978061,
              "observation_residual_rms_K": 0.02038577526869547,
              "future_predictive_rmse_K": 0.018843925377748125
            }
          },
          "learned": {
            "coefficients_K": [
              4.667730218968888,
              -0.240358207569627,
              -0.25716162785557334,
              -0.06862144376495359,
              0.019205601344522403,
              0.005267449758085576,
              0.0031163075538431805,
              0.0002471538007392785
            ],
            "initial_K": [
              0.21010042319285815,
              0.4287745518230999,
              0.6636619886489934,
              0.9156008875512869,
              1.1713679250313083,
              1.4035523649732953,
              1.5803213556764621,
              1.67831880343788,
              1.6898231559584704,
              1.6215202185351032,
              1.4884614475856581,
              1.3074593015678615,
              1.0919684475466258,
              0.8496532666313885,
              0.5838148047156848,
              0.29797358165533383
            ],
            "metrics": {
              "initial_rmse_K": 0.043552581635038445,
              "observation_residual_rms_K": 0.016095577604168174,
              "future_predictive_rmse_K": 0.016435478223122794
            }
          }
        }
      },
      {
        "split": "train",
        "index": 33,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.231496683913301,
          0.9051197302526449,
          -0.8541240170377448,
          0.21282873221278964,
          -0.07448360488766297,
          0.025905859080025972,
          0.05610292262468423,
          -0.001201629729490051
        ],
        "initial_K": [
          0.40551197398923083,
          0.7842762369302634,
          1.1462085462621419,
          1.5165272644093553,
          1.8826327279073833,
          2.1840404979316816,
          2.3626795026431253,
          2.4074513242095326,
          2.3361902881542016,
          2.148154022101256,
          1.8229861013948017,
          1.3749974937351825,
          0.8882367199877453,
          0.47635803927686216,
          0.20656707400198182,
          0.06776799780194559
        ],
        "observed_K": [
          0.3875454615444212,
          0.7650805198148263,
          1.1245447765841472,
          1.40961295032164,
          1.7140450733339712,
          1.8995790383857896,
          2.0236689360864344,
          2.076491155064591,
          1.977884173204034,
          1.8702376321705014,
          1.6209051271008112,
          1.263713183388297,
          1.0106113382359836,
          0.6811720570057052,
          0.4246404931061594,
          0.16708329479294357
        ],
        "future_observed_K": [
          0.36783374059285995,
          0.7487963886652929,
          1.0402339367587243,
          1.3390779637812351,
          1.6262498658120685,
          1.78162757970074,
          1.896812580303397,
          1.941170538240628,
          1.8624906297756636,
          1.7512706425823577,
          1.5291764146981952,
          1.3131001502585673,
          1.0302373195735253,
          0.7573675093135335,
          0.466727912838697,
          0.2293208739560789
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.217294710630644,
              0.9455741430257651,
              -0.840250529980853,
              0.3936143896205047,
              -0.10853671495068855,
              0.06893989933766112,
              0.02471810655442695,
              13.757663058672959
            ],
            "initial_K": [
              5.146567988044829,
              1.7199068807574318,
              -3.3284888554592595,
              -0.16094864552581267,
              6.085375897515084,
              4.617084678813466,
              -1.4507965955382165,
              -0.7952604926014826,
              5.5163172944166465,
              5.933778012142484,
              -0.6262282240571839,
              -2.8127778535944232,
              2.598314278939667,
              4.961469069245275,
              -0.7578660295307632,
              -4.709417860073275
            ],
            "metrics": {
              "initial_rmse_K": 3.440067843140041,
              "observation_residual_rms_K": 0.017731883947366276,
              "future_predictive_rmse_K": 0.0195184267008321
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.142465864865818,
              0.9251971790199915,
              -0.7933679703524398,
              0.3186388724453036,
              -0.04540418158929554,
              0.005225090076569356,
              0.00015477429959844042,
              0.004486629008109552
            ],
            "initial_K": [
              0.4229040070109248,
              0.826865454365292,
              1.201967808070634,
              1.5441556535184957,
              1.846376992611821,
              2.0961007538245693,
              2.2766865117329784,
              2.3643495035594158,
              2.326875737783954,
              2.1371263662067292,
              1.7969402167582333,
              1.350655004727843,
              0.8765776492960936,
              0.4630103148659913,
              0.1782063200941138,
              0.04009845519198468
            ],
            "metrics": {
              "initial_rmse_K": 0.041572626457001445,
              "observation_residual_rms_K": 0.026310070646790286,
              "future_predictive_rmse_K": 0.027254871948246825
            }
          },
          "learned": {
            "coefficients_K": [
              6.216939602112751,
              0.9477672728065216,
              -0.8244525993961441,
              0.3018744817591876,
              -0.014177798843296159,
              0.000516790767856821,
              2.4136066786483835e-05,
              -0.0012112619299880858
            ],
            "initial_K": [
              0.42602013110660664,
              0.8346689727047261,
              1.2132156443840931,
              1.5561691900767065,
              1.8620486390503816,
              2.123762151623643,
              2.319564677589525,
              2.4136293771828354,
              2.3682232637582388,
              2.161656041793594,
              1.8044091258451243,
              1.3467036270947872,
              0.870768885731801,
              0.4652228015835221,
              0.1903259718372905,
              0.05215248196214023
            ],
            "metrics": {
              "initial_rmse_K": 0.03378839064732612,
              "observation_residual_rms_K": 0.01955504207730413,
              "future_predictive_rmse_K": 0.019552000714910773
            }
          }
        }
      },
      {
        "split": "train",
        "index": 34,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.637051868681029,
          0.1322591934251235,
          -0.4880317870560029,
          0.07324075094357102,
          0.04176662534155273,
          -0.06454271205846379,
          0.0672311552941281,
          0.03293059694093649
        ],
        "initial_K": [
          0.3885362006235893,
          0.7384221217642539,
          1.075237581039718,
          1.438894012182841,
          1.8016145723033368,
          2.09188748858163,
          2.283657789276496,
          2.402201119763979,
          2.4422066681858277,
          2.3429849851589286,
          2.071910996585088,
          1.6907480069445116,
          1.3048947015756212,
          0.9675178410324916,
          0.6584519566534353,
          0.3390531235472958
        ],
        "observed_K": [
          0.37580511887989276,
          0.6683515584099596,
          1.0156904878377395,
          1.3427741579535795,
          1.6089090561139976,
          1.8665366314872314,
          2.056653925951618,
          2.130699877358508,
          2.0815237856571778,
          2.016555417817262,
          1.8341601183823135,
          1.605200713713869,
          1.3091271766523986,
          0.9850166297545565,
          0.6550364543936084,
          0.33655808372677837
        ],
        "future_observed_K": [
          0.3260753870926099,
          0.6904358746958899,
          0.9786423453475299,
          1.3103444485323088,
          1.571625674000486,
          1.7496844318928813,
          1.9349914798663426,
          2.0077186055323346,
          2.013255355319262,
          1.9100491601514522,
          1.7845467632073262,
          1.5108240949696292,
          1.240310600189759,
          0.9363877261703034,
          0.6641336214304056,
          0.3058884190771183
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.601763385287584,
              0.07312648169156066,
              -0.538934816363303,
              -0.02727328252390673,
              -0.025985043284050505,
              0.9913978964764919,
              1.969429550514246,
              -8.526029465286308
            ],
            "initial_K": [
              -1.6433968308778721,
              0.7411421692121446,
              3.3149449451949917,
              1.5305996773011454,
              -0.9446160787380695,
              1.3519459863958334,
              5.238762464637492,
              4.042634975704198,
              -0.2716807397873158,
              -0.14903525781658944,
              4.127241438996179,
              4.691099483368584,
              0.02538523228314682,
              -2.215596638303401,
              1.2579656063477522,
              3.5661494793091295
            ],
            "metrics": {
              "initial_rmse_K": 2.208098631782945,
              "observation_residual_rms_K": 0.011881494070028665,
              "future_predictive_rmse_K": 0.02097156167211446
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.5223072299779625,
              0.07155061829016772,
              -0.5088644471550191,
              -0.022078278184083786,
              -0.010870327376416038,
              0.07513998947748964,
              0.012331732554762446,
              -0.002780496292125369
            ],
            "initial_K": [
              0.34616694946575777,
              0.679930203318674,
              1.0118148943244012,
              1.3646390520731115,
              1.7360842419746232,
              2.0770708335207257,
              2.316283206606231,
              2.410208098455768,
              2.367297573961987,
              2.224038542061504,
              2.005717795918883,
              1.7173350196183375,
              1.3674369586045525,
              0.9876006273824858,
              0.6211601524224418,
              0.2943970489727249
            ],
            "metrics": {
              "initial_rmse_K": 0.057523209958831735,
              "observation_residual_rms_K": 0.023405176662506594,
              "future_predictive_rmse_K": 0.030473781196329083
            }
          },
          "learned": {
            "coefficients_K": [
              6.601386317363295,
              0.07329608855522396,
              -0.528802058912041,
              -0.020916684564591337,
              -0.0033943418757697965,
              0.007431767163777025,
              0.0019230551926710346,
              0.0007506547341081728
            ],
            "initial_K": [
              0.32706504133226266,
              0.6666834635404004,
              1.0265722055292497,
              1.4018699947760462,
              1.7691459186933371,
              2.0896680745706093,
              2.3220275799934402,
              2.4358626384003994,
              2.4191033114215843,
              2.278048279920662,
              2.033629486590399,
              1.7162046605223764,
              1.359529904324887,
              0.9944453682692732,
              0.6429340592058437,
              0.313491806656979
            ],
            "metrics": {
              "initial_rmse_K": 0.04168112001704069,
              "observation_residual_rms_K": 0.0149095210723787,
              "future_predictive_rmse_K": 0.02085915419025378
            }
          }
        }
      },
      {
        "split": "train",
        "index": 35,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.67902519007656,
          -1.8882098328600534,
          -0.2679789176216225,
          -0.14242842867391986,
          -0.017445360597385107,
          0.016465334247782234,
          0.007282742224101914,
          -0.007799547528435854
        ],
        "initial_K": [
          0.042685263062799295,
          0.13599047917869556,
          0.3128604933655381,
          0.5815180255453464,
          0.9242537932406141,
          1.2978703499929523,
          1.6458016493166305,
          1.9240550101823992,
          2.117220150833965,
          2.2247111866792957,
          2.2363041789072846,
          2.131071654536691,
          1.8981781602600867,
          1.5472662599366624,
          1.09788703452465,
          0.5716421848163293
        ],
        "observed_K": [
          0.15351632011971572,
          0.29624721206984156,
          0.5402225670996376,
          0.6813806659447496,
          0.9846777259321593,
          1.2374896166489107,
          1.4885731162524984,
          1.740589195211135,
          1.8693251232542998,
          1.936077045837215,
          1.9231990472454363,
          1.8111704161156263,
          1.6216626981408364,
          1.2968170337149287,
          0.9519956616822316,
          0.47766141835379394
        ],
        "future_observed_K": [
          0.15501390777072346,
          0.30870830150556794,
          0.5197523125197785,
          0.7578046005026609,
          0.961074354279015,
          1.208878309238559,
          1.4491547222065093,
          1.6113581733156552,
          1.758242330792635,
          1.7970020136875386,
          1.7719348665185113,
          1.6632818906818942,
          1.4745547796332068,
          1.2126802945047823,
          0.8348143092622202,
          0.3921179198082594
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.691679215213835,
              -1.9209770952824023,
              -0.19456869029506854,
              -0.17662717094620348,
              0.4165016690470986,
              0.30760334972140135,
              -0.7653941672431592,
              -6.239368144837421
            ],
            "initial_K": [
              -2.130256274706469,
              -0.16856970292824036,
              2.590577841014718,
              1.4261494657398357,
              -1.245333949149531,
              -0.15385600497228014,
              3.374331828668044,
              3.743597792321455,
              0.9473518365821247,
              0.3338262319869776,
              2.9582075315876097,
              3.9319662953782846,
              1.417354159592842,
              -0.21110715375885825,
              1.4579473871223336,
              2.5004297040431815
            ],
            "metrics": {
              "initial_rmse_K": 1.5754035314656387,
              "observation_residual_rms_K": 0.01729847534806992,
              "future_predictive_rmse_K": 0.02057056808130241
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.623176465069165,
              -1.8795803614406454,
              -0.18371254930008615,
              -0.14298329552373237,
              0.17423521084317808,
              0.023313860704620454,
              -0.0047925736500466325,
              -0.0020347736379002787
            ],
            "initial_K": [
              0.10787621249171964,
              0.22004172355531176,
              0.358260732909499,
              0.5607134192558173,
              0.8563160993088069,
              1.2314294258772436,
              1.6209792647950998,
              1.9398566726958,
              2.131987550809522,
              2.194909546046887,
              2.1609941111260116,
              2.056864837930387,
              1.8774962521462302,
              1.5923379960370125,
              1.1738533870030885,
              0.6268078448013678
            ],
            "metrics": {
              "initial_rmse_K": 0.05434960109279333,
              "observation_residual_rms_K": 0.025171562507536615,
              "future_predictive_rmse_K": 0.01829557117908143
            }
          },
          "learned": {
            "coefficients_K": [
              5.691354127878505,
              -1.9254325386835236,
              -0.1909105162701033,
              -0.13546058553749332,
              0.05440626136814373,
              0.0023058718220525676,
              -0.000747371352975153,
              0.0005493308760936425
            ],
            "initial_K": [
              0.06989798299868383,
              0.17386419397324016,
              0.34078297745563446,
              0.5863167310886852,
              0.9044290045074195,
              1.2647186675897604,
              1.6196122153449406,
              1.9194045703268887,
              2.127960219668112,
              2.230485107728376,
              2.228620777533846,
              2.1266522901546936,
              1.9202506225767322,
              1.597955738194899,
              1.154902768172269,
              0.6078510030697784
            ],
            "metrics": {
              "initial_rmse_K": 0.028529539856671834,
              "observation_residual_rms_K": 0.01945255674683736,
              "future_predictive_rmse_K": 0.020494495520622682
            }
          }
        }
      },
      {
        "split": "train",
        "index": 36,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.077052119412995,
          1.6626027137497503,
          -0.7529511596486475,
          -0.10928685366586206,
          0.03781877394135748,
          0.11637528212600587,
          -0.015348629532256583,
          -0.016862847298180897
        ],
        "initial_K": [
          0.463064798229815,
          0.9091495820958837,
          1.3271733063239166,
          1.7206912055144348,
          2.092381082429327,
          2.4018753641524135,
          2.5574355753519034,
          2.4829716758569607,
          2.196496645465346,
          1.8011866263302119,
          1.396850463878017,
          1.0200556405823449,
          0.6714026522384001,
          0.369577793507988,
          0.1538434091653632,
          0.04161781969537265
        ],
        "observed_K": [
          0.42557576194654023,
          0.8494247973246639,
          1.2172251062351438,
          1.5569582831923159,
          1.832505855818208,
          2.0131056851182576,
          2.1101293244670374,
          2.0380443976680938,
          1.9249936043656768,
          1.6801863843289486,
          1.4346403152298453,
          1.0725003395134465,
          0.8021471601817395,
          0.571197472680703,
          0.3139245174340258,
          0.0938747231510925
        ],
        "future_observed_K": [
          0.4413736129167379,
          0.8000250723608823,
          1.1370220273608076,
          1.514306613573787,
          1.7144453434567486,
          1.8709208703533486,
          1.9365791987394763,
          1.8868684297291687,
          1.7647987433744206,
          1.5842523525740193,
          1.37491868236434,
          1.1275532962036834,
          0.8622257269905946,
          0.5762668333490821,
          0.36664438980277314,
          0.17969673875199652
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.073426440189825,
              1.65445182815064,
              -0.8097307454306408,
              0.04781237473904015,
              -0.13628960431994794,
              0.7681958655731627,
              -1.3443694169459919,
              19.0352983338289
            ],
            "initial_K": [
              6.708865572443279,
              2.0248128427741348,
              -4.69329931404431,
              -0.42476577700290097,
              7.728126095886883,
              5.457520823865647,
              -2.6482867691202907,
              -1.4939910855980783,
              6.829083340005317,
              6.679466635852338,
              -2.481211464456575,
              -4.680341439704089,
              3.6630975751952564,
              6.92101981980528,
              -1.5924118744975095,
              -7.197354979929582
            ],
            "metrics": {
              "initial_rmse_K": 4.777776086978272,
              "observation_residual_rms_K": 0.01719191430147915,
              "future_predictive_rmse_K": 0.022568427232796704
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.00032913476856,
              1.6187986690618836,
              -0.764551065560071,
              0.038705092033013505,
              -0.057014052305596315,
              0.0582230701325552,
              -0.008417871103970711,
              0.006207763725448742
            ],
            "initial_K": [
              0.45125805720824436,
              0.8920063681339897,
              1.3191187811360838,
              1.7254755053430801,
              2.0821167066506936,
              2.339477597337557,
              2.450162236065421,
              2.392651625472982,
              2.1800345832498027,
              1.8529622446236322,
              1.4621578980607335,
              1.0510954762725175,
              0.6548014303849404,
              0.31529830458062647,
              0.08478222907415905,
              -0.007777400454877237
            ],
            "metrics": {
              "initial_rmse_K": 0.05171835851016226,
              "observation_residual_rms_K": 0.02714944173744323,
              "future_predictive_rmse_K": 0.025825381370919397
            }
          },
          "learned": {
            "coefficients_K": [
              6.0730795488870815,
              1.6582891026805182,
              -0.7945066311311718,
              0.03666872001285172,
              -0.017803068716042716,
              0.005758588786002406,
              -0.0013127134136131262,
              -0.0016759192385655509
            ],
            "initial_K": [
              0.4491323694009575,
              0.8996142292799112,
              1.3427158486874688,
              1.7564693370094089,
              2.1084724619234625,
              2.3606256025830756,
              2.476431834976364,
              2.4325649997632937,
              2.2297685269576606,
              1.8952411969689424,
              1.4761920732325198,
              1.0312544296541732,
              0.6225072144307557,
              0.3039450730467085,
              0.10524516797589789,
              0.018854230295581087
            ],
            "metrics": {
              "initial_rmse_K": 0.049258100353086434,
              "observation_residual_rms_K": 0.020392826325812803,
              "future_predictive_rmse_K": 0.022381715137748778
            }
          }
        }
      },
      {
        "split": "train",
        "index": 37,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          7.3866051830332555,
          1.7062311719307266,
          -0.4371005708088875,
          0.06765382617616834,
          -0.0041516446366505234,
          -0.08875026803904028,
          -0.05856934215862787,
          0.02125780220038267
        ],
        "initial_K": [
          0.5732154236013277,
          1.1635063701931228,
          1.7384724728233727,
          2.219600462118125,
          2.543122579609081,
          2.7140246048250765,
          2.7815343378935427,
          2.7599508088554363,
          2.603518381319882,
          2.2791683501163607,
          1.8389282547657464,
          1.3877012022336774,
          0.9923105372444078,
          0.656518117112191,
          0.3746625427801375,
          0.1591073819482037
        ],
        "observed_K": [
          0.5217504577434176,
          1.017177688831681,
          1.518596682324959,
          1.874911060005344,
          2.1963161408684297,
          2.366244624745016,
          2.4430162946382703,
          2.3897635136991324,
          2.306451486106918,
          2.0261023408311947,
          1.721704641949682,
          1.4463366517866867,
          1.0808868630895663,
          0.8162279504497577,
          0.49900291209395214,
          0.26734298769955783
        ],
        "future_observed_K": [
          0.5264970388258534,
          1.002361183725819,
          1.402197583331034,
          1.7857308179015114,
          2.076421522645037,
          2.1965195889178872,
          2.313391629568863,
          2.2911912531314504,
          2.176745956445555,
          1.9668766428135644,
          1.7216529995401444,
          1.4076881464074296,
          1.0925564366690934,
          0.8339032475593253,
          0.5672834156168921,
          0.27510645893864266
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              7.364871167616819,
              1.6955043282309532,
              -0.42254252956091276,
              -0.040411685718261064,
              0.07826417770884955,
              -0.7779791931904708,
              -2.382107671227237,
              1.5144606618329546
            ],
            "initial_K": [
              0.10254892476557093,
              0.6389925364799186,
              1.804598347979477,
              2.948986767428383,
              2.9980960715410276,
              2.1107582832713083,
              1.8754290782763567,
              2.9522438760029557,
              3.7093705696536663,
              2.5987985177972037,
              0.8017898714788249,
              0.5752571253183998,
              1.657917962978353,
              1.6867375127879491,
              0.1180105667775308,
              -0.8556777809845131
            ],
            "metrics": {
              "initial_rmse_K": 0.7125127871542019,
              "observation_residual_rms_K": 0.01778363035427329,
              "future_predictive_rmse_K": 0.024237239377078956
            }
          },
          "tikhonov": {
            "coefficients_K": [
              7.2762305555292,
              1.658966494658812,
              -0.3989663762222991,
              -0.03271408340354509,
              0.03274026616932317,
              -0.05896456770566086,
              -0.014915747918249683,
              0.0004938937018621782
            ],
            "initial_K": [
              0.570648997587311,
              1.1432355933015024,
              1.6890389154905896,
              2.154746963287574,
              2.497059612778737,
              2.7042321901810524,
              2.7821822590544825,
              2.7286854655509503,
              2.5329860945646874,
              2.2035387642894864,
              1.788904021856335,
              1.3630941271255939,
              0.9869008290822562,
              0.6811079956478376,
              0.43110488110324896,
              0.21053122264487026
            ],
            "metrics": {
              "initial_rmse_K": 0.04368167478899965,
              "observation_residual_rms_K": 0.028517511354950256,
              "future_predictive_rmse_K": 0.039928085021780683
            }
          },
          "learned": {
            "coefficients_K": [
              7.364450513842705,
              1.6994368184149025,
              -0.4145981161831042,
              -0.030992913381487106,
              0.010223395545886778,
              -0.0058319270623868845,
              -0.002326015939721682,
              -0.00013333721986935786
            ],
            "initial_K": [
              0.5928884356179487,
              1.1686551544133061,
              1.703685699858124,
              2.167533533237865,
              2.5283241474441294,
              2.7587869932514675,
              2.8401365715014077,
              2.7656891920812354,
              2.545837375005762,
              2.2112984049838578,
              1.8094993067661527,
              1.393218118486526,
              1.0067283116318864,
              0.6762442357725222,
              0.40763772931082487,
              0.18974719056423214
            ],
            "metrics": {
              "initial_rmse_K": 0.03663802493364564,
              "observation_residual_rms_K": 0.0193137001252636,
              "future_predictive_rmse_K": 0.02441064663496109
            }
          }
        }
      },
      {
        "split": "train",
        "index": 38,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.534548641452784,
          -0.8343694506108263,
          -0.22650011804348594,
          0.09960961426254948,
          -0.012581107975428817,
          -0.006799642247134575,
          -0.01918689639000181,
          -0.020983040632652515
        ],
        "initial_K": [
          0.20852737257697218,
          0.44663216277837636,
          0.7032939357373617,
          0.9512209766550559,
          1.1918080627118037,
          1.4440743783330432,
          1.6972146458738775,
          1.9050408193404489,
          2.027656473037311,
          2.052855784606303,
          1.9758233979414097,
          1.788045529380388,
          1.498909899218358,
          1.1464293068010458,
          0.770564330716908,
          0.3877658728333728
        ],
        "observed_K": [
          0.20487627425361604,
          0.46977541812953216,
          0.6872603283615629,
          0.9231709542663624,
          1.1643985472749505,
          1.3769771207956865,
          1.5716435058208815,
          1.7040334779159012,
          1.8193232782121973,
          1.8210168385694643,
          1.7239553007258246,
          1.5237081363059826,
          1.300109149303876,
          1.057500597276652,
          0.731660452769163,
          0.36371515028594137
        ],
        "future_observed_K": [
          0.2300467985354095,
          0.46428614940999247,
          0.7246237306102968,
          0.9225555176035186,
          1.1508440945314264,
          1.3284679432883497,
          1.4727043576903176,
          1.6344552213644727,
          1.6825467046238838,
          1.6800202578762051,
          1.5961783592612693,
          1.444534148062619,
          1.2319835921130553,
          0.9744966467520325,
          0.6662405102097207,
          0.3782235069551336
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.545112724301499,
              -0.8732486522515424,
              -0.3225733452443464,
              0.09194936925604616,
              0.32698796363451627,
              -1.351949286451867,
              0.39914463872908956,
              11.083320663538382
            ],
            "initial_K": [
              3.7956980170362864,
              0.9260674065670222,
              -2.9748065346735357,
              -0.2082620565829758,
              4.8020235605955985,
              3.3480416741054624,
              -1.70739168344376,
              -0.88022283613969,
              4.863037988681951,
              5.655302438835923,
              0.21926996837875024,
              -2.0194123053984905,
              2.231165104347114,
              4.653536249665232,
              0.6098724993470386,
              -2.7708578815625104
            ],
            "metrics": {
              "initial_rmse_K": 2.799734459327625,
              "observation_residual_rms_K": 0.010291355219983473,
              "future_predictive_rmse_K": 0.016634368637037128
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.478373989191218,
              -0.8544302904273917,
              -0.3045750655011615,
              0.07443488885162737,
              0.13678892792287664,
              -0.10246688591849529,
              0.00249927443923504,
              0.003614476367326289
            ],
            "initial_K": [
              0.20965336984034066,
              0.43102415036887276,
              0.6648465116954014,
              0.903315531176972,
              1.1446963257316989,
              1.400040126039833,
              1.6735257465735647,
              1.9304358278742975,
              2.095257670234298,
              2.0997650102651537,
              1.9409850848201777,
              1.6857612195393805,
              1.4108542664369468,
              1.1382529640348713,
              0.8306945946655703,
              0.44744294852774974
            ],
            "metrics": {
              "initial_rmse_K": 0.05173638109120095,
              "observation_residual_rms_K": 0.021694322222141817,
              "future_predictive_rmse_K": 0.018490551360820902
            }
          },
          "learned": {
            "coefficients_K": [
              5.544796008293537,
              -0.875274032957417,
              -0.3165084977556294,
              0.07051868255887346,
              0.042713376526049,
              -0.010134550769024158,
              0.0003897459393428694,
              -0.0009758055797951246
            ],
            "initial_K": [
              0.20853307905477925,
              0.4230030661820285,
              0.6498186420946159,
              0.8957744209456544,
              1.1644811936121364,
              1.44840270363782,
              1.722235436428776,
              1.945654903382482,
              2.0766683151583454,
              2.08801499131203,
              1.976951157092129,
              1.7633749801908731,
              1.477828491826883,
              1.1467785210787798,
              0.7850141409671988,
              0.3997341361821419
            ],
            "metrics": {
              "initial_rmse_K": 0.030184971550835906,
              "observation_residual_rms_K": 0.01618412065244371,
              "future_predictive_rmse_K": 0.017486825664222494
            }
          }
        }
      },
      {
        "split": "train",
        "index": 39,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.734236038637679,
          0.42438019349595785,
          -0.6386746479654994,
          -0.010148625004670148,
          0.018610472092837005,
          0.04636347422252944,
          -0.037330963834364024,
          -0.020390608435317075
        ],
        "initial_K": [
          0.2963686971501236,
          0.6198043010133767,
          0.9595319869247074,
          1.2898593947513022,
          1.6065806150728101,
          1.9054049540168552,
          2.137034118749028,
          2.2261575069182418,
          2.1439822104109747,
          1.9347139366269452,
          1.662262450996416,
          1.356854994304386,
          1.0267960573593742,
          0.6968759100755215,
          0.40779785877197894,
          0.18135078497830265
        ],
        "observed_K": [
          0.3127165708450287,
          0.6611065098652582,
          0.9598779587416727,
          1.2076536996322782,
          1.4867959642948612,
          1.6845921186361887,
          1.7855765914834443,
          1.8951477868566897,
          1.8434974628476555,
          1.7112797079001965,
          1.5337784337955407,
          1.297624183559519,
          1.0173535525744093,
          0.757227295541016,
          0.4891431383586992,
          0.23842421436734496
        ],
        "future_observed_K": [
          0.2982949879065259,
          0.5907101094549744,
          0.9259389304531536,
          1.152579023416541,
          1.3490734216818077,
          1.5642698121804242,
          1.7159803258398445,
          1.7442217726454754,
          1.726687364981515,
          1.6176277890259456,
          1.4795092309878375,
          1.270941692258662,
          1.0524684751840734,
          0.7630580969356722,
          0.5133164661224732,
          0.25649028643755
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.719819036279788,
              0.4400497877430793,
              -0.610415046065358,
              0.1466769587401041,
              0.17647607301694665,
              0.13974457790395095,
              -0.7318530710830705,
              -0.6531345130689487
            ],
            "initial_K": [
              -0.034603756851050965,
              0.5962321008004029,
              1.3972240121072723,
              1.5418321959709602,
              1.2694442649864728,
              1.475386354414083,
              2.2094065755138397,
              2.5951136494408664,
              2.2236799393522486,
              1.6875586224293633,
              1.532502105257124,
              1.497723735154944,
              1.1531108174980083,
              0.6333757069522976,
              0.29849936539100863,
              0.14888202608284673
            ],
            "metrics": {
              "initial_rmse_K": 0.2426692244271755,
              "observation_residual_rms_K": 0.013051211508876101,
              "future_predictive_rmse_K": 0.0235647283674886
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.650977606624432,
              0.43056678870833864,
              -0.5763563709748564,
              0.11873798819121832,
              0.07382526428100993,
              0.010591515425399222,
              -0.004582553531616003,
              -0.00021299927466135454
            ],
            "initial_K": [
              0.35474793412689765,
              0.6896800663557306,
              0.9978322284118432,
              1.2871904136796422,
              1.567949042494734,
              1.8327239501429848,
              2.046507887873105,
              2.158450677860938,
              2.1296783312990395,
              1.9565804586181663,
              1.6728128795406974,
              1.3317635538715535,
              0.9850525289633134,
              0.6696242549778925,
              0.40381558076801594,
              0.18681585092423975
            ],
            "metrics": {
              "initial_rmse_K": 0.04560254089081782,
              "observation_residual_rms_K": 0.020931500871089418,
              "future_predictive_rmse_K": 0.025928305909538086
            }
          },
          "learned": {
            "coefficients_K": [
              5.71949234170359,
              0.4410704229853108,
              -0.598938356457293,
              0.1124908846660114,
              0.023052496706076526,
              0.001047560388289657,
              -0.0007146200524162196,
              5.750373209954404e-05
            ],
            "initial_K": [
              0.3393871678142108,
              0.6728823732576925,
              0.9973336300186414,
              1.3111302716140552,
              1.6083707451939804,
              1.8720395080107501,
              2.072089619053549,
              2.172302985917463,
              2.144230168206582,
              1.9812000687439675,
              1.7045238932919065,
              1.3584220105897493,
              0.9963750102284061,
              0.6650709553207376,
              0.39162141566198383,
              0.17741524024633287
            ],
            "metrics": {
              "initial_rmse_K": 0.036183134976159576,
              "observation_residual_rms_K": 0.01373408798072553,
              "future_predictive_rmse_K": 0.023778090082853736
            }
          }
        }
      },
      {
        "split": "train",
        "index": 40,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.402337487043905,
          1.3678937290634257,
          -0.37030411595807133,
          -0.039154870354926395,
          -0.008193275498619215,
          -0.009840264385605868,
          -0.031432436062948065,
          0.06747639643596279
        ],
        "initial_K": [
          0.5044998527826412,
          0.9754781627592591,
          1.423451172837239,
          1.8487963728537955,
          2.1887021067647114,
          2.3785591784388034,
          2.4304958077087333,
          2.388563331639642,
          2.2411737447392035,
          1.9561254783874977,
          1.581962003911037,
          1.2260329504998502,
          0.9295960749061354,
          0.6481749383745075,
          0.36693103394257776,
          0.14356965522598536
        ],
        "observed_K": [
          0.4369060182471307,
          0.8626657380228119,
          1.2463619167927893,
          1.6023846315319183,
          1.8777477619408882,
          2.0427763472788705,
          2.15294317945672,
          2.0971443167157906,
          1.9566188220571439,
          1.7860658271181524,
          1.5219782313250365,
          1.2862273999198963,
          0.9835025735476561,
          0.6955345231172331,
          0.46260302054938807,
          0.2607432589974257
        ],
        "future_observed_K": [
          0.41203819192272456,
          0.8351309085407753,
          1.2415624772765819,
          1.4869482414929824,
          1.7359091087416443,
          1.8936978073655975,
          1.967358232501683,
          1.9602445937124722,
          1.8899634086356316,
          1.68150323090213,
          1.4950638498535491,
          1.242159466303149,
          0.9929445221039267,
          0.735068240483745,
          0.48274320034851725,
          0.23311654194531817
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.402625262343646,
              1.346884030290309,
              -0.42855076006234055,
              -0.2015957118486233,
              -0.11265479263315782,
              0.11257856210234968,
              2.788379921148649,
              -16.752669729747343
            ],
            "initial_K": [
              -4.351530282286286,
              0.34540141714924744,
              6.229471933743561,
              3.0122890734078105,
              -2.7753588710748893,
              0.39540090145089035,
              7.478717918575725,
              5.5316058849529455,
              -2.4710529362246945,
              -2.379378517400081,
              5.547039703039284,
              6.602612233696539,
              -1.9595075420864427,
              -5.52659512415842,
              1.9107041193696872,
              6.781947346873997
            ],
            "metrics": {
              "initial_rmse_K": 4.264129286871434,
              "observation_residual_rms_K": 0.011307762023817763,
              "future_predictive_rmse_K": 0.019898929613737477
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.3255658529792,
              1.3178589056000825,
              -0.4046393719161382,
              -0.16319583838178708,
              -0.047126897694888106,
              0.008532549848881037,
              0.01745965243575033,
              -0.005463356214802758
            ],
            "initial_K": [
              0.44480173413725627,
              0.897913243013736,
              1.3553307286214313,
              1.7917464249264694,
              2.159062599389272,
              2.3991785220230146,
              2.4719974398688547,
              2.3807216743461925,
              2.168556299939346,
              1.8870457838684052,
              1.5699168166246944,
              1.2378935592156806,
              0.9164061478014374,
              0.6328738891848649,
              0.39635440608628447,
              0.1921368498934885
            ],
            "metrics": {
              "initial_rmse_K": 0.04645324933565991,
              "observation_residual_rms_K": 0.023585926821120203,
              "future_predictive_rmse_K": 0.023579701225050233
            }
          },
          "learned": {
            "coefficients_K": [
              6.402259568440854,
              1.3500079434174201,
              -0.4204933832230265,
              -0.1546096957935184,
              -0.014715729966691987,
              0.0008439171236402899,
              0.002722721655671517,
              0.0014749504318260335
            ],
            "initial_K": [
              0.45675890024028243,
              0.9192738603248594,
              1.3816022530011525,
              1.816999399545609,
              2.1790550224369145,
              2.4174703706604395,
              2.4998228345131626,
              2.424101489491426,
              2.2159945624059985,
              1.9175838983730247,
              1.575674034547116,
              1.2319605664266655,
              0.9152632168417519,
              0.6383118549563287,
              0.40032682885794213,
              0.1921411503674131
            ],
            "metrics": {
              "initial_rmse_K": 0.03695279631279938,
              "observation_residual_rms_K": 0.01508122411850003,
              "future_predictive_rmse_K": 0.018927903634438838
            }
          }
        }
      },
      {
        "split": "train",
        "index": 41,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.557973799045162,
          -2.105364403632521,
          -0.17808059893875397,
          -0.1173007171843814,
          0.088403773607182,
          -0.06190088141161166,
          0.012190643088919878,
          -0.0007513931851863706
        ],
        "initial_K": [
          0.039125943190137125,
          0.12179687715959242,
          0.2765042935773756,
          0.5099312153908238,
          0.8105123314373001,
          1.156088009592087,
          1.5167528072378884,
          1.8516318859545395,
          2.10995416254743,
          2.246901474713739,
          2.2468539701452612,
          2.129139479456627,
          1.9217953418574822,
          1.6252761519325416,
          1.2088997903610257,
          0.6535915934188332
        ],
        "observed_K": [
          0.11596064891585103,
          0.2781126711873037,
          0.48098808076512156,
          0.6577994398371351,
          0.8930157987735603,
          1.1694856240859557,
          1.3981789304068186,
          1.6341589236617373,
          1.8006868832288099,
          1.9312843348882218,
          1.9443759051882659,
          1.8082378327699535,
          1.6331889073858996,
          1.2953399221998785,
          0.9665606519247056,
          0.47480085206523964
        ],
        "future_observed_K": [
          0.17183657403284822,
          0.3260663311756022,
          0.5061724633490162,
          0.6918672600976085,
          0.9328371356798036,
          1.1153103187250963,
          1.406418223947573,
          1.587754869289642,
          1.735846336001019,
          1.8014323666445693,
          1.7643471718901584,
          1.6822137443896692,
          1.4566808978723254,
          1.1741428797210558,
          0.8327390986328066,
          0.4146047565459763
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.528104336707504,
              -2.088824781386838,
              -0.10084946976134375,
              0.013527479674815945,
              0.013104116762180448,
              -0.7744737889284751,
              1.4924600124254233,
              -7.174445684630595
            ],
            "initial_K": [
              -2.11764349891266,
              -0.21441406060261947,
              2.398528969208831,
              1.2210957393427393,
              -1.1251903079360952,
              0.2427706431687655,
              3.3507353626001337,
              2.9014889356110363,
              0.13214511069926527,
              0.714851924857592,
              4.178018610735478,
              4.30565355904713,
              0.35729927475273293,
              -1.1575497014727198,
              2.070020318262886,
              3.7699567181198357
            ],
            "metrics": {
              "initial_rmse_K": 1.8403594042342,
              "observation_residual_rms_K": 0.015093791293498327,
              "future_predictive_rmse_K": 0.022291361536801058
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.461570307674578,
              -2.0438109580937365,
              -0.09522247982098896,
              0.01095077056193469,
              0.005481847292943134,
              -0.058698886246887495,
              0.009345151603469161,
              -0.0023397197611608705
            ],
            "initial_K": [
              0.062078623267826316,
              0.16622470590717037,
              0.3321053397000092,
              0.5544270617961247,
              0.8184542555921828,
              1.1141032589877071,
              1.4334882751825953,
              1.7556239214425802,
              2.036078902152115,
              2.2171077747574204,
              2.255574019175895,
              2.1452385675155012,
              1.909798849729081,
              1.5722248801709706,
              1.1357234448516995,
              0.6011377894301455
            ],
            "metrics": {
              "initial_rmse_K": 0.052017599220610077,
              "observation_residual_rms_K": 0.023626755722807726,
              "future_predictive_rmse_K": 0.02601412142245929
            }
          },
          "learned": {
            "coefficients_K": [
              5.527788592154747,
              -2.093669524518437,
              -0.09895335322711114,
              0.010374623042313383,
              0.0017117482462747152,
              -0.005805649673275355,
              0.0014573169047855342,
              0.0006316576361478783
            ],
            "initial_K": [
              0.07288846943679528,
              0.17356312661312656,
              0.3243632665042191,
              0.5369273694889843,
              0.8092530804810413,
              1.1264803339850031,
              1.4634067984395251,
              1.7862650832475024,
              2.0551339365611603,
              2.2301748565403314,
              2.2806847762687825,
              2.191346385978924,
              1.9620642344398171,
              1.604042994609386,
              1.1371674493205424,
              0.5900591709647165
            ],
            "metrics": {
              "initial_rmse_K": 0.046360900709761926,
              "observation_residual_rms_K": 0.01667788426226751,
              "future_predictive_rmse_K": 0.022516183814046253
            }
          }
        }
      },
      {
        "split": "train",
        "index": 42,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.916228712449492,
          -0.19745069780927021,
          -0.5123069714916797,
          0.2965874811767775,
          -0.07867275538195224,
          0.07581549454479707,
          0.021295383760314507,
          -0.012164544020435417
        ],
        "initial_K": [
          0.3290531034693983,
          0.6292963877190743,
          0.8984143557645503,
          1.162288167564234,
          1.4441634565046468,
          1.7295571823165998,
          1.9703531207325355,
          2.126928110847051,
          2.1923131889736336,
          2.165339486018302,
          2.0189443029683876,
          1.724057485905342,
          1.3067843333612488,
          0.8588321992352485,
          0.4779883598423972,
          0.20266765306801687
        ],
        "observed_K": [
          0.3081665532104365,
          0.6069903630792106,
          0.8665008362561456,
          1.1475388411786969,
          1.4051802872065409,
          1.6111364222841837,
          1.802263483660462,
          1.8462014618579021,
          1.8720214077663182,
          1.839770945270369,
          1.709603913048343,
          1.504698528042983,
          1.273919041007911,
          0.8781843293886058,
          0.5835671591264626,
          0.2966564458006262
        ],
        "future_observed_K": [
          0.3026297353564091,
          0.5653528537433736,
          0.866024215313658,
          1.1162467932267,
          1.363556876568446,
          1.5157658629546058,
          1.6605450023544328,
          1.7845572145322988,
          1.7839832967332314,
          1.7497265712653682,
          1.6248211421518468,
          1.4284576735367773,
          1.1849267947892013,
          0.9362602847058601,
          0.6446677808403941,
          0.2599481929450487
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.902424851682034,
              -0.16042028591199597,
              -0.446221947159382,
              0.31367999031069843,
              -0.6216774565820063,
              1.595785260774553,
              2.3855053821381036,
              -3.9763531356955846
            ],
            "initial_K": [
              0.09276875973541154,
              1.076222329662383,
              1.5329506603391516,
              0.5527945108182708,
              0.22377724974480273,
              2.1311230833544954,
              3.8148705677418167,
              2.477259219213608,
              0.16125106151527713,
              0.7986007751803867,
              3.4664382774476565,
              3.622183965275287,
              0.6903639304429403,
              -0.9627333313031791,
              0.5637306403059561,
              1.723739496024712
            ],
            "metrics": {
              "initial_rmse_K": 1.222591087732875,
              "observation_residual_rms_K": 0.015661304276003495,
              "future_predictive_rmse_K": 0.02286885070733439
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.831385652251806,
              -0.15696325568762406,
              -0.4213245786975221,
              0.25393034669697945,
              -0.26006643135868873,
              0.12094769227279292,
              0.01493702294290861,
              -0.0012967624842252859
            ],
            "initial_K": [
              0.3011143400094239,
              0.5935537442545411,
              0.8874873651650469,
              1.1971955570645518,
              1.5077321394137442,
              1.7702262574834233,
              1.9419664723792622,
              2.0274566450501745,
              2.065891375172843,
              2.071257912243539,
              1.9941947748786384,
              1.7596917783739634,
              1.351884706063075,
              0.8592544271290083,
              0.4265952579032959,
              0.14927168521889778
            ],
            "metrics": {
              "initial_rmse_K": 0.058113102619888286,
              "observation_residual_rms_K": 0.026761552012919423,
              "future_predictive_rmse_K": 0.030417700203937966
            }
          },
          "learned": {
            "coefficients_K": [
              5.90208772734764,
              -0.16079235880449838,
              -0.4378323263319388,
              0.24057043393297795,
              -0.0812077086434405,
              0.011962406359357141,
              0.0023293336443883103,
              0.00035008890339268084
            ],
            "initial_K": [
              0.31092531388929096,
              0.6188000918657118,
              0.9211835385187531,
              1.2141908797155605,
              1.4899968050898067,
              1.7374920101271232,
              1.944554042571807,
              2.096771807381359,
              2.172497378571166,
              2.142370176880808,
              1.9811546390968413,
              1.688279258667526,
              1.3016784556049297,
              0.8899645379465008,
              0.5221917652827891,
              0.23200629117340882
            ],
            "metrics": {
              "initial_rmse_K": 0.030442726537812378,
              "observation_residual_rms_K": 0.023360039529841916,
              "future_predictive_rmse_K": 0.022436384376082124
            }
          }
        }
      },
      {
        "split": "train",
        "index": 43,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.635098764516489,
          0.581826087546068,
          -0.29219692061384167,
          0.19418871107896724,
          0.06441197215231965,
          -0.005546470531667946,
          0.05306948793904239,
          0.03297431808585333
        ],
        "initial_K": [
          0.5270811352521804,
          0.9645655362045453,
          1.3152547017362333,
          1.6340020953864884,
          1.9295737328660167,
          2.159346785115226,
          2.301610819317363,
          2.371747461022079,
          2.363771600627764,
          2.2325829984126284,
          1.9584281770887473,
          1.592996029136021,
          1.2166093588259603,
          0.8727205011277279,
          0.5619095833441965,
          0.2740366380316136
        ],
        "observed_K": [
          0.42766066798956326,
          0.8034129496798765,
          1.1880101218499854,
          1.5090908048989744,
          1.7290435539717477,
          1.9478750120965942,
          2.0453852275745765,
          2.108621399693874,
          2.0741596049580635,
          2.002396118736406,
          1.7685181659101077,
          1.4933632835470785,
          1.2498781122814653,
          0.913267053179586,
          0.6101129283272287,
          0.3381955859470922
        ],
        "future_observed_K": [
          0.38651459333702537,
          0.7543719706040297,
          1.1045663679333306,
          1.4230120446953791,
          1.6481164706201055,
          1.8345693537854482,
          1.9870629131051325,
          1.9637496838684891,
          1.976308977023961,
          1.8543433790360602,
          1.6723108445646828,
          1.426066522607761,
          1.2159618619338113,
          0.8731207627504571,
          0.5964694176537289,
          0.30062901731377784
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.65263001032711,
              0.5423035064908922,
              -0.2554499125008677,
              0.2863674266943659,
              0.21461216783997422,
              -1.1797390703288493,
              0.5335608969733687,
              2.768330934024098
            ],
            "initial_K": [
              1.3245477100846381,
              0.9876814751286457,
              0.4232477167345745,
              1.5142187594593481,
              2.9994144852904348,
              2.5990027661931157,
              1.1827238899285735,
              1.4222057194961224,
              3.130238962975383,
              3.484057839142112,
              1.7836988080124678,
              0.4998283020358454,
              1.0153109749620295,
              1.6113205360105427,
              0.8383262960866069,
              -0.10869321589451131
            ],
            "metrics": {
              "initial_rmse_K": 0.7552339375951123,
              "observation_residual_rms_K": 0.015827131990431932,
              "future_predictive_rmse_K": 0.021243399518593567
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.572561644881598,
              0.5306169569871072,
              -0.24119684710242306,
              0.2318202696678101,
              0.08977874302078963,
              -0.08941473614756162,
              0.003340932038638641,
              0.0009028040459829074
            ],
            "initial_K": [
              0.4885326037000669,
              0.9479069506961992,
              1.346458686574354,
              1.660723482327144,
              1.8928213182769238,
              2.071471241638413,
              2.223965648477827,
              2.3393410429053176,
              2.3626110263913276,
              2.2362702775840773,
              1.9557812255660598,
              1.5845561613433443,
              1.210282066329719,
              0.8830372917514114,
              0.5931675551747373,
              0.3041953444553176
            ],
            "metrics": {
              "initial_rmse_K": 0.03685213563289927,
              "observation_residual_rms_K": 0.025767028061441065,
              "future_predictive_rmse_K": 0.02308433121518831
            }
          },
          "learned": {
            "coefficients_K": [
              6.652250037092284,
              0.5435613052357776,
              -0.25064708305706995,
              0.21962362354033846,
              0.028034091010965916,
              -0.008843619817890822,
              0.0005209970842891694,
              -0.00024373135580449306
            ],
            "initial_K": [
              0.4971500939350894,
              0.9548072190212371,
              1.3465573605869023,
              1.665779177343181,
              1.9218752900012155,
              2.1271817778439015,
              2.282111686105042,
              2.368629174451745,
              2.3576185818948314,
              2.2265888441062995,
              1.9768058771925514,
              1.6386049087101537,
              1.2609105518800892,
              0.891263602678808,
              0.5584537623593705,
              0.2665480923429177
            ],
            "metrics": {
              "initial_rmse_K": 0.02414887111583248,
              "observation_residual_rms_K": 0.01874102966103838,
              "future_predictive_rmse_K": 0.020972183223066872
            }
          }
        }
      },
      {
        "split": "train",
        "index": 44,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.757763163547185,
          -0.7900906183493999,
          -0.12690942053753623,
          -0.15986577087770168,
          -0.03886003970210744,
          -0.025543989484258657,
          0.08650651697086881,
          0.007957475751637983
        ],
        "initial_K": [
          0.21791062075247666,
          0.4335881263940916,
          0.6841390596126506,
          1.0037203628312454,
          1.3555591873344737,
          1.6491282322095004,
          1.8326213466946784,
          1.9362909997688724,
          2.0091687658776105,
          2.0415809642734373,
          1.979627552045661,
          1.80244253039878,
          1.548675088155778,
          1.2588622137006729,
          0.9209094375564679,
          0.4978354380494513
        ],
        "observed_K": [
          0.2702671298835882,
          0.5048720679547424,
          0.7343445209477578,
          1.037179007891531,
          1.2759505210227795,
          1.4746250518885249,
          1.6679500968825918,
          1.7886246979417249,
          1.8431286139827427,
          1.8010017936266627,
          1.7594179383695652,
          1.5895353938812056,
          1.3833291157321734,
          1.1110718074333437,
          0.7706202799876599,
          0.36743633227361927
        ],
        "future_observed_K": [
          0.21359910298138163,
          0.5082099700778461,
          0.7430453666164261,
          0.9914215272848839,
          1.173323532906559,
          1.385989347378776,
          1.5670517491933327,
          1.682940571617705,
          1.7533689135592976,
          1.6941253386031947,
          1.6329661874739954,
          1.4725870238628123,
          1.2759237808590356,
          1.0445634637799588,
          0.7056624494222048,
          0.381769074749623
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.797749026543841,
              -0.7660806800734516,
              -0.1189151809671366,
              -0.19387000310595287,
              -0.06262933656768566,
              0.6025910412607489,
              -1.0142340754460377,
              10.267450727773412
            ],
            "initial_K": [
              3.544174845580808,
              1.0468771056522648,
              -2.480667941210399,
              -0.11495812532062821,
              4.325211132107618,
              3.2385755546928374,
              -0.8728186080038802,
              -0.01026976427539772,
              4.5657560197813005,
              4.49393893502573,
              -0.32716872830982746,
              -1.265852239432128,
              3.3747326493616496,
              4.946388439192056,
              -0.09075460702387228,
              -3.5597900108127516
            ],
            "metrics": {
              "initial_rmse_K": 2.5844165900939866,
              "observation_residual_rms_K": 0.013253822360511109,
              "future_predictive_rmse_K": 0.0253957710211027
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.727969663029253,
              -0.7495717700545893,
              -0.11228019787162774,
              -0.15694171966174045,
              -0.02619974053598595,
              0.04567155595194048,
              -0.006350703615197339,
              0.003348406054000801
            ],
            "initial_K": [
              0.21749373635424135,
              0.4513622841227942,
              0.7170548587775946,
              1.018164506000381,
              1.3340084954022042,
              1.6225368669734168,
              1.8407069635756377,
              1.9667086137958425,
              2.0073554204717308,
              1.9856613944802872,
              1.916800613447316,
              1.790955869362102,
              1.5809198616244753,
              1.271231296873549,
              0.8795555018699752,
              0.4454427170936034
            ],
            "metrics": {
              "initial_rmse_K": 0.03223704972230155,
              "observation_residual_rms_K": 0.02189221213597772,
              "future_predictive_rmse_K": 0.0204347770558736
            }
          },
          "learned": {
            "coefficients_K": [
              5.797417880899352,
              -0.7678574993385757,
              -0.11667940281841026,
              -0.14868462195370122,
              -0.008181066986863937,
              0.004517173507775372,
              -0.0009903518025618759,
              -0.0009039741801744641
            ],
            "initial_K": [
              0.2133308482895008,
              0.4525908472581036,
              0.7297285787382475,
              1.036487864322737,
              1.347337132024419,
              1.628208238746287,
              1.8477058578194807,
              1.9873200861799727,
              2.0452148363472675,
              2.0301176371523018,
              1.9496644460188488,
              1.8029231719284842,
              1.5824850714584087,
              1.2826203285532156,
              0.9066600601710765,
              0.4701718041921843
            ],
            "metrics": {
              "initial_rmse_K": 0.027243783431235836,
              "observation_residual_rms_K": 0.01504799816615303,
              "future_predictive_rmse_K": 0.025188523470395918
            }
          }
        }
      },
      {
        "split": "train",
        "index": 45,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.614353054383203,
          -0.7123130322801808,
          -0.3778328962459471,
          -0.21609964071400956,
          0.17827783886108858,
          0.0881555084095545,
          0.018889500167290366,
          -0.05626101222056732
        ],
        "initial_K": [
          0.21031163021211335,
          0.42404192958939624,
          0.6375828765218714,
          0.8769198110467229,
          1.1966153111447158,
          1.5899747807610929,
          1.9363191609015755,
          2.1025088305806108,
          2.0809084384473095,
          1.9698391184931903,
          1.8358077528910404,
          1.6638542294493475,
          1.4349412502163237,
          1.1672891587026801,
          0.8596814721088072,
          0.4709963195221136
        ],
        "observed_K": [
          0.2674472394850203,
          0.4724529257965373,
          0.7290722077166562,
          1.007835235645025,
          1.1974218630540758,
          1.4577443782400064,
          1.6248297090878923,
          1.783154073668465,
          1.8503916961319775,
          1.8094001885309097,
          1.6556747539774437,
          1.544919937407394,
          1.2865328774992437,
          1.0612832651108868,
          0.6676915030293353,
          0.3716870900908171
        ],
        "future_observed_K": [
          0.2368209663686172,
          0.4776079653190825,
          0.6891462782576666,
          0.9445154304099711,
          1.1938122683134433,
          1.3767383393689927,
          1.559548620512209,
          1.6883539124608156,
          1.692851795676504,
          1.6820048086906068,
          1.626650884840391,
          1.4761791269378253,
          1.216365357116649,
          0.9562747795104326,
          0.6773150823793075,
          0.3809981497135486
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.646145392977544,
              -0.6850431117347933,
              -0.34949704205506715,
              -0.03017123179171606,
              0.40888971978481536,
              0.2804490552789851,
              -4.323065141972152,
              10.987756538678008
            ],
            "initial_K": [
              2.7254199129188166,
              0.5472489627718218,
              -1.911419112868796,
              0.7727150201024409,
              4.178340720276019,
              2.0258485288232184,
              -1.5926259852094153,
              0.8246938653661449,
              5.880296229532737,
              4.459755859061758,
              -1.6565427379683515,
              -1.9982769151312512,
              4.152364483443409,
              5.81091589581493,
              -0.6540952350298599,
              -4.768478346056321
            ],
            "metrics": {
              "initial_rmse_K": 2.9680610160715584,
              "observation_residual_rms_K": 0.02072465861848456,
              "future_predictive_rmse_K": 0.022659077766592085
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.578190669510037,
              -0.6702805477061757,
              -0.32999652961329085,
              -0.02442422719267754,
              0.1710509028722741,
              0.02125578351288597,
              -0.027069200385307763,
              0.0035833111343281693
            ],
            "initial_K": [
              0.24892760338319628,
              0.48420257102479314,
              0.706959533679684,
              0.9381646623129247,
              1.205306109803219,
              1.512617354739829,
              1.81669413346712,
              2.037728826617395,
              2.11014582736297,
              2.0311963323726494,
              1.856875884269039,
              1.6463645249072265,
              1.4140032564009655,
              1.1369776625142718,
              0.7985692253238269,
              0.41081700949783423
            ],
            "metrics": {
              "initial_rmse_K": 0.05718586852847235,
              "observation_residual_rms_K": 0.028334983643331625,
              "future_predictive_rmse_K": 0.02575483906995832
            }
          },
          "learned": {
            "coefficients_K": [
              5.645822906363088,
              -0.6866319754537611,
              -0.3429259899546027,
              -0.023139207308812644,
              0.053411937138825936,
              0.0021023164236500585,
              -0.004221269487580258,
              -0.0009673918553259076
            ],
            "initial_K": [
              0.21702915324934585,
              0.44505972772660307,
              0.6929397044101092,
              0.9658591329674171,
              1.2612361723275813,
              1.5610902805652132,
              1.828767640623754,
              2.019122776335288,
              2.0987331013983965,
              2.060555828473615,
              1.9215378326191226,
              1.7074901118474675,
              1.43893958687563,
              1.1268785012983222,
              0.7771643665407593,
              0.3972468709821022
            ],
            "metrics": {
              "initial_rmse_K": 0.0645611273431643,
              "observation_residual_rms_K": 0.02426980679343465,
              "future_predictive_rmse_K": 0.022062735023048726
            }
          }
        }
      },
      {
        "split": "train",
        "index": 46,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.769207113517317,
          2.149877906493377,
          -0.2076022475983318,
          0.04800269454851337,
          -0.13232572040465687,
          0.03403587382913866,
          0.008417592687185841,
          0.012900429072827485
        ],
        "initial_K": [
          0.6480334172409228,
          1.2561694201598281,
          1.799869402188178,
          2.253138532645432,
          2.569533456683529,
          2.7041132839689785,
          2.6554066634037516,
          2.4701841909485975,
          2.204755781928597,
          1.8923130454802104,
          1.5457735889243391,
          1.1761721358612254,
          0.8042288741919115,
          0.4662026142198936,
          0.2095526808761643,
          0.06337570675464615
        ],
        "observed_K": [
          0.5589361868892567,
          1.0288052294002372,
          1.4975963853299057,
          1.9007906462068207,
          2.159806049004221,
          2.2931733862083425,
          2.3158845774350345,
          2.2049259728732675,
          2.0793525892174998,
          1.7815255011316686,
          1.521238644025118,
          1.1787663175357939,
          0.8818905675582508,
          0.6350093841652938,
          0.40675105034724884,
          0.21390393584771455
        ],
        "future_observed_K": [
          0.5218033672496001,
          0.9723016061539707,
          1.3939350763027143,
          1.7079245484300725,
          1.9928518481850335,
          2.086130757102736,
          2.1533994767500313,
          2.0792527585071126,
          1.9363237522577281,
          1.7332009448900056,
          1.461846784712969,
          1.1862074543687848,
          0.9420419414478597,
          0.6703232968922405,
          0.4028913342162205,
          0.21490037721797264
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.793063949543323,
              2.1350789322191495,
              -0.28345671595283245,
              -0.09182415961394151,
              -0.012415133707999118,
              -1.4027463459635456,
              1.910220456881261,
              6.394252806995399
            ],
            "initial_K": [
              3.000230538780536,
              1.5765329951247609,
              -0.703825935745027,
              1.3017620777115084,
              4.957265143626682,
              4.354342505565614,
              0.7268665923944821,
              0.30200175520968364,
              3.471803667446722,
              4.358050406788642,
              1.1633996936909823,
              -1.0594796398747048,
              0.513948831470054,
              2.077493755523031,
              0.6144355075570267,
              -0.9927414873168965
            ],
            "metrics": {
              "initial_rmse_K": 1.7037335400739797,
              "observation_residual_rms_K": 0.01405435204789868,
              "future_predictive_rmse_K": 0.019048656458984528
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.711305377976524,
              2.089068339742395,
              -0.26764098491362004,
              -0.0743335290938757,
              -0.005193624900011772,
              -0.10631689460901247,
              0.01196099032267742,
              0.00208528439798981
            ],
            "initial_K": [
              0.5869195566090201,
              1.1782097891980543,
              1.7440999182697314,
              2.2184457235447033,
              2.5341887986318135,
              2.6663235197280217,
              2.6402367060527325,
              2.4967621738822223,
              2.254370060488031,
              1.9139292545138127,
              1.499241288343046,
              1.0785479378900307,
              0.7312079240269699,
              0.4899185186137983,
              0.3214575583598682,
              0.16744378540395038
            ],
            "metrics": {
              "initial_rmse_K": 0.06205451651439707,
              "observation_residual_rms_K": 0.026696245043314557,
              "future_predictive_rmse_K": 0.017189960001838166
            }
          },
          "learned": {
            "coefficients_K": [
              6.792675955249447,
              2.140030955521661,
              -0.2781273179190169,
              -0.07042265559233386,
              -0.0016217486258415673,
              -0.010515338261348914,
              0.0018652403015851735,
              -0.0005629673413865439
            ],
            "initial_K": [
              0.6235301036526903,
              1.2235953178857693,
              1.7695402708798167,
              2.2232078372580766,
              2.5464618979170965,
              2.71174616420916,
              2.7099241112294985,
              2.552510260440458,
              2.2688427444180452,
              1.9007254089021828,
              1.4965614225445387,
              1.1045089345654278,
              0.7632204051120186,
              0.492251512727373,
              0.28850791152987587,
              0.132597292643834
            ],
            "metrics": {
              "initial_rmse_K": 0.04933218598040678,
              "observation_residual_rms_K": 0.017939479382084025,
              "future_predictive_rmse_K": 0.018546766049950467
            }
          }
        }
      },
      {
        "split": "train",
        "index": 47,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.037695980759662,
          -0.9596319341869672,
          -0.07742917080644764,
          0.19224246559053937,
          0.09897911183311195,
          -0.061145921060858664,
          -0.02936152230314217,
          0.053497238779133004
        ],
        "initial_K": [
          0.3089705504984976,
          0.5822227884772575,
          0.8269801126233869,
          1.0630270057502123,
          1.2866317769266364,
          1.5017791450492703,
          1.7445209808556341,
          2.0183459717847776,
          2.233753634630015,
          2.280177133399619,
          2.1497915812776607,
          1.9281179226816954,
          1.667201134353644,
          1.3386179908811813,
          0.9211333992358226,
          0.4589376132644354
        ],
        "observed_K": [
          0.2739639179863544,
          0.544037141503108,
          0.8234022885805113,
          1.0504369135936125,
          1.2696631148981965,
          1.5011227728367413,
          1.6721278670980761,
          1.8294859345531291,
          1.9280070329930905,
          1.9311153319916476,
          1.8604106608282254,
          1.7408134984888222,
          1.457042606900871,
          1.1719564513097442,
          0.8183623589929842,
          0.38303535497130153
        ],
        "future_observed_K": [
          0.26508363813583,
          0.5258480358329176,
          0.760263079874817,
          0.9891434946170674,
          1.240170820027333,
          1.4294507967888876,
          1.6097452386710487,
          1.7379425133919768,
          1.8551789526654658,
          1.8373044099975453,
          1.7435877896234002,
          1.5820250736266925,
          1.3704976875931536,
          1.0962106672569025,
          0.8156685759908668,
          0.37899153211785525
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.046346897995419,
              -0.9342842717378255,
              -0.015357305943725382,
              0.2687455605558991,
              -0.004629163749476882,
              0.19705643977167786,
              -1.5673857009940477,
              -2.7971901654011972
            ],
            "initial_K": [
              -1.0885450849307619,
              0.21345345821870498,
              2.145205541984576,
              1.8544677226122435,
              0.2947551123298233,
              0.4981353519637848,
              2.3854888402527923,
              3.0874607415609483,
              1.9079378580409034,
              1.2220333003293729,
              2.1482310695409463,
              2.8170142313331628,
              1.8956199835751282,
              0.7510408538840199,
              0.7063760738271951,
              0.8084418205118074
            ],
            "metrics": {
              "initial_rmse_K": 0.813163696881138,
              "observation_residual_rms_K": 0.012573518681614623,
              "future_predictive_rmse_K": 0.023911690693389994
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.973575510996967,
              -0.9141506025625641,
              -0.014500430778582797,
              0.21755500979721257,
              -0.0019365188229929855,
              0.014935293753940846,
              -0.00981430448719046,
              -0.0009122155764220552
            ],
            "initial_K": [
              0.31137999281764167,
              0.6003869256153413,
              0.8539215114376524,
              1.0764259850994358,
              1.2887237242289973,
              1.5118215147434892,
              1.7462053933228503,
              1.965391267827207,
              2.128718077102093,
              2.1992264459839217,
              2.1524324492572777,
              1.9779147091475866,
              1.6830583177251195,
              1.2974637589726632,
              0.8661969165423526,
              0.42882374818432956
            ],
            "metrics": {
              "initial_rmse_K": 0.043370162259507135,
              "observation_residual_rms_K": 0.021473409393848755,
              "future_predictive_rmse_K": 0.027387749619875505
            }
          },
          "learned": {
            "coefficients_K": [
              6.046001553374398,
              -0.936451216207652,
              -0.015068566282623782,
              0.20610889478942007,
              -0.0006046926377178462,
              0.0014771844722596566,
              -0.0015304783105482957,
              0.0002462722007246455
            ],
            "initial_K": [
              0.30979493911920464,
              0.5984484913895315,
              0.8555417579960886,
              1.0861809595438952,
              1.3067201017711985,
              1.5328300574330538,
              1.7659148167505787,
              1.9857711086622136,
              2.1544679935163615,
              2.2297874841326677,
              2.1810135953447283,
              1.9995605722295808,
              1.7008962542134722,
              1.3181122742129765,
              0.8896046325243815,
              0.44552783056923045
            ],
            "metrics": {
              "initial_rmse_K": 0.03719565749901835,
              "observation_residual_rms_K": 0.013486072525626825,
              "future_predictive_rmse_K": 0.023434597470371875
            }
          }
        }
      },
      {
        "split": "train",
        "index": 48,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.315614463782192,
          -0.20792907974924846,
          -0.24034752369020795,
          0.033223658172685966,
          -0.0636800096085495,
          0.010868700418997106,
          -0.015581399037905655,
          -0.036046107028568614
        ],
        "initial_K": [
          0.2419905066136783,
          0.5250156506912851,
          0.8298943263371199,
          1.1107641785982132,
          1.3577895559668371,
          1.5836030962441336,
          1.769066954427409,
          1.8725377325815409,
          1.8863968069821773,
          1.8374011854965968,
          1.7296759574583551,
          1.5341387186169793,
          1.2468446693093964,
          0.9169775185813023,
          0.5970100898951851,
          0.29611072157281404
        ],
        "observed_K": [
          0.25505994768854057,
          0.5360481064241772,
          0.7498744400934569,
          1.0529499554892683,
          1.2479531081011237,
          1.4608095770567016,
          1.5897078267923939,
          1.6528607080194988,
          1.6693552517657784,
          1.644201686257086,
          1.5228157397410138,
          1.352619516661843,
          1.1296193781978177,
          0.8680580462340337,
          0.5768942958413286,
          0.31624738920234635
        ],
        "future_observed_K": [
          0.2373416050407402,
          0.5310538416266604,
          0.7711481565763793,
          0.9972545056250737,
          1.1927182583519365,
          1.3740599311127846,
          1.5373289599119606,
          1.5824666570363646,
          1.5757831830833955,
          1.523979733855764,
          1.4611614504174342,
          1.3138377032907036,
          1.0703600571823737,
          0.8338543596005025,
          0.5701877814853771,
          0.2581650694321833
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.29771379396073,
              -0.21054911676432347,
              -0.2777280370017359,
              -0.03463344727442247,
              -0.2811755082688319,
              -0.08073365893339905,
              2.4813656379598164,
              0.2279016172268774
            ],
            "initial_K": [
              1.044348759860559,
              0.8582098280761118,
              0.10928072540240669,
              0.36135323274576725,
              1.6935092323229786,
              2.5414918945419585,
              1.9843044934279512,
              1.0592286778565747,
              1.2116664821021823,
              2.218980355959997,
              2.571607118024326,
              1.642663539651898,
              0.5127457951076968,
              0.3977281584606323,
              0.9946415955086554,
              1.0064351526547157
            ],
            "metrics": {
              "initial_rmse_K": 0.6307950032992521,
              "observation_residual_rms_K": 0.012398240652453209,
              "future_predictive_rmse_K": 0.01806226391843877
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.233952652363781,
              -0.20601181865248505,
              -0.26223194293142005,
              -0.02803648159066431,
              -0.11762419603081534,
              -0.00611896222928761,
              0.015537259207828977,
              7.432294296527258e-05
            ],
            "initial_K": [
              0.22159516519709865,
              0.4731478528592058,
              0.7667751890617303,
              1.084012406030928,
              1.3798204659478501,
              1.60815426972067,
              1.7511060331161756,
              1.8230838657343253,
              1.84434826107897,
              1.8125067721728398,
              1.7039232446742207,
              1.5027501681284114,
              1.2242476032852687,
              0.9079081951356114,
              0.5908476941407426,
              0.2893107453560042
            ],
            "metrics": {
              "initial_rmse_K": 0.031991866297305764,
              "observation_residual_rms_K": 0.020044880228812616,
              "future_predictive_rmse_K": 0.024606268870799287
            }
          },
          "learned": {
            "coefficients_K": [
              5.297411208450286,
              -0.21103745661762174,
              -0.27250634645417876,
              -0.0265614119381671,
              -0.03672904415531848,
              -0.0006051997463432543,
              0.0024229366690207903,
              -2.0065075845538314e-05
            ],
            "initial_K": [
              0.24293430411899747,
              0.5030213960102425,
              0.7863225324931032,
              1.0818528666003207,
              1.3642347631727572,
              1.6039180497023562,
              1.7784375472910283,
              1.8770921175402524,
              1.8973207330932076,
              1.8387410525723413,
              1.7020792197533603,
              1.4936192618941662,
              1.2289496107059046,
              0.9303668999262488,
              0.6190297395042523,
              0.30789217978292555
            ],
            "metrics": {
              "initial_rmse_K": 0.021548639353870833,
              "observation_residual_rms_K": 0.014338357523943359,
              "future_predictive_rmse_K": 0.018416468284517484
            }
          }
        }
      },
      {
        "split": "train",
        "index": 49,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.821662948497197,
          0.9223004833387807,
          -0.12136966524360654,
          -0.1373177870079228,
          0.2571459484505998,
          0.1128143112349112,
          -0.04178330924820034,
          0.0008916740261980926
        ],
        "initial_K": [
          0.5821145912702149,
          1.082418850206277,
          1.470007767078549,
          1.778511239696627,
          2.064983778641042,
          2.340362569482906,
          2.5365481476526734,
          2.555567763919707,
          2.364953575881616,
          2.042582848353399,
          1.7165810015426857,
          1.4584437453954715,
          1.2404829782435942,
          0.9936256058622883,
          0.6881028461581689,
          0.347135414586625
        ],
        "observed_K": [
          0.4492726824236885,
          0.8659635732747163,
          1.2925727156194131,
          1.6278508014717934,
          1.9126978286072829,
          2.0945062399433847,
          2.1278271780851092,
          2.2029639723698704,
          2.0572122860426925,
          1.907110457390435,
          1.724829557733571,
          1.4671230130717734,
          1.2161095797007668,
          0.8861093560415928,
          0.6296538983856601,
          0.3138552586632145
        ],
        "future_observed_K": [
          0.40888108741955853,
          0.8251350935499201,
          1.2201087770774854,
          1.5370673304444933,
          1.768522039687851,
          1.9269900670750992,
          2.0344901078062705,
          2.089429274264037,
          1.982571461235158,
          1.8432390623500574,
          1.623397824475035,
          1.4239403263640216,
          1.1964654265104435,
          0.9535702235809337,
          0.5873475814585131,
          0.3005040609629934
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.807710710577897,
              0.9409428983848519,
              -0.0977716644358452,
              -0.18934824877565462,
              -0.1864968369943455,
              -0.3718568210817819,
              -0.4434737711542237,
              -8.029012020971651
            ],
            "initial_K": [
              -2.569466671742513,
              0.2168305422801352,
              4.18452148655537,
              3.143113705739188,
              -0.14765756556659881,
              0.8122127172179892,
              4.500496309333971,
              4.292374773388949,
              0.550514843944373,
              -0.0969414283964376,
              3.1638367809795946,
              3.921699614536675,
              0.2892321893937366,
              -1.6341048324847796,
              1.1269437804567277,
              2.997576036426213
            ],
            "metrics": {
              "initial_rmse_K": 2.016746139281052,
              "observation_residual_rms_K": 0.01835078758734551,
              "future_predictive_rmse_K": 0.02322649449112786
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.725775856516312,
              0.9206657369234328,
              -0.0923164035055282,
              -0.1532812673528957,
              -0.07801725210282674,
              -0.028183757220510086,
              -0.002776844665247269,
              -0.0026184096881949983
            ],
            "initial_K": [
              0.45406356173878876,
              0.9312854232248922,
              1.4172478725314615,
              1.8582348650868574,
              2.1931122940120615,
              2.386575353794014,
              2.439321763044444,
              2.376876270584336,
              2.2318086079549686,
              2.030533739773281,
              1.7893641777141678,
              1.5188790013244362,
              1.2294341232137542,
              0.930519600707127,
              0.6262588324105549,
              0.3158483258853442
            ],
            "metrics": {
              "initial_rmse_K": 0.09488301442008029,
              "observation_residual_rms_K": 0.026867354876397825,
              "future_predictive_rmse_K": 0.02992675572390223
            }
          },
          "learned": {
            "coefficients_K": [
              6.807321879716053,
              0.9431252866276563,
              -0.09593341511281991,
              -0.14521675522652902,
              -0.024361476584380905,
              -0.0027875319509593336,
              -0.0004330312491801757,
              0.0007068959717172885
            ],
            "initial_K": [
              0.48758938975186134,
              0.9735083833104001,
              1.443249194154743,
              1.8650687932210697,
              2.1979130260148674,
              2.4074772443464467,
              2.4800747452737903,
              2.425986678613772,
              2.2724518979465294,
              2.052601188080722,
              1.7957976411689471,
              1.5214680069630586,
              1.2374907595808735,
              0.9437095145355243,
              0.6382715211632524,
              0.32221478667940606
            ],
            "metrics": {
              "initial_rmse_K": 0.07732594621824955,
              "observation_residual_rms_K": 0.01936027037702671,
              "future_predictive_rmse_K": 0.02322196819878155
            }
          }
        }
      },
      {
        "split": "train",
        "index": 50,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.254541743408774,
          0.05443725511970432,
          -0.034346459716696226,
          -0.07381571647501592,
          -0.14936530772355305,
          -0.07926499406790707,
          -0.05391954471075803,
          0.042162473319272975
        ],
        "initial_K": [
          0.3090726371883093,
          0.6737400252140845,
          1.0991674831308214,
          1.514262416355398,
          1.8178870720667848,
          1.9756932404118037,
          2.0491183641096162,
          2.1048894202404815,
          2.127845661816087,
          2.0613555441002465,
          1.901604767854853,
          1.6927885303052332,
          1.444531300957446,
          1.1239757992729134,
          0.7370807547038055,
          0.3495715610569148
        ],
        "observed_K": [
          0.32966250082619397,
          0.7029720576966935,
          1.0101356136976434,
          1.3155286416754444,
          1.5333238935039595,
          1.7814841586834609,
          1.9187254033311982,
          1.9623098131706422,
          1.9302763467457045,
          1.9005706797376836,
          1.7273856541173516,
          1.5633205050876304,
          1.328109215377044,
          1.0002797687955618,
          0.7019994265686985,
          0.32734550295227743
        ],
        "future_observed_K": [
          0.34482803445582005,
          0.6617909676939181,
          0.988743221116741,
          1.2737804597051696,
          1.5089318100822382,
          1.6562923241208636,
          1.8078724108927524,
          1.8206929462263985,
          1.8992204562032455,
          1.7819682254056444,
          1.6529481495955949,
          1.450963177016292,
          1.2401657574040252,
          0.9227688719078684,
          0.6749736589835604,
          0.33467178558397254
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.295454632182461,
              0.014024445212928891,
              -0.10680200958453008,
              -0.09314366771100617,
              -0.20570453378446965,
              1.0519964320049695,
              -0.5660409655032969,
              -7.005600674304392
            ],
            "initial_K": [
              -1.954986951536505,
              0.395022508187743,
              3.429251451898459,
              2.15632247956078,
              -0.6281107840566071,
              0.6938392916958649,
              4.326451949436596,
              4.098324776172994,
              0.4559199908383791,
              -0.2895082977133656,
              2.8939389750133304,
              4.117158394740524,
              1.116542177403714,
              -1.018109165204953,
              0.7593284433554345,
              2.2238790774646056
            ],
            "metrics": {
              "initial_rmse_K": 1.7892926446858193,
              "observation_residual_rms_K": 0.015943452280053075,
              "future_predictive_rmse_K": 0.023820228718062324
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.219685085198376,
              0.013722220773510175,
              -0.10084289214976311,
              -0.07540169779735346,
              -0.08605241101994664,
              0.07973287124387643,
              -0.003544308452060915,
              -0.0022846562726909635
            ],
            "initial_K": [
              0.35704467154261565,
              0.709756583528826,
              1.0580742290360097,
              1.4001551713393772,
              1.7181251974187857,
              1.9728104871151273,
              2.1228212084400875,
              2.157183477108501,
              2.1069187528871174,
              2.015849590026394,
              1.8966143697249511,
              1.7200930172982933,
              1.452328572810067,
              1.0994682670871745,
              0.7115587227293921,
              0.341089628794283
            ],
            "metrics": {
              "initial_rmse_K": 0.05068224992926419,
              "observation_residual_rms_K": 0.024820946310766978,
              "future_predictive_rmse_K": 0.026377459717067484
            }
          },
          "learned": {
            "coefficients_K": [
              6.295095059463466,
              0.014056972993729497,
              -0.10479397665444401,
              -0.07143462525981091,
              -0.02687051568195383,
              0.007886028977438432,
              -0.0005527123413434163,
              0.0006167920639787993
            ],
            "initial_K": [
              0.3581594383224616,
              0.7199009610265382,
              1.0817424512315823,
              1.4286017790600598,
              1.735139635210332,
              1.9739641062054398,
              2.1262229493761113,
              2.187480387998497,
              2.165443468602998,
              2.0722311646688176,
              1.916958784313559,
              1.7033333789056613,
              1.433360429471225,
              1.1136172302753886,
              0.7578043806029952,
              0.3824256559433556
            ],
            "metrics": {
              "initial_rmse_K": 0.047049175197971624,
              "observation_residual_rms_K": 0.018357944857873194,
              "future_predictive_rmse_K": 0.023152792737722534
            }
          }
        }
      },
      {
        "split": "train",
        "index": 51,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.022260283288814,
          -1.8483862805090934,
          -0.10526559126424993,
          0.07026272794724665,
          0.10298068908119853,
          -0.014229878285847465,
          -0.05417273209484872,
          -0.0181777874519865
        ],
        "initial_K": [
          0.0844738914457073,
          0.20599324306609268,
          0.35476936897989786,
          0.5098360706342111,
          0.6982835653957554,
          0.9722021140562099,
          1.3257524260863978,
          1.6728767663526154,
          1.9200176713573547,
          2.0361747444723837,
          2.0405246884864012,
          1.947821820424017,
          1.7496593068048978,
          1.4375689614325489,
          1.0223145947573677,
          0.5312048997895066
        ],
        "observed_K": [
          0.09931302443390885,
          0.2824609202433811,
          0.44852634339482955,
          0.6092737122537327,
          0.865364790388961,
          1.079618383354924,
          1.2518090272407014,
          1.4861985683973817,
          1.6508465387606046,
          1.7309723963670824,
          1.7704915491584035,
          1.6403781911712827,
          1.4934456887832108,
          1.1735969381034026,
          0.8060928051393179,
          0.4554582016014003
        ],
        "future_observed_K": [
          0.19138442463660707,
          0.31059534240310327,
          0.4913662552364367,
          0.6536626338729872,
          0.8450859117996614,
          1.0186804862979983,
          1.2206570362211844,
          1.4080671489710828,
          1.5401985971834309,
          1.646925047923237,
          1.6435833381799132,
          1.5399689954643037,
          1.3147339925108805,
          1.1145845325602095,
          0.7343865727493677,
          0.41668041574028536
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.038558007308005,
              -1.8274865167619656,
              -0.07138294403472777,
              0.09730239372780805,
              -0.36462756758307574,
              -0.5302297284665134,
              0.1736222543629759,
              0.3399378888155219
            ],
            "initial_K": [
              0.011491465764173758,
              0.0006786102701874519,
              0.1869032554371549,
              0.6720681333520102,
              1.112206605423232,
              1.1584516337232853,
              1.043270744802208,
              1.2833834181552044,
              1.8864369974286612,
              2.3112581317056367,
              2.2317175574782655,
              1.899339236281452,
              1.6424912949789439,
              1.4133111645764864,
              1.0262068244142988,
              0.5127931426461567
            ],
            "metrics": {
              "initial_rmse_K": 0.20427192565496846,
              "observation_residual_rms_K": 0.01935568381479842,
              "future_predictive_rmse_K": 0.025394234737793755
            }
          },
          "tikhonov": {
            "coefficients_K": [
              4.977915959994192,
              -1.788104489188819,
              -0.0674000662967797,
              0.07876827128588954,
              -0.1525347095545209,
              -0.04018715024434261,
              0.0010871489187313625,
              0.00011086004842615734
            ],
            "initial_K": [
              0.04451854189685708,
              0.14868978528408483,
              0.3317053243884114,
              0.566545490090988,
              0.8115522312701677,
              1.0478969669862397,
              1.2875182635459128,
              1.5454934259919166,
              1.8049695598596323,
              2.0091365411911752,
              2.0886590723300937,
              2.0011609175845853,
              1.7515253462743114,
              1.3816260567411305,
              0.9432465805669193,
              0.4758276589335748
            ],
            "metrics": {
              "initial_rmse_K": 0.06912691390040947,
              "observation_residual_rms_K": 0.0253194184099131,
              "future_predictive_rmse_K": 0.02889283422474455
            }
          },
          "learned": {
            "coefficients_K": [
              5.038270223802546,
              -1.8317251215645638,
              -0.07004084098979606,
              0.07462407486888364,
              -0.047630115839252495,
              -0.003974734966939968,
              0.00016953395348860782,
              -2.9929052741496745e-05
            ],
            "initial_K": [
              0.08096517592617122,
              0.18820790579531166,
              0.3381480773140586,
              0.5340204626151522,
              0.769805395258849,
              1.0359291062057547,
              1.3203399251798746,
              1.603774063642182,
              1.8545792185120509,
              2.0303534284499443,
              2.0889133699329068,
              2.003520760084915,
              1.7731768722609393,
              1.4215956362585622,
              0.9859485974921108,
              0.5028581155816391
            ],
            "metrics": {
              "initial_rmse_K": 0.04173197661754815,
              "observation_residual_rms_K": 0.020881733613761798,
              "future_predictive_rmse_K": 0.025368795418898627
            }
          }
        }
      },
      {
        "split": "train",
        "index": 52,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.105636137376169,
          1.7552904139536019,
          -0.03813701213056751,
          0.06562985335018198,
          -0.06520429320531954,
          0.04388171223428406,
          0.005566994417785528,
          -0.018492276102046946
        ],
        "initial_K": [
          0.6017260966969367,
          1.1631680972867195,
          1.6403127412965375,
          2.0019319593153746,
          2.240523495117559,
          2.354937822873387,
          2.3365047795083473,
          2.191012800108817,
          1.9616269665915818,
          1.7028219190045086,
          1.4331367094527154,
          1.137707234862986,
          0.8190474052747813,
          0.519831263017481,
          0.2854370977765702,
          0.12210184369368915
        ],
        "observed_K": [
          0.4899555869143806,
          0.9402709412028852,
          1.3357406227480069,
          1.6665577146397779,
          1.8596885801212426,
          2.053183723299487,
          2.0637596602312933,
          1.9501141917665576,
          1.8360028045056487,
          1.621060831734191,
          1.3805216516795826,
          1.1405525781995092,
          0.8868469676454646,
          0.6251540072107221,
          0.42049832028322043,
          0.18569732689159216
        ],
        "future_observed_K": [
          0.45400534597528996,
          0.8804348935120754,
          1.2577604087521748,
          1.543611885762786,
          1.7356524461432492,
          1.864829843116925,
          1.951318639035476,
          1.8824930133053959,
          1.7270981635182254,
          1.5453080682742364,
          1.3302386379559792,
          1.115273592436043,
          0.8824127852350511,
          0.6299315897264411,
          0.4269500509775981,
          0.25835583081081626
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.1141264490574985,
              1.7078217317593585,
              -0.08936162564623396,
              -0.05025474884721105,
              -0.09007249734973839,
              0.7908655864861037,
              1.7079834867832446,
              0.19775403691319995
            ],
            "initial_K": [
              1.4183866359180737,
              1.6152287751324672,
              1.0631686083466447,
              1.174913331051153,
              2.25134026964267,
              3.1047918113342923,
              2.7834527091732753,
              1.8334713784019647,
              1.411532327568242,
              1.7038902034812549,
              1.869312466457932,
              1.350422594707467,
              0.5855135927010324,
              0.27211485657928436,
              0.4024091236214188,
              0.39766529650934035
            ],
            "metrics": {
              "initial_rmse_K": 0.46917256157637577,
              "observation_residual_rms_K": 0.014244271620472955,
              "future_predictive_rmse_K": 0.02265943595790701
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.040539294782684,
              1.6710184602094615,
              -0.08437561065026963,
              -0.04068224366272781,
              -0.03768004244210745,
              0.05994125270779571,
              0.01069466819032035,
              6.449125805026894e-05
            ],
            "initial_K": [
              0.5747605977802714,
              1.1006944092607869,
              1.55288366754907,
              1.9246095481113508,
              2.201280137842675,
              2.350602452877715,
              2.3459147217186898,
              2.197554826026627,
              1.9552228569001038,
              1.6765700111429664,
              1.394108215267113,
              1.111701321352239,
              0.8278839737232015,
              0.5566188558810954,
              0.32339754269765586,
              0.1426147121421659
            ],
            "metrics": {
              "initial_rmse_K": 0.04043959302258332,
              "observation_residual_rms_K": 0.023656465430992906,
              "future_predictive_rmse_K": 0.027426599238298616
            }
          },
          "learned": {
            "coefficients_K": [
              6.113777233123144,
              1.7117827904746057,
              -0.08768149726960786,
              -0.03854184873377321,
              -0.011765878019415917,
              0.005928526696998144,
              0.0016677654259819835,
              -1.7410801194423395e-05
            ],
            "initial_K": [
              0.5718282261181997,
              1.1110344099235019,
              1.5868088573701287,
              1.9706070370440547,
              2.2370152404880943,
              2.367971109905524,
              2.3596335123028096,
              2.2266562852658303,
              1.999184073727426,
              1.7137314965224046,
              1.403987743068561,
              1.0964010326697236,
              0.8101085854978586,
              0.5574774776309029,
              0.3430150126034347,
              0.16181527076449712
            ],
            "metrics": {
              "initial_rmse_K": 0.035282984043424045,
              "observation_residual_rms_K": 0.01579729628591148,
              "future_predictive_rmse_K": 0.022403259749493587
            }
          }
        }
      },
      {
        "split": "train",
        "index": 53,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.579542366923636,
          1.5171774716999176,
          -0.0032102298820188015,
          -0.01105817764746834,
          0.026342835175566463,
          -0.0029785297179734517,
          0.03767797621122116,
          0.03171820103422069
        ],
        "initial_K": [
          0.6290890338885619,
          1.1777354628465018,
          1.6340233284942944,
          2.0176918197792664,
          2.3068626279995135,
          2.451440626984301,
          2.445329390942464,
          2.335095663259657,
          2.156847651361357,
          1.9100395020953582,
          1.6028715888383667,
          1.2809710092038318,
          0.9886451441834052,
          0.7289656905964921,
          0.4817556967106602,
          0.23839159151121475
        ],
        "observed_K": [
          0.5012458990578359,
          1.0028828956845033,
          1.4187908045006918,
          1.7033002771120718,
          2.0085692421050823,
          2.150309404145676,
          2.1307457024172716,
          2.0972390870110793,
          2.0066553760354804,
          1.7870499353817195,
          1.532350931396835,
          1.2969177575240434,
          1.0264197751238475,
          0.7894764672233295,
          0.5038005782849885,
          0.24509326632325923
        ],
        "future_observed_K": [
          0.4419399212299309,
          0.8763146127363848,
          1.2920581526607788,
          1.5923148013520512,
          1.8210917786407792,
          1.9286671658844845,
          2.017135913193087,
          1.997485156473845,
          1.8966999693502147,
          1.7059912703301938,
          1.5160491612256661,
          1.2653535935968612,
          1.0495673008470392,
          0.7725287266697232,
          0.5151457648937465,
          0.26040980448264855
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.61447469403431,
              1.5481110742560458,
              0.04135225940087061,
              -0.02210955966345324,
              0.10772296511831005,
              -0.06456874408078435,
              -0.2422138418685382,
              23.55072637235912
            ],
            "initial_K": [
              8.584184575680187,
              2.64086916301825,
              -6.018337820331689,
              -0.7747279034494119,
              9.524184328184877,
              6.5961453578830245,
              -4.032618652673975,
              -3.00855027304627,
              7.698148426749944,
              8.33133966009941,
              -2.754794245190684,
              -5.997053326271802,
              3.964090321109004,
              8.57390032752882,
              -0.9927386478372753,
              -7.836332072450812
            ],
            "metrics": {
              "initial_rmse_K": 5.880246518941989,
              "observation_residual_rms_K": 0.016688592048440844,
              "future_predictive_rmse_K": 0.02130380274345724
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.534865550551222,
              1.5147495405574711,
              0.03904497163614274,
              -0.017898139263194026,
              0.04506376548978158,
              -0.004893791653228408,
              -0.001516640348066479,
              0.007680328530626856
            ],
            "initial_K": [
              0.6154176694095153,
              1.1793363376804964,
              1.6571975983270777,
              2.0299379505840496,
              2.2845014145957117,
              2.41436197797427,
              2.424736892677087,
              2.3282763999905365,
              2.1382219436080216,
              1.8742726127470173,
              1.5717644259120456,
              1.2716176123161143,
              0.9961913799342973,
              0.7412735572154653,
              0.4932292852555989,
              0.24607860978065496
            ],
            "metrics": {
              "initial_rmse_K": 0.01984688048990765,
              "observation_residual_rms_K": 0.027395808581622123,
              "future_predictive_rmse_K": 0.01691671133140625
            }
          },
          "learned": {
            "coefficients_K": [
              6.614096900087818,
              1.5517017059647404,
              0.04057477685224226,
              -0.016956473242158872,
              0.01407150134352873,
              -0.00048402349225407467,
              -0.00023651040790998015,
              -0.002073469756945523
            ],
            "initial_K": [
              0.6154455524790119,
              1.1890825386471668,
              1.6824339386429008,
              2.066301701160966,
              2.3250504112123602,
              2.4547804016487214,
              2.4592864017623333,
              2.350228068839899,
              2.149648875463337,
              1.887704115722052,
              1.5950048482071453,
              1.2961529400687861,
              1.0076880998359212,
              0.7374231555937725,
              0.4840701838815687,
              0.24046876472427314
            ],
            "metrics": {
              "initial_rmse_K": 0.021026841068600186,
              "observation_residual_rms_K": 0.019910995327165282,
              "future_predictive_rmse_K": 0.021527074175378802
            }
          }
        }
      },
      {
        "split": "train",
        "index": 54,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          4.536864262028001,
          -0.8287452937450923,
          0.02214853030056616,
          -0.3982640989576656,
          -0.11384324572692203,
          -0.06813836752039089,
          0.08520590954030745,
          -0.0437778860907326
        ],
        "initial_K": [
          0.05629902552252655,
          0.19783449425712002,
          0.4482357849095396,
          0.7685739683839701,
          1.0896257572016372,
          1.3352021644301546,
          1.4563431180491104,
          1.4788372655347082,
          1.4889825857063967,
          1.5336402536275777,
          1.558804011165908,
          1.488005500257579,
          1.3290582513131068,
          1.1376991242213825,
          0.8957013561612286,
          0.5174739650885701
        ],
        "observed_K": [
          0.18407760383872832,
          0.3565564947579093,
          0.5132553719921957,
          0.7264440406333507,
          0.9591204747645498,
          1.1900347127122384,
          1.2950963612035875,
          1.4076532319982218,
          1.426427704377903,
          1.407656802513955,
          1.4116575174478685,
          1.2675130226048714,
          1.137332886546145,
          0.9494992999602756,
          0.658007897921424,
          0.36893183018799536
        ],
        "future_observed_K": [
          0.17528180786840444,
          0.36378624328474374,
          0.5533163358568567,
          0.7061207774829136,
          0.9530630496092377,
          1.0668756842322156,
          1.230176060312211,
          1.2957395707093473,
          1.3523517225586128,
          1.3673287730870414,
          1.3185718949340808,
          1.2299511941128507,
          1.061284204742518,
          0.8629414491588573,
          0.5619645799469591,
          0.3001941849468204
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              4.550935633546557,
              -0.8173454720881583,
              -0.06442559447397231,
              -0.6077515481984564,
              0.11369987729674148,
              0.8990798419646231,
              5.470400370277241,
              7.274414880157539
            ],
            "initial_K": [
              4.629820499518212,
              1.8775049964079087,
              -3.324082223370158,
              -2.181577514060446,
              3.409494608848348,
              4.645107950415754,
              0.5561818279713706,
              -1.3816900712261668,
              1.6079272688683892,
              3.846281984417595,
              1.8417465855880562,
              -0.3222316819589124,
              0.8492227759187585,
              2.4235749534946387,
              1.261241734917788,
              -0.4077844068844505
            ],
            "metrics": {
              "initial_rmse_K": 2.285761083745072,
              "observation_residual_rms_K": 0.014106697823264121,
              "future_predictive_rmse_K": 0.020381695518226165
            }
          },
          "tikhonov": {
            "coefficients_K": [
              4.496162411999567,
              -0.7997318144095256,
              -0.06083090852406783,
              -0.49198726761882516,
              0.047564088131903805,
              0.0681430232046561,
              0.034253326967759644,
              0.002372321569379004
            ],
            "initial_K": [
              0.10566447007146182,
              0.2262679825465967,
              0.4037594675433893,
              0.6762799470149794,
              1.0190392966350952,
              1.337315732862643,
              1.5338775164744036,
              1.5832010583620817,
              1.538576837429178,
              1.4753185860325972,
              1.4327573224249064,
              1.3990724013794051,
              1.3301158409694116,
              1.174342319869284,
              0.8943229926409073,
              0.4877528889166788
            ],
            "metrics": {
              "initial_rmse_K": 0.06496104333063918,
              "observation_residual_rms_K": 0.02370591936816898,
              "future_predictive_rmse_K": 0.019906005133402113
            }
          },
          "learned": {
            "coefficients_K": [
              4.550675701199279,
              -0.8192411930204875,
              -0.06321429970763445,
              -0.466102582854343,
              0.014852245984716255,
              0.006739727884105875,
              0.0053415882966234085,
              -0.0006404591949734512
            ],
            "initial_K": [
              0.07385982621924303,
              0.20361376950912086,
              0.42137514955856914,
              0.7186066280365565,
              1.045168956706225,
              1.3298565166071796,
              1.515151434052068,
              1.5856474305495472,
              1.5706790453241002,
              1.5198264279411062,
              1.4693614621088518,
              1.4208946682737578,
              1.3412450433761594,
              1.180040263023086,
              0.8969981620260793,
              0.4885844983847469
            ],
            "metrics": {
              "initial_rmse_K": 0.051586312739052176,
              "observation_residual_rms_K": 0.020640508620712896,
              "future_predictive_rmse_K": 0.01916329829748235
            }
          }
        }
      },
      {
        "split": "train",
        "index": 55,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.977087635004515,
          0.4876261097338171,
          0.03789113637389908,
          -0.033390567803224885,
          0.06630603202985959,
          0.06963314141156367,
          0.02573758904930523,
          -0.025485033588200246
        ],
        "initial_K": [
          0.4755707264085351,
          0.8974743316210038,
          1.2390600312099906,
          1.5162781600266033,
          1.7626889378902855,
          1.974790040813269,
          2.099532302591121,
          2.0955243572922777,
          1.9888595032249488,
          1.8414161805372251,
          1.6777625922090265,
          1.4767223496562392,
          1.2270342735682382,
          0.9498613855886114,
          0.6600180490973055,
          0.3448116291964577
        ],
        "observed_K": [
          0.3880342421829139,
          0.7472975803931047,
          1.142372186370041,
          1.3215744336198887,
          1.5897482934215543,
          1.759614666929279,
          1.8309359319791305,
          1.901032406713803,
          1.8248812895896378,
          1.722789338405808,
          1.5532963131050066,
          1.393475889348664,
          1.1319546355552612,
          0.9035676731877695,
          0.6459912814832576,
          0.2900594745621198
        ],
        "future_observed_K": [
          0.387512773956833,
          0.7268460277372893,
          0.9906003256121458,
          1.2772028112534204,
          1.5171104000374391,
          1.6476532535492425,
          1.735275439384592,
          1.7745688215018605,
          1.7167465840149247,
          1.6835410047275554,
          1.498324876457257,
          1.3191131563473693,
          1.0847367526855656,
          0.8429362915970258,
          0.6008954851266849,
          0.25454464476694016
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.993713722928613,
              0.47368885942561795,
              0.07543552751656335,
              -0.0562234771431001,
              0.4634964301187493,
              0.38762296202133334,
              -1.3660822917529842,
              -6.70587972354104
            ],
            "initial_K": [
              -2.0580002688434034,
              0.445767856064741,
              3.799029264464467,
              2.602648662988977,
              -0.5765755896940705,
              0.24726829291487085,
              3.890561882542969,
              4.194780440026542,
              0.8820249242824965,
              -0.2508348065584749,
              2.2764917907552102,
              3.3876439280132464,
              0.8801480115993389,
              -0.8367991510546684,
              0.8983415647245295,
              2.1931403661071274
            ],
            "metrics": {
              "initial_rmse_K": 1.7107402478403364,
              "observation_residual_rms_K": 0.022352361199905173,
              "future_predictive_rmse_K": 0.02197162365479142
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.921575807548041,
              0.46348094404463575,
              0.07122653211494584,
              -0.045514050894084654,
              0.19389453687319674,
              0.029378703940196416,
              -0.008553827916970166,
              -0.0021869117134371086
            ],
            "initial_K": [
              0.4915059213154895,
              0.9174615495583021,
              1.2482734949051595,
              1.5014488543113589,
              1.7165664814777002,
              1.9110602235323486,
              2.0565454657309856,
              2.101456697802208,
              2.02013537582579,
              1.8399548562309531,
              1.6208133354996659,
              1.4092424098757341,
              1.2094392808242778,
              0.9908368070336221,
              0.7185450981417696,
              0.3811382364892112
            ],
            "metrics": {
              "initial_rmse_K": 0.03916370252695944,
              "observation_residual_rms_K": 0.028735484897489,
              "future_predictive_rmse_K": 0.02311582627314603
            }
          },
          "learned": {
            "coefficients_K": [
              5.993371384516829,
              0.47478751588960993,
              0.07401723001503756,
              -0.04311944246153322,
              0.06054503449634593,
              0.002905718895828262,
              -0.001333915013149652,
              0.0005904038194251126
            ],
            "initial_K": [
              0.45719113940494827,
              0.8808848532100787,
              1.2488785918661838,
              1.5530662653385339,
              1.7928301096154904,
              1.9657341901990988,
              2.0635810746189267,
              2.077131063813953,
              2.005821658676374,
              1.8639810522748945,
              1.6764349578564957,
              1.4649706345373388,
              1.2362528776022108,
              0.981683448055807,
              0.6892495361761923,
              0.35727425889551523
            ],
            "metrics": {
              "initial_rmse_K": 0.021977642631687607,
              "observation_residual_rms_K": 0.02443810754823299,
              "future_predictive_rmse_K": 0.021713865859398777
            }
          }
        }
      },
      {
        "split": "train",
        "index": 56,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          7.001561327593583,
          1.2998776154496294,
          0.2537780360637027,
          0.2802529678720732,
          -0.03539763744078141,
          0.000728669636222683,
          0.029826984354479932,
          0.016233024195489158
        ],
        "initial_K": [
          0.7188404653482491,
          1.3364636535834562,
          1.810052084274829,
          2.143951509960058,
          2.3449107335523505,
          2.418485095109365,
          2.3971314427804917,
          2.3320977437701194,
          2.244935087838998,
          2.1081929975032296,
          1.885756260925437,
          1.578818491020739,
          1.2252239740652537,
          0.8692093443141993,
          0.5418464678469335,
          0.2556631133953572
        ],
        "observed_K": [
          0.5574974679155199,
          1.0606658434415697,
          1.454637353513974,
          1.7891749625331514,
          2.035499358200959,
          2.1734879430518976,
          2.2201495492310843,
          2.1767870070906787,
          2.066483281717232,
          1.9094477889844423,
          1.724855074188887,
          1.433841786505341,
          1.189638882144154,
          0.9073462664962663,
          0.5879231699529327,
          0.3231645317422588
        ],
        "future_observed_K": [
          0.5116015249388897,
          0.9448086093044059,
          1.3240061848200706,
          1.6805159151113995,
          1.8675463946607183,
          2.0108841487248403,
          2.107456932182068,
          2.1272273505181776,
          2.0124757759444942,
          1.8406688933869935,
          1.6889162433802356,
          1.4243331203282121,
          1.1702965494089215,
          0.8954382772269849,
          0.5669642799613881,
          0.28834537409830446
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.989646233882391,
              1.3288561743425846,
              0.28515074329275925,
              0.18184274681022838,
              0.2019648761958359,
              0.40704093403811786,
              3.5394933115333154,
              5.644599622621088
            ],
            "initial_K": [
              3.9744581951430016,
              2.495680282403076,
              -0.8634375803578819,
              0.20159253234731012,
              4.147233680249351,
              4.663697556582727,
              1.4694101977161491,
              0.21670698792177556,
              2.5559306986690875,
              3.9132029483709463,
              1.916915824792297,
              0.058009928049458814,
              0.9383270998507041,
              1.9966493499801212,
              0.8229998460934203,
              -0.5444840713479948
            ],
            "metrics": {
              "initial_rmse_K": 1.662628744229135,
              "observation_residual_rms_K": 0.010476841408043431,
              "future_predictive_rmse_K": 0.023114965848252098
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.905521677410653,
              1.3002195469208775,
              0.2692404924229219,
              0.14720541050806543,
              0.0844879994536554,
              0.03085043009394459,
              0.022162805917988884,
              0.0018408085950361132
            ],
            "initial_K": [
              0.7194972804086704,
              1.3294547769456688,
              1.7811542060386563,
              2.09027488237228,
              2.2918679303623097,
              2.4028224124434083,
              2.4236203304910324,
              2.358374553328253,
              2.2206690777437674,
              2.024402947362395,
              1.7798536779754817,
              1.5002614248900683,
              1.2043925945302865,
              0.9072372216085183,
              0.610884537307903,
              0.30905709247234164
            ],
            "metrics": {
              "initial_rmse_K": 0.051666135723287016,
              "observation_residual_rms_K": 0.023888219441972267,
              "future_predictive_rmse_K": 0.03221084471142193
            }
          },
          "learned": {
            "coefficients_K": [
              6.989247011546917,
              1.331938274325741,
              0.2797894950840615,
              0.1394605644573347,
              0.02638201634734117,
              0.003051280881923219,
              0.0034561485026926844,
              -0.0004969658439625672
            ],
            "initial_K": [
              0.6974094915386799,
              1.3174484162316906,
              1.8071401978804362,
              2.1485503744208465,
              2.352326762034319,
              2.44227283322176,
              2.4420747675034953,
              2.369248390701147,
              2.234584172127369,
              2.0443558145129486,
              1.8045631835936007,
              1.5255832852900737,
              1.2230568901062544,
              0.912938682176317,
              0.6050224936732418,
              0.3013560612344592
            ],
            "metrics": {
              "initial_rmse_K": 0.040678663619853436,
              "observation_residual_rms_K": 0.013895253468024445,
              "future_predictive_rmse_K": 0.02361369867255687
            }
          }
        }
      },
      {
        "split": "train",
        "index": 57,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.712185026762046,
          -2.148883415573631,
          0.1371157158908792,
          0.13103311524614839,
          0.01344667994597199,
          -0.02182913564887371,
          0.0061897881029503825,
          -0.004702910910876542
        ],
        "initial_K": [
          0.14620743833205976,
          0.297347206533123,
          0.45748818388641344,
          0.6352755409202611,
          0.8473289314036915,
          1.1092560949207542,
          1.4199870931430167,
          1.7535797958707868,
          2.0626299468291034,
          2.288812913881418,
          2.379195127637193,
          2.3052966440529143,
          2.0710237439244676,
          1.6994812079424904,
          1.2134950003755374,
          0.6347817153625511
        ],
        "observed_K": [
          0.18756566303220842,
          0.3345121092078143,
          0.5329193505506999,
          0.7084953911248192,
          0.928979302104531,
          1.1939759100101561,
          1.4164239329115547,
          1.6319029825606763,
          1.8089185828623262,
          1.9847155357062496,
          1.9928984296640124,
          1.90779862821877,
          1.6977534815150028,
          1.3753334938380715,
          0.9678270195825518,
          0.5208210695724023
        ],
        "future_observed_K": [
          0.16815002433836185,
          0.32675136403440763,
          0.5052284479114494,
          0.76995310720107,
          0.9343840835519139,
          1.166378454957157,
          1.3977921157957933,
          1.5877604188551642,
          1.7484939043587262,
          1.816791532170041,
          1.8354720769687014,
          1.8012336190627574,
          1.5581030828926992,
          1.2574218109592246,
          0.8934220622138056,
          0.4637749155565172
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.693899752408902,
              -2.1363388827708607,
              0.16462171668778608,
              0.24491559343322783,
              -0.1054151941140389,
              0.1717673692668519,
              4.524313150336004,
              -0.8752352447685009
            ],
            "initial_K": [
              1.3980265958649873,
              1.1200462717746242,
              -0.2851619275585569,
              -0.6717393834887169,
              0.8426376603075469,
              2.5051306258617707,
              2.231623549960701,
              0.6878707499002358,
              0.5513296936734768,
              2.5570520650804363,
              4.109742582454306,
              2.9574994612204524,
              0.6530949644168902,
              0.3368042751231103,
              1.956357137248845,
              2.306610905922473
            ],
            "metrics": {
              "initial_rmse_K": 1.152092946769803,
              "observation_residual_rms_K": 0.010458638883243825,
              "future_predictive_rmse_K": 0.021564231228413586
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.625370276776216,
              -2.0903011385712813,
              0.15543649493145736,
              0.1982641656243219,
              -0.044098355270833604,
              0.013018585539830596,
              0.02832933005873203,
              -0.00028543044130032634
            ],
            "initial_K": [
              0.17059919874646032,
              0.3235444151140044,
              0.46855934851995273,
              0.6360237786495738,
              0.8473759935207412,
              1.1012753043723928,
              1.38685742132535,
              1.694790418640097,
              2.002573721635729,
              2.2544274142527487,
              2.3732729576372504,
              2.304362077496071,
              2.0473692157132493,
              1.645080975062692,
              1.1470612467652852,
              0.5891686710566011
            ],
            "metrics": {
              "initial_rmse_K": 0.036107320306404234,
              "observation_residual_rms_K": 0.022358094960666618,
              "future_predictive_rmse_K": 0.02999485320680117
            }
          },
          "learned": {
            "coefficients_K": [
              5.69357453824483,
              -2.141293828356196,
              0.1615265892702187,
              0.18783299033778025,
              -0.01377004470657585,
              0.0012876112600830217,
              0.004417778688631779,
              7.705808226663668e-05
            ],
            "initial_K": [
              0.1642036652142811,
              0.3210190791994589,
              0.47434566203996065,
              0.641068641898732,
              0.8428169856762301,
              1.094753671271595,
              1.3967892167045528,
              1.727808989554044,
              2.0438389571341804,
              2.2845801213471337,
              2.390560105495671,
              2.3240373136867,
              2.080910065357013,
              1.6866515875671366,
              1.181603713260168,
              0.6071865215120449
            ],
            "metrics": {
              "initial_rmse_K": 0.018586269925594378,
              "observation_residual_rms_K": 0.01430792693790126,
              "future_predictive_rmse_K": 0.02112553809741318
            }
          }
        }
      },
      {
        "split": "train",
        "index": 58,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.680715768509236,
          -0.03317899553262472,
          0.10313753826028263,
          -0.1760193851138685,
          -0.021400955484898454,
          0.07316451045795482,
          -0.008601005401304453,
          -0.022451892111355395
        ],
        "initial_K": [
          0.33796939464911785,
          0.6777501590716828,
          1.0047266373801034,
          1.3036302278384826,
          1.5714953828545364,
          1.7937048637151558,
          1.9270281882053135,
          1.9400330563882415,
          1.8637979531485505,
          1.7686533594303682,
          1.685706565902378,
          1.5774215951537,
          1.3911918353723347,
          1.115868873756083,
          0.776094339825091,
          0.39794660760490463
        ],
        "observed_K": [
          0.3433403006733418,
          0.6036847095636959,
          0.9056010826994795,
          1.1847019034943487,
          1.4289266404759013,
          1.6008194057072056,
          1.7003097027235163,
          1.7363750960536901,
          1.7355883552708793,
          1.6798480617754683,
          1.5326717583014644,
          1.4213583915842258,
          1.2299286792980306,
          0.9484854722061464,
          0.6847273693543426,
          0.3236156526061075
        ],
        "future_observed_K": [
          0.29990232899624975,
          0.6055336895980643,
          0.8728230307014472,
          1.1465293699972787,
          1.3440108829310355,
          1.467642086170717,
          1.6086197154370794,
          1.637834869698956,
          1.628834684201924,
          1.6120270457620223,
          1.485035261138417,
          1.3368677705076286,
          1.0896406756786787,
          0.9471690783505831,
          0.6420809308736387,
          0.3487200781256677
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.670544786372198,
              -0.029684850153820688,
              0.09570589550875365,
              -0.3295527779661336,
              -0.20208443763895712,
              0.5350463567106968,
              0.14726506593453922,
              16.7352497780952
            ],
            "initial_K": [
              6.168046536918915,
              1.7737032946379658,
              -4.65653878933343,
              -0.9532064453733056,
              6.706728646786646,
              5.020722590807383,
              -2.4480438941806066,
              -1.9287833328629351,
              5.534290167673051,
              6.156298874648463,
              -1.3566499087970314,
              -3.4221550560557144,
              3.6087960021581185,
              6.651576092138253,
              -0.38987124759542946,
              -5.432167383511731
            ],
            "metrics": {
              "initial_rmse_K": 4.191618006886054,
              "observation_residual_rms_K": 0.013169874569441586,
              "future_predictive_rmse_K": 0.024809641704996204
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.60229640166937,
              -0.029045146617548437,
              0.09036589607658183,
              -0.2667796918796285,
              -0.08453801561157043,
              0.04055221193841239,
              0.0009221113836186742,
              0.005457675245580801
            ],
            "initial_K": [
              0.2956393815551398,
              0.6077925912661207,
              0.9454558624841003,
              1.2934823672984956,
              1.6044689053668109,
              1.8203462585017984,
              1.911145077979867,
              1.8946397612686983,
              1.8200680019561106,
              1.7330986822216046,
              1.6482033423705627,
              1.5426809112151594,
              1.3750591554883078,
              1.1180491028216293,
              0.7805568610506229,
              0.39749951745991596
            ],
            "metrics": {
              "initial_rmse_K": 0.035782955099302294,
              "observation_residual_rms_K": 0.022340252935433496,
              "future_predictive_rmse_K": 0.024400868689640077
            }
          },
          "learned": {
            "coefficients_K": [
              5.67022090615605,
              -0.029753700100056863,
              0.09390648564247348,
              -0.25274374282084106,
              -0.02639763427064719,
              0.004010841619730401,
              0.0001437974004556348,
              -0.0014734167320858606
            ],
            "initial_K": [
              0.3057857108254044,
              0.6305272134316627,
              0.9745275562999159,
              1.3134446104696054,
              1.6071413255017701,
              1.8166742807057321,
              1.9212828827179664,
              1.9279543532610408,
              1.8669431051528391,
              1.773277435992882,
              1.665738597570822,
              1.5382582133346798,
              1.3679082995360887,
              1.1306928653560837,
              0.8149091424641723,
              0.4285083201924923
            ],
            "metrics": {
              "initial_rmse_K": 0.026713150905204857,
              "observation_residual_rms_K": 0.016573541095065276,
              "future_predictive_rmse_K": 0.024454488958285114
            }
          }
        }
      },
      {
        "split": "train",
        "index": 59,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.1579851709091615,
          0.5614883179398836,
          0.3751878822282224,
          -0.17225211741743487,
          -0.007075731033951284,
          0.040931961455446135,
          -0.03639750483567249,
          0.04797109798252143
        ],
        "initial_K": [
          0.5006310863967001,
          0.9544386050429577,
          1.3544327668637572,
          1.699572956001382,
          1.9537696666050295,
          2.080545390667326,
          2.095010259347314,
          2.0402125776317446,
          1.934138760774527,
          1.7847659764295192,
          1.6320466035951715,
          1.5105492725685146,
          1.3766457199569733,
          1.140743805695151,
          0.7841514927562059,
          0.3831924735834376
        ],
        "observed_K": [
          0.41724965411800696,
          0.8294677902311689,
          1.1927014715233109,
          1.4616029993959385,
          1.6606007058638041,
          1.8377395235139473,
          1.8548383699277535,
          1.8904850753200413,
          1.8251846588242011,
          1.7104057111178277,
          1.6205723410149977,
          1.3866626706461398,
          1.2311817049518252,
          0.9309051787143807,
          0.6582396930799557,
          0.3476217540501107
        ],
        "future_observed_K": [
          0.37858835027261684,
          0.7783254470883959,
          1.0817987197912557,
          1.354945028523441,
          1.6038149837423565,
          1.6954072572252958,
          1.8003284924816614,
          1.8127112961835463,
          1.7731631196992974,
          1.7106610759020846,
          1.549274693272376,
          1.3329339405636207,
          1.1567267576832418,
          0.8755649796373297,
          0.6135865827532534,
          0.3250293519183967
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.158116566928469,
              0.5747523658917548,
              0.4064328622393885,
              -0.06206531167382294,
              0.032322351661496336,
              0.015966007146200285,
              0.17034177633070652,
              -6.448252093488783
            ],
            "initial_K": [
              -1.6139725908928249,
              0.638811469135725,
              3.501169644053319,
              2.4621895520658663,
              -0.047090326850131925,
              0.9313183817436704,
              3.8541004009170727,
              3.4692528019864985,
              0.395589707731411,
              0.06752079968508906,
              2.9004249450451685,
              3.51837215710354,
              0.49001281692419785,
              -1.0703847936161448,
              1.219652790671864,
              2.6670721123977956
            ],
            "metrics": {
              "initial_rmse_K": 1.6251754852313318,
              "observation_residual_rms_K": 0.01767852267688515,
              "future_predictive_rmse_K": 0.019481925387915267
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.083999965378183,
              0.5623665489165435,
              0.3837555627685759,
              -0.05024313503573971,
              0.01352141461899237,
              0.0012100949711783668,
              0.0010666079566364472,
              -0.002102894566531167
            ],
            "initial_K": [
              0.5145165068234978,
              0.9893064897498975,
              1.3905835820133152,
              1.69689827988614,
              1.9019700852357135,
              2.0113507416136214,
              2.0373995260077935,
              1.997523492038395,
              1.9127769586670218,
              1.801481457043971,
              1.670800214637169,
              1.5146230377498509,
              1.3193741958514447,
              1.0715171410586455,
              0.7633301043020487,
              0.3990698630610666
            ],
            "metrics": {
              "initial_rmse_K": 0.040579561066754824,
              "observation_residual_rms_K": 0.024764437072113895,
              "future_predictive_rmse_K": 0.02833361330884624
            }
          },
          "learned": {
            "coefficients_K": [
              6.157764838443835,
              0.576085425323947,
              0.3987913340095298,
              -0.04759971761911861,
              0.00422216390285237,
              0.00011968519205807512,
              0.0001663307212060661,
              0.0005677215848723023
            ],
            "initial_K": [
              0.5219261096997603,
              1.0037752321332152,
              1.4122174052721874,
              1.72489553536717,
              1.9322636542464071,
              2.038123251482886,
              2.0581248809984762,
              2.014870648976582,
              1.9306779084316417,
              1.8210825965759403,
              1.6911124483688047,
              1.5346755145290296,
              1.337609664721725,
              1.0849040622086712,
              0.7699133095146282,
              0.40070351875868665
            ],
            "metrics": {
              "initial_rmse_K": 0.03681520260892456,
              "observation_residual_rms_K": 0.0179644496677416,
              "future_predictive_rmse_K": 0.019233260687904458
            }
          }
        }
      },
      {
        "split": "train",
        "index": 60,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.733654630870454,
          -0.8302207090270527,
          0.2355958066303669,
          0.07730134181066958,
          0.020706089467498127,
          -0.05698028509506873,
          -0.06345351261252874,
          0.009214450182150594
        ],
        "initial_K": [
          0.2892871860172772,
          0.5976796906857408,
          0.8997883758998438,
          1.1441185006181915,
          1.315668273629672,
          1.461003440667477,
          1.6349289918572942,
          1.829919058241867,
          1.9785610735128698,
          2.026180866058999,
          1.9772921872149127,
          1.859377559452008,
          1.6661592289676417,
          1.3661876237823019,
          0.9585968066926344,
          0.48799522327487616
        ],
        "observed_K": [
          0.26408638949639623,
          0.5471093051119921,
          0.771746606490309,
          1.0574058271946714,
          1.260929814791711,
          1.4505445041628109,
          1.6058860382701305,
          1.7103823098750044,
          1.7972627884067116,
          1.806081796630742,
          1.731819152000577,
          1.633535108345035,
          1.4358262166722662,
          1.1164508435763651,
          0.7755897430949041,
          0.40297920573141566
        ],
        "future_observed_K": [
          0.28946930834988177,
          0.5275558407046753,
          0.7853295631425911,
          0.9891013228399381,
          1.208702808466795,
          1.3813198840868688,
          1.5118725820090653,
          1.6542632583031414,
          1.705888340782918,
          1.6965041235452578,
          1.6169964393372926,
          1.546156271924024,
          1.3553709295565621,
          1.0643540892846335,
          0.7572159631187085,
          0.38394460513118456
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.757029426267817,
              -0.8112253258662409,
              0.1613007769682386,
              0.019282721334736113,
              -0.344133179303651,
              0.299275384117375,
              -1.3818385647112634,
              4.679050757708891
            ],
            "initial_K": [
              1.4357815974535733,
              0.5957554843409969,
              -0.4350206953145943,
              0.9065415051570929,
              2.722614060692514,
              2.0185845681513896,
              0.33816031254267553,
              1.1048856069322053,
              3.2662726091128684,
              3.000010892708878,
              0.711494280139783,
              0.5298430371650862,
              2.815211287911982,
              3.177572236945445,
              0.2038594511097962,
              -1.7519884069861515
            ],
            "metrics": {
              "initial_rmse_K": 1.2200238008941555,
              "observation_residual_rms_K": 0.011395667491477317,
              "future_predictive_rmse_K": 0.021981771331850888
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.68774014740105,
              -0.7937435563110237,
              0.15230085013154251,
              0.01560975600943132,
              -0.1439612887777515,
              0.022682667870664027,
              -0.008652487015555644,
              0.0015259252076768523
            ],
            "initial_K": [
              0.2564579176453811,
              0.530666490984224,
              0.8218129855983607,
              1.1068581805283118,
              1.354877812240755,
              1.547741742906982,
              1.6902812145198405,
              1.8022616003749183,
              1.8986959498978593,
              1.9718525476966278,
              1.9863923689325989,
              1.8937782598161252,
              1.6624157053207147,
              1.30455326959934,
              0.874224023137545,
              0.43097001602334184
            ],
            "metrics": {
              "initial_rmse_K": 0.05629521591323899,
              "observation_residual_rms_K": 0.020483092992594567,
              "future_predictive_rmse_K": 0.026794600946664887
            }
          },
          "learned": {
            "coefficients_K": [
              5.756700606373927,
              -0.8131068519572232,
              0.15826808804168488,
              0.014788487573948845,
              -0.044953000408090756,
              0.002243443304161784,
              -0.0013493002715467594,
              -0.0004119563058874165
            ],
            "initial_K": [
              0.281864862477722,
              0.5645534847929637,
              0.8426402828640995,
              1.104624939094493,
              1.3390267446812405,
              1.540243476711668,
              1.7091031541785517,
              1.8478842429553994,
              1.9530414514228898,
              2.0100633380040565,
              1.9947172407579332,
              1.8821506371589583,
              1.6595462652294253,
              1.3338656967396632,
              0.9290541985284326,
              0.47542988603057307
            ],
            "metrics": {
              "initial_rmse_K": 0.03748299704435032,
              "observation_residual_rms_K": 0.013669074472935196,
              "future_predictive_rmse_K": 0.021720017473431764
            }
          }
        }
      },
      {
        "split": "train",
        "index": 61,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.196892698692273,
          -0.6318120878261785,
          0.15480941725940475,
          0.16567557550451373,
          -0.023894484066107724,
          0.005946652677862525,
          -0.0980220000633031,
          -0.005920915079247767
        ],
        "initial_K": [
          0.2764147415664181,
          0.5777125251076924,
          0.8638743781554554,
          1.071089004824776,
          1.2021015425821746,
          1.3300052933372801,
          1.5037487741544047,
          1.6854308483807734,
          1.8012436258131332,
          1.8263490139317058,
          1.7858600085539051,
          1.6851900343549437,
          1.484232419074067,
          1.1580018818662456,
          0.7540286101030176,
          0.35680941624502405
        ],
        "observed_K": [
          0.22446634823695794,
          0.4972500657778478,
          0.7923289535896633,
          0.9703416512226074,
          1.1416041067795812,
          1.3364142231342664,
          1.4352521911605303,
          1.5580163286065796,
          1.6535610465741695,
          1.6012491919102567,
          1.5661423788589859,
          1.4293354200977695,
          1.2553672360582582,
          0.9931184175654006,
          0.7209391202876047,
          0.3391754728156258
        ],
        "future_observed_K": [
          0.26055372175044045,
          0.4708962184427962,
          0.7607390703369027,
          0.9181163072505716,
          1.0703221808150019,
          1.2483047044365216,
          1.4341085697239229,
          1.48417755898458,
          1.4911477550227301,
          1.5159987436589264,
          1.4726685186076967,
          1.343924754109765,
          1.1490397347648746,
          0.9276209508049931,
          0.6243216616220807,
          0.31190097886077617
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.205947925996402,
              -0.6213735617628293,
              0.1683549701731147,
              0.07140687192420596,
              0.04936147140653632,
              -0.8968941038342176,
              -4.977859453532229,
              -7.767272918023968
            ],
            "initial_K": [
              -4.2588548830234645,
              -1.0400366013702524,
              4.601625379570658,
              3.8191028970116054,
              -1.2802592529778392,
              -1.8309623270648319,
              2.7504846199014175,
              4.685021711747226,
              1.5152807305060674,
              -0.6207094739060497,
              1.583564604042569,
              3.510716879399091,
              1.717959549754902,
              -0.29384923186013445,
              0.668421326662761,
              1.7184644009921812
            ],
            "metrics": {
              "initial_rmse_K": 2.3032741285907816,
              "observation_residual_rms_K": 0.017417485957389844,
              "future_predictive_rmse_K": 0.02617960009952476
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.143291241289464,
              -0.6079830658450116,
              0.15896144806720108,
              0.057805318491308315,
              0.020649392348713023,
              -0.06797736182822699,
              -0.0311692446475817,
              -0.00253305171374589
            ],
            "initial_K": [
              0.26451948184997814,
              0.5477564683189952,
              0.8270169286098349,
              1.056577926866691,
              1.2224056086141488,
              1.3593867611180734,
              1.5074449364002707,
              1.6618688274864275,
              1.7762084766353323,
              1.807548940600626,
              1.7481187168173273,
              1.6145719203054643,
              1.4191056333665129,
              1.1584806960955412,
              0.8267842304048509,
              0.43194237539260694
            ],
            "metrics": {
              "initial_rmse_K": 0.041097335378815145,
              "observation_residual_rms_K": 0.02560353826833281,
              "future_predictive_rmse_K": 0.022847894321317074
            }
          },
          "learned": {
            "coefficients_K": [
              5.205650581807608,
              -0.6228147526766545,
              0.16518965216677414,
              0.05476403562620526,
              0.006447928818639331,
              -0.006723343043141521,
              -0.004860645290917964,
              0.0006838517519513523
            ],
            "initial_K": [
              0.2917319533610415,
              0.5699637952130825,
              0.8222568737945353,
              1.0413152482748194,
              1.2292440840161238,
              1.395522002166365,
              1.5472385393907244,
              1.6793094551058183,
              1.7741310598310955,
              1.8107515071228668,
              1.7740256261824157,
              1.6564313530037917,
              1.4555703699020648,
              1.1743370174211725,
              0.8239853385862896,
              0.4244237714845574
            ],
            "metrics": {
              "initial_rmse_K": 0.037392030643677854,
              "observation_residual_rms_K": 0.02134039072084961,
              "future_predictive_rmse_K": 0.02594281907824582
            }
          }
        }
      },
      {
        "split": "train",
        "index": 62,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.449216402660909,
          2.1452946615392077,
          0.4977116872914661,
          0.000595851330408854,
          0.009899100975606277,
          0.11179741125112118,
          -0.011096816764857206,
          0.020180673570462354
        ],
        "initial_K": [
          0.8025520025336064,
          1.4809697981908998,
          1.9834246434716132,
          2.3214551788479816,
          2.5108481519578203,
          2.547216236148251,
          2.431699205110111,
          2.195164676822903,
          1.8938487048410821,
          1.5920183265461683,
          1.3382070294550399,
          1.134857852094087,
          0.9347635926783298,
          0.6931299856185031,
          0.42536621628332016,
          0.18821473370492098
        ],
        "observed_K": [
          0.5723647373482305,
          1.1277796535006681,
          1.5625012240731133,
          1.9151345564701745,
          2.1011311106155897,
          2.200461723766221,
          2.1544641176423593,
          1.990438271196242,
          1.8416475437243518,
          1.6598941718815297,
          1.3991457361149802,
          1.1429591831266483,
          0.9087568294534182,
          0.6914396820831412,
          0.436634875228,
          0.2379341061888771
        ],
        "future_observed_K": [
          0.48234350662528713,
          1.037334477683473,
          1.4352350944975902,
          1.724850168361392,
          1.9231534266236423,
          2.012329204641845,
          2.0136176602493165,
          1.9260476560462316,
          1.7896310282980112,
          1.590499900409639,
          1.4077540328699423,
          1.126071026195475,
          0.8983294669432383,
          0.6745636705574317,
          0.44959201112659364,
          0.17213934627603034
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.4731198745960885,
              2.1465856763037445,
              0.4834115889564543,
              0.03649612990112379,
              -0.1824323637269816,
              -0.7469211121670439,
              2.4542053165249884,
              8.220994099630774
            ],
            "initial_K": [
              4.107796330696056,
              2.155610668102398,
              -1.2517781090793378,
              0.8707272419058262,
              5.4470217211057985,
              4.804772534654611,
              0.187451971205415,
              -0.5802335300856192,
              3.227310176560933,
              4.445328326610421,
              0.8699871224960178,
              -1.3496442275501752,
              0.9442815174869373,
              2.7401926075840017,
              0.5112591503645023,
              -1.5978462793008872
            ],
            "metrics": {
              "initial_rmse_K": 2.1521429831352714,
              "observation_residual_rms_K": 0.012648270099397375,
              "future_predictive_rmse_K": 0.023404875623458332
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.39521202057637,
              2.1003271154241263,
              0.4564391898496863,
              0.02954436114879682,
              -0.0763169603409094,
              -0.056610614878460495,
              0.0153671927944616,
              0.002681018603639121
            ],
            "initial_K": [
              0.7202608272378213,
              1.3902384549058464,
              1.9532837746585496,
              2.3493144145523424,
              2.5355458669513324,
              2.5163118110837366,
              2.351530283897719,
              2.123835196500441,
              1.8880907707670502,
              1.6513193310684469,
              1.3990726447736148,
              1.1325957567994258,
              0.8742363576185646,
              0.6419807984392951,
              0.4300412361980379,
              0.21905730177522165
            ],
            "metrics": {
              "initial_rmse_K": 0.0526076533010172,
              "observation_residual_rms_K": 0.024629337573283776,
              "future_predictive_rmse_K": 0.026273256193350542
            }
          },
          "learned": {
            "coefficients_K": [
              6.472750154305866,
              2.151564387923949,
              0.4743227488383149,
              0.027989958168805236,
              -0.02383054763176961,
              -0.0055991079011397495,
              0.0023964158944359756,
              -0.000723798594068777
            ],
            "initial_K": [
              0.7589532026410877,
              1.4453670992552339,
              1.996107403274332,
              2.367626274594405,
              2.544592992561816,
              2.542676717146447,
              2.402761800313499,
              2.177502442599223,
              1.9149190043633992,
              1.646384788969355,
              1.3849512848971544,
              1.1329406923507614,
              0.890559610028588,
              0.6583752700251392,
              0.4350559476863253,
              0.21677168258351126
            ],
            "metrics": {
              "initial_rmse_K": 0.033005040008293116,
              "observation_residual_rms_K": 0.015449440123018241,
              "future_predictive_rmse_K": 0.02326405136249513
            }
          }
        }
      },
      {
        "split": "train",
        "index": 63,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.93829240091501,
          -1.0912752182280652,
          0.3144760477294403,
          -0.12302081876389812,
          -0.09922380488295146,
          -0.06953930035785845,
          0.013717846567510834,
          0.011427651026838775
        ],
        "initial_K": [
          0.22732403220366734,
          0.48958539466954604,
          0.7960626096195866,
          1.1130413918117346,
          1.3809087457434157,
          1.5664084181120186,
          1.6956899018647351,
          1.821429345692973,
          1.9588940589875612,
          2.0679932804776717,
          2.0957466594931597,
          2.017358129831911,
          1.830912865931033,
          1.532310044381331,
          1.1145791486236805,
          0.5895035209776566
        ],
        "observed_K": [
          0.24389044921855244,
          0.5187737126325488,
          0.7951385092284827,
          1.052598643972154,
          1.2635644063489004,
          1.4769723777599806,
          1.609981123698549,
          1.731123710927907,
          1.8367567360537325,
          1.8610805086118742,
          1.8249833429123303,
          1.76786301305439,
          1.5270568998215606,
          1.2717200896495324,
          0.8777483649511203,
          0.42679493674355606
        ],
        "future_observed_K": [
          0.22897992496386216,
          0.5331760349769856,
          0.806742085859982,
          1.02876329728009,
          1.2236558334577283,
          1.3751506302103806,
          1.579859469989842,
          1.7217796061354729,
          1.773426257988509,
          1.822706467308176,
          1.709973690503856,
          1.6335377461172835,
          1.432906583576341,
          1.1555762859159395,
          0.8323904673136485,
          0.4043650118021258
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.951155285980013,
              -1.0798189164663894,
              0.3652552839753897,
              -0.1414698368700372,
              -0.5836940899727012,
              0.025287544721683628,
              -3.017553370331729,
              3.53394129668423
            ],
            "initial_K": [
              0.33399874359794013,
              0.043911710829220324,
              0.28655461770446333,
              1.683117670159227,
              2.4318825931020065,
              1.3008380036358926,
              0.3580218823647572,
              1.696194673945381,
              3.4213333000993944,
              2.578434071468729,
              0.5161493182436117,
              0.9348404623500399,
              3.330969827511067,
              3.3619986535403603,
              0.18028446741558043,
              -1.762481876125542
            ],
            "metrics": {
              "initial_rmse_K": 1.1684291473943782,
              "observation_residual_rms_K": 0.01289506061359904,
              "future_predictive_rmse_K": 0.026038413048272337
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.8795295867420965,
              -1.056549000134731,
              0.34487552577284575,
              -0.11452271688733362,
              -0.2441768434373553,
              0.0019165925720157223,
              -0.018894639375618402,
              0.0011524837806421134
            ],
            "initial_K": [
              0.20337121076811093,
              0.46776694600674895,
              0.7972847693388139,
              1.1340656811138623,
              1.4062971913594642,
              1.5825069064298112,
              1.6869808700615363,
              1.772163845675102,
              1.8768036796781054,
              1.9975278520926267,
              2.08444509650033,
              2.062236074879315,
              1.871746399328446,
              1.5097829422441589,
              1.0330848662977086,
              0.5161570159692971
            ],
            "metrics": {
              "initial_rmse_K": 0.04537469412795697,
              "observation_residual_rms_K": 0.02325880212872764,
              "future_predictive_rmse_K": 0.03575002299341882
            }
          },
          "learned": {
            "coefficients_K": [
              5.950815378346273,
              -1.0823234086217572,
              0.35838795403502915,
              -0.10849738936341614,
              -0.07624606472946571,
              0.00018956177452370422,
              -0.002946498734348323,
              -0.00031113776643830904
            ],
            "initial_K": [
              0.258699462030492,
              0.5345661076382016,
              0.8262208414162155,
              1.1113456308370542,
              1.3614933537248888,
              1.5606639160200655,
              1.7132427134764383,
              1.836903845734786,
              1.946232974869494,
              2.0371760505015053,
              2.0816440120824127,
              2.036714921022262,
              1.864370317025701,
              1.5500646056802052,
              1.108809927160007,
              0.5771480859822677
            ],
            "metrics": {
              "initial_rmse_K": 0.022613236858397424,
              "observation_residual_rms_K": 0.017999093425941564,
              "future_predictive_rmse_K": 0.0252989622593489
            }
          }
        }
      },
      {
        "split": "train",
        "index": 64,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.762544452662647,
          -0.18326696570810672,
          0.1910108859525244,
          -0.04211503431898649,
          0.08570932977497683,
          -0.020693709581435252,
          0.06412064942804202,
          -0.0488263803189397
        ],
        "initial_K": [
          0.38682216603483194,
          0.7470349402899793,
          1.051166732956382,
          1.2963339795985642,
          1.5126802162266384,
          1.7117284544971618,
          1.8564286191930452,
          1.9150686279959317,
          1.9126410490515973,
          1.8841557789147456,
          1.807028217202263,
          1.6388115808405237,
          1.4010729228351029,
          1.151937558695724,
          0.8779825450407788,
          0.497760295442321
        ],
        "observed_K": [
          0.31496498643024884,
          0.6325138061890697,
          0.911803508543832,
          1.2151529310617064,
          1.3778695400054697,
          1.590565340359865,
          1.6912467577898118,
          1.762218337217394,
          1.749026939510946,
          1.723315392539604,
          1.6335795153800592,
          1.4520674423983735,
          1.2276561375407828,
          1.0426964995216772,
          0.7151152668416193,
          0.36287381257224066
        ],
        "future_observed_K": [
          0.3114090138926925,
          0.5660404612042109,
          0.8903769423131925,
          1.1641197653985302,
          1.3487794322249145,
          1.4787172450324564,
          1.5897019724121242,
          1.6915605582716384,
          1.6777426122984835,
          1.648955387929524,
          1.5656312371028958,
          1.394978714055099,
          1.19149712120636,
          0.9332225196719462,
          0.6430699859129773,
          0.34234492759794366
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.758508177439589,
              -0.16427657301691057,
              0.17595149556253029,
              -0.1945042811591113,
              0.152841296521384,
              -0.7577566561981911,
              0.8549349293262654,
              -0.9169407788103185
            ],
            "initial_K": [
              0.10745844436842689,
              0.6027328296155806,
              1.1678415635799355,
              1.3839518702446247,
              1.474177087413412,
              1.7734108981647785,
              1.996898198498622,
              1.8104017285784175,
              1.6327917280814603,
              1.9524162956972637,
              2.253920246951243,
              1.725200580655964,
              0.793481465084322,
              0.6746785517390844,
              1.341917294120076,
              1.3297120149549584
            ],
            "metrics": {
              "initial_rmse_K": 0.3491601098276109,
              "observation_residual_rms_K": 0.017121533812811,
              "future_predictive_rmse_K": 0.018553737113555242
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.689201100921512,
              -0.16073644045295762,
              0.16613411825887447,
              -0.1574551806758819,
              0.06393812439185363,
              -0.05743186199566434,
              0.005353239925451182,
              -0.00029903138922532727
            ],
            "initial_K": [
              0.33379410728942877,
              0.6713317561798884,
              1.0019626153944496,
              1.3010847027689947,
              1.5449025712967883,
              1.72416523336963,
              1.8429790594105826,
              1.9054914897042023,
              1.9073357133193698,
              1.843402297217719,
              1.7226081767025896,
              1.567737296185917,
              1.3927579821045315,
              1.1794270290534652,
              0.8846468457849976,
              0.48186613610152307
            ],
            "metrics": {
              "initial_rmse_K": 0.04141351227697867,
              "observation_residual_rms_K": 0.024006482834316965,
              "future_predictive_rmse_K": 0.02429488395870496
            }
          },
          "learned": {
            "coefficients_K": [
              5.758179273084989,
              -0.16465759003944797,
              0.1726433518434946,
              -0.14917106849538644,
              0.019965162553641638,
              -0.005680333855540641,
              0.0008348036896305451,
              8.07299504785006e-05
            ],
            "initial_K": [
              0.3432378292239629,
              0.6826668346085172,
              1.0099130126728992,
              1.3101957162974365,
              1.5646917863716385,
              1.7562264139842274,
              1.8752191920656303,
              1.9226210201026563,
              1.9084988972839678,
              1.847003636397585,
              1.7493201721205005,
              1.6167891885966479,
              1.4377433121669982,
              1.1920242062031743,
              0.8637569942001537,
              0.4564142195864918
            ],
            "metrics": {
              "initial_rmse_K": 0.03800363888694754,
              "observation_residual_rms_K": 0.018403864658113812,
              "future_predictive_rmse_K": 0.01833642955678038
            }
          }
        }
      },
      {
        "split": "train",
        "index": 65,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.549390240569277,
          0.9366933001650856,
          0.5877593970290373,
          0.05942250102173068,
          -0.06873429415077123,
          0.04055234888607873,
          0.026383566434586586,
          0.0036112426608306577
        ],
        "initial_K": [
          0.6522743332161202,
          1.2221237090887824,
          1.6688343408350153,
          1.9884272114317698,
          2.18067479318023,
          2.2412271364256826,
          2.1875370486890344,
          2.072770631304096,
          1.9564491494518772,
          1.8600363779013434,
          1.756302143006003,
          1.6006210067787565,
          1.3687633325207633,
          1.0685969919425378,
          0.7259849921035333,
          0.3653214322751845
        ],
        "observed_K": [
          0.4995564610981763,
          0.9912915574932947,
          1.3736109650886446,
          1.6918494116543337,
          1.8890461827480598,
          2.002677889280029,
          2.00788085258475,
          1.9988486265722716,
          1.8698918698896712,
          1.7981666909369658,
          1.6336171880695343,
          1.4554203140347513,
          1.2045550928713369,
          0.9591108742078067,
          0.6207579846153312,
          0.34693042111661265
        ],
        "future_observed_K": [
          0.4620301188884828,
          0.8560282501218507,
          1.232270072160681,
          1.5448374702584604,
          1.7236171108793006,
          1.8214208419657685,
          1.9438545372016938,
          1.882407796368894,
          1.8428261104327492,
          1.7141248671155598,
          1.5959779756945105,
          1.3798309788686445,
          1.1535536544830187,
          0.9211830952458568,
          0.64410437110597,
          0.35551416519969187
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.569895412839519,
              1.0214739346913628,
              0.648390679082822,
              0.12401147888460545,
              -0.2972912584034297,
              0.06414905524669298,
              0.9254196123764287,
              -5.018992534812502
            ],
            "initial_K": [
              -0.7841656148470739,
              1.0617694842205396,
              3.156377091316529,
              2.4225586381599955,
              0.7972438611251149,
              1.7014834525381648,
              3.655592848949853,
              2.9057164303136496,
              0.46498920363475515,
              0.5714692250248059,
              3.0207256222447167,
              3.2797466756958737,
              0.5077614480696185,
              -0.8422548548675732,
              1.102517821980131,
              2.294311902894949
            ],
            "metrics": {
              "initial_rmse_K": 1.2772789856359923,
              "observation_residual_rms_K": 0.013834449379701717,
              "future_predictive_rmse_K": 0.02623876012822514
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.490822807563496,
              0.9994613429199373,
              0.6122131182364154,
              0.10038982019982227,
              -0.12436590040146478,
              0.004861982614002559,
              0.005794585116171434,
              -0.001636786524145849
            ],
            "initial_K": [
              0.6354719604887165,
              1.218700506731626,
              1.6989419221786415,
              2.0343978737245303,
              2.2053222126342105,
              2.2258223876401915,
              2.1445096566268016,
              2.0269032290234636,
              1.9232853246957569,
              1.841004672416511,
              1.7443061120420658,
              1.5853764834424835,
              1.3418459115549481,
              1.029771711101376,
              0.6857696722445293,
              0.3395328155951573
            ],
            "metrics": {
              "initial_rmse_K": 0.030069090174144216,
              "observation_residual_rms_K": 0.023734592311079848,
              "future_predictive_rmse_K": 0.023962906086556244
            }
          },
          "learned": {
            "coefficients_K": [
              6.5695201650941,
              1.0238431036486164,
              0.6361999924073181,
              0.09510805983636361,
              -0.038834192295475085,
              0.00048087739954267265,
              0.0009036286626832727,
              0.00044188570096433127
            ],
            "initial_K": [
              0.6677263861096232,
              1.2659124144665936,
              1.7387029878056213,
              2.0543883511715326,
              2.210962843435502,
              2.2352876748530695,
              2.1736729997225215,
              2.074387672292071,
              1.9689303553789752,
              1.8622501669023164,
              1.7372740312414612,
              1.5697212611108122,
              1.3434721916487868,
              1.0582712006156663,
              0.7274576693652026,
              0.36945663763974607
            ],
            "metrics": {
              "initial_rmse_K": 0.030392498527145373,
              "observation_residual_rms_K": 0.015299876729091473,
              "future_predictive_rmse_K": 0.025951386789759133
            }
          }
        }
      },
      {
        "split": "train",
        "index": 66,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.377151029532955,
          -0.022901057977835454,
          0.3716982183094127,
          0.02257113236419665,
          0.040942194019253045,
          -0.05918513030169778,
          0.04391371244828015,
          0.05596765320253615
        ],
        "initial_K": [
          0.4980538570729661,
          0.9154662687631491,
          1.2577746226006197,
          1.5606608650788967,
          1.7996083317991083,
          1.9291992626934822,
          1.9793769814196467,
          2.0280807299460024,
          2.0837998053842783,
          2.072573779106311,
          1.9510837821510334,
          1.7611487737261113,
          1.548277297774329,
          1.2889488937468658,
          0.935977650047964,
          0.4914121927959733
        ],
        "observed_K": [
          0.4061244483180046,
          0.7552860156992878,
          1.0637126647442112,
          1.377774996496634,
          1.5628975835475727,
          1.7858400688955438,
          1.8685751526695584,
          1.9238145585027415,
          1.9201154353022196,
          1.8507317358986886,
          1.7493199642889947,
          1.6033979968300758,
          1.3856888490197508,
          1.0936390279039376,
          0.7648924603869798,
          0.33804485352592795
        ],
        "future_observed_K": [
          0.381361711519516,
          0.7556942432461462,
          1.0053728915867233,
          1.2873656428149487,
          1.484412138506305,
          1.6558937660646051,
          1.7621875588273619,
          1.8399768777788386,
          1.8721968392880552,
          1.7909880322260654,
          1.6843799128465888,
          1.5382489233590817,
          1.3249826923014145,
          0.982696337155468,
          0.7140162347758091,
          0.37696658632150354
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.352319765471773,
              -0.008289707399657504,
              0.3313046534424943,
              -0.03352681844731359,
              -0.11926998526238711,
              1.5160932381648657,
              -1.433997031617197,
              12.135981773175168
            ],
            "initial_K": [
              4.556028623402669,
              1.7570222241536,
              -2.534236798749731,
              0.011562956219069331,
              5.10934858579092,
              3.8553008919050917,
              -0.9613382007683817,
              -0.11082134131596222,
              4.943070296489352,
              4.6291374619875185,
              -0.9206457671642463,
              -1.649051413423249,
              4.029194806234472,
              5.68771784097083,
              -0.5759627456342815,
              -4.647121469558498
            ],
            "metrics": {
              "initial_rmse_K": 3.06822159289913,
              "observation_residual_rms_K": 0.014373242968967711,
              "future_predictive_rmse_K": 0.024449446490542797
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.275865812731428,
              -0.008111065597164166,
              0.3128192022395746,
              -0.02714064299587765,
              -0.04989423230163529,
              0.11490767770183832,
              -0.008979081213445306,
              0.003957768672862717
            ],
            "initial_K": [
              0.4647611902308677,
              0.876134255800121,
              1.2174641115472384,
              1.5047106938780042,
              1.7499373244057872,
              1.9373652550126284,
              2.0389180708557397,
              2.050045111589033,
              2.0046743428447007,
              1.9488576360591043,
              1.893993445304014,
              1.7961621448902954,
              1.5904698697383581,
              1.2543982818768304,
              0.8350183006948658,
              0.4060486957747344
            ],
            "metrics": {
              "initial_rmse_K": 0.06148052334652087,
              "observation_residual_rms_K": 0.02551465060646789,
              "future_predictive_rmse_K": 0.030635218919130448
            }
          },
          "learned": {
            "coefficients_K": [
              6.3519569448299835,
              -0.008308934241154852,
              0.32507564467579375,
              -0.025712705659909973,
              -0.015579851111776203,
              0.011365014980022403,
              -0.0014002305577298958,
              -0.0010684847159132499
            ],
            "initial_K": [
              0.4504599260633516,
              0.8737981534234699,
              1.2464040213733205,
              1.5519296230149304,
              1.7831014038760955,
              1.9403526607520385,
              2.0298286476073932,
              2.0627266394754935,
              2.0528040874457627,
              2.0086916644182655,
              1.925505342775682,
              1.7852065696871158,
              1.5680802407031635,
              1.2663099684957217,
              0.889114738985375,
              0.45815297774607466
            ],
            "metrics": {
              "initial_rmse_K": 0.03430670890128284,
              "observation_residual_rms_K": 0.01913558200907959,
              "future_predictive_rmse_K": 0.024436329461698974
            }
          }
        }
      },
      {
        "split": "train",
        "index": 67,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.466717240808767,
          -1.8038748890594545,
          0.21080446742917136,
          -0.19346272688791696,
          -0.1845297818279423,
          -0.07289109513156321,
          0.03968065410954879,
          -0.02764378086439712
        ],
        "initial_K": [
          0.04515344325732723,
          0.1837662828296276,
          0.4339605319771972,
          0.7412570102839432,
          1.0361644031722588,
          1.2774476751210773,
          1.46441985107022,
          1.6335126526254866,
          1.8264986833495833,
          2.031707651881183,
          2.1653505252605476,
          2.1397971802882454,
          1.9428679865026832,
          1.6201592879037081,
          1.1929654743232865,
          0.6452236016819289
        ],
        "observed_K": [
          0.19557342743586714,
          0.3134341924906113,
          0.5736923845984928,
          0.7584031742254789,
          1.0078169181533418,
          1.2020904438561963,
          1.4040888381610217,
          1.5438427764565104,
          1.7290628336043292,
          1.827302899709851,
          1.8674577988999819,
          1.7570981489136284,
          1.606178486073481,
          1.2828994205460909,
          0.951151990757722,
          0.5012309158343453
        ],
        "future_observed_K": [
          0.15471857174010048,
          0.3697759647935252,
          0.551120337976707,
          0.7427013422943499,
          0.9855579775929072,
          1.1691525961855274,
          1.3712578305011118,
          1.5484287788276325,
          1.6393444825483832,
          1.7644009367395095,
          1.7308567070618064,
          1.6230201515216323,
          1.457399754243765,
          1.200807425016408,
          0.8219986949328596,
          0.43764864356738703
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.480430123959064,
              -1.7956221258168332,
              0.2870883419767329,
              -0.13724220621995775,
              -0.4014219094213302,
              -1.0933012472191679,
              3.821617221517365,
              1.5886460904183093
            ],
            "initial_K": [
              1.5008252201954582,
              0.6638899401217638,
              -0.889282748456779,
              -0.213998403036875,
              2.0864308691005053,
              2.767751424864007,
              1.0995634991458574,
              -0.05292853737950387,
              1.268420032768944,
              3.2802183745386593,
              3.357408756349583,
              1.7408109668771232,
              0.7021473769899997,
              1.19888651284439,
              1.9857460421810362,
              1.5954423215889055
            ],
            "metrics": {
              "initial_rmse_K": 1.061041715400734,
              "observation_residual_rms_K": 0.017363666122648374,
              "future_predictive_rmse_K": 0.019385984715409067
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.414469882478241,
              -1.7569267705180334,
              0.2710699809866444,
              -0.11110036369350022,
              -0.1679268925503093,
              -0.08286344413655163,
              0.02392934618561041,
              0.00051808694561663
            ],
            "initial_K": [
              0.08349582539169242,
              0.23645305890462204,
              0.4791028729422009,
              0.7685438447870216,
              1.0342351362408526,
              1.2379196430812258,
              1.404426576945699,
              1.5896413935404996,
              1.8137361124521223,
              2.0275654500270917,
              2.146765859660549,
              2.1147324073296714,
              1.9281031541642788,
              1.6087081764000648,
              1.169605396889965,
              0.6207552201599529
            ],
            "metrics": {
              "initial_rmse_K": 0.03237060921897235,
              "observation_residual_rms_K": 0.026568350283373877,
              "future_predictive_rmse_K": 0.027430300156603585
            }
          },
          "learned": {
            "coefficients_K": [
              5.480117102378245,
              -1.7997868255266973,
              0.28169066409805193,
              -0.10525509475931788,
              -0.05243644130608881,
              -0.008195660226915303,
              0.0037316292122869005,
              -0.0001398687059961854
            ],
            "initial_K": [
              0.1332407758447443,
              0.2947905962681138,
              0.49751215148724803,
              0.7331469608976734,
              0.9801519459482171,
              1.219294217228525,
              1.4445538405823783,
              1.6597557052391156,
              1.8634326836217552,
              2.035396825470148,
              2.1371944931765317,
              2.1259513342534255,
              1.970349074777717,
              1.6592147550892276,
              1.2029652076611312,
              0.6330175737457984
            ],
            "metrics": {
              "initial_rmse_K": 0.047883096756741524,
              "observation_residual_rms_K": 0.021863947180425145,
              "future_predictive_rmse_K": 0.019175634522315146
            }
          }
        }
      },
      {
        "split": "train",
        "index": 68,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.497213537212789,
          1.8426262619163172,
          0.6448388993575288,
          -0.3163491971866164,
          0.13514075224614613,
          0.06290629675936818,
          -8.753881532577522e-05,
          -0.0022427274396822658
        ],
        "initial_K": [
          0.7366456912892974,
          1.3824137027213395,
          1.8861089032425993,
          2.2423834925224244,
          2.461925622189349,
          2.539109034655574,
          2.4548964176359607,
          2.2150088036706626,
          1.880595472474757,
          1.5510099678838614,
          1.3068820950469138,
          1.1623544301116113,
          1.064570854789038,
          0.9342249458704015,
          0.7127749855607736,
          0.3891288114184478
        ],
        "observed_K": [
          0.5689502857672781,
          1.102866165464152,
          1.4685916397558438,
          1.8476040184914067,
          2.0392022312782982,
          2.15341042814009,
          2.126360974254059,
          1.9856158192421365,
          1.857140681909282,
          1.6179836774420893,
          1.4045435840077252,
          1.2523872701983476,
          1.029802136245881,
          0.7519142986873631,
          0.5331772235243573,
          0.2874619950929445
        ],
        "future_observed_K": [
          0.48877388816779593,
          0.925197284665319,
          1.3501530706365892,
          1.6691858843145841,
          1.898854552380154,
          1.9697936607638709,
          2.000922842488648,
          1.925994376885215,
          1.7886296279704303,
          1.6297651086478184,
          1.4205044934279067,
          1.2014963001540793,
          0.9613721497162104,
          0.7625677294805354,
          0.5651670253567852,
          0.2413582365566903
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.47187166173431,
              1.8258690062172536,
              0.6164230462283772,
              -0.2610293732907668,
              -0.00893778550170209,
              1.2290983846515393,
              2.0275630492834433,
              1.2406940695316433
            ],
            "initial_K": [
              2.152687522783782,
              2.101704714888742,
              0.9118830717088107,
              1.0912250862764856,
              2.725103465033582,
              3.605014185448967,
              2.7333268379552664,
              1.5319369228598076,
              1.3666232856729812,
              1.7533015281064208,
              1.6806062822228358,
              1.2322649113642385,
              0.9953591523952607,
              0.9071034983799511,
              0.606934880625369,
              0.2186150735487955
            ],
            "metrics": {
              "initial_rmse_K": 0.6634103254906019,
              "observation_residual_rms_K": 0.0198353379378643,
              "future_predictive_rmse_K": 0.021338012428063984
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.3939788307,
              1.7865218357247408,
              0.5820291491822326,
              -0.21130859890733364,
              -0.0037389452602267117,
              0.09315577531256754,
              0.012695739868000516,
              0.00040461334012980974
            ],
            "initial_K": [
              0.7125140915806963,
              1.3381859577293709,
              1.8346003046301584,
              2.19963938880269,
              2.4304710820037045,
              2.5020443193592756,
              2.395408290601888,
              2.1426305744681295,
              1.8316188464031793,
              1.557072610446316,
              1.361385291589052,
              1.2182054051021312,
              1.0675242567089023,
              0.8652255654476018,
              0.6058327745037313,
              0.3099719540917991
            ],
            "metrics": {
              "initial_rmse_K": 0.055428289951027464,
              "observation_residual_rms_K": 0.0291578730908118,
              "future_predictive_rmse_K": 0.025298560873869027
            }
          },
          "learned": {
            "coefficients_K": [
              6.471502012737318,
              1.8301038594255719,
              0.6048333974895034,
              -0.20019112325148308,
              -0.0011675139145793465,
              0.009213629611853113,
              0.001979819816034713,
              -0.00010923406735406913
            ],
            "initial_K": [
              0.7007063425870692,
              1.3445655560480905,
              1.881065914475064,
              2.2699628294532914,
              2.484572150517082,
              2.517923473992311,
              2.3904756972813455,
              2.151637859417643,
              1.8679640952843235,
              1.6002851451174258,
              1.381728742245014,
              1.209087161623978,
              1.051163893471246,
              0.8679223180369491,
              0.6304945525315613,
              0.3341241279540208
            ],
            "metrics": {
              "initial_rmse_K": 0.04833651768452537,
              "observation_residual_rms_K": 0.022315482958868225,
              "future_predictive_rmse_K": 0.02105820888480732
            }
          }
        }
      },
      {
        "split": "train",
        "index": 69,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.206728794943119,
          1.327734962552261,
          0.40632531128126614,
          0.026763285026096255,
          -0.0999501113164358,
          0.006184004824409791,
          -0.02261571401249786,
          0.04209796148873313
        ],
        "initial_K": [
          0.6167052843400225,
          1.1770377109166374,
          1.653045220770125,
          2.0183311105790724,
          2.22663649473472,
          2.2584305037086887,
          2.1667417321332545,
          2.0330165424708286,
          1.8895086590048416,
          1.7225140205145377,
          1.5325048437103281,
          1.3372593115004747,
          1.1225368242435463,
          0.8516186434883879,
          0.5364501587588646,
          0.24275771515494812
        ],
        "observed_K": [
          0.5082687963519638,
          0.9504503010685991,
          1.3571125887481161,
          1.638411535897856,
          1.8661102822473397,
          1.9646232204488014,
          1.978994368404641,
          1.928402063869054,
          1.8446547746861846,
          1.6739795437308964,
          1.4824136639225665,
          1.2529133713638558,
          1.0502800392647857,
          0.7881914915177597,
          0.5385019350168608,
          0.2627511066886445
        ],
        "future_observed_K": [
          0.45181853054677656,
          0.864897730155378,
          1.2231869951431265,
          1.514069722190687,
          1.7113613074173208,
          1.822875545184374,
          1.867990822973182,
          1.830290540531333,
          1.7795972846973207,
          1.58948115552698,
          1.4148481723626403,
          1.246474118344028,
          1.0143219679395266,
          0.7671383430527321,
          0.5091850798038375,
          0.2560344927991753
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.233430669565139,
              1.3294212408963053,
              0.3533906182005096,
              0.07948601175889641,
              0.1121191135968705,
              -0.15344973399616754,
              -0.5439022443504168,
              12.047427819698123
            ],
            "initial_K": [
              4.55850946354909,
              1.8712740048837866,
              -2.1490694266274786,
              0.7008186010695784,
              5.83612527673972,
              4.173952171621601,
              -1.2199159213900144,
              -0.5419923265229039,
              4.933280874773729,
              5.048805285367779,
              -0.8140295822597359,
              -2.481296113382106,
              2.6669369164742798,
              4.920684248020078,
              -0.2320023135287428,
              -3.9426512354533787
            ],
            "metrics": {
              "initial_rmse_K": 3.0049588031612373,
              "observation_residual_rms_K": 0.0075442868437078335,
              "future_predictive_rmse_K": 0.015709458078613736
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.158407617921618,
              1.3007724363852489,
              0.33367286005725116,
              0.06434554688523388,
              0.04690280699665554,
              -0.011630256064467066,
              -0.003405685169856943,
              0.003928889586730249
            ],
            "initial_K": [
              0.6339128944739199,
              1.1999828565745974,
              1.6489869168246265,
              1.958630669363247,
              2.1321796074664983,
              2.19192184183747,
              2.1671800190021617,
              2.079560249543415,
              1.9375576383158786,
              1.7470409257001678,
              1.5237519825638839,
              1.28937041091356,
              1.055303694727668,
              0.8161138220318076,
              0.560748242694117,
              0.28628960595996944
            ],
            "metrics": {
              "initial_rmse_K": 0.045731382692468674,
              "observation_residual_rms_K": 0.02018313336603412,
              "future_predictive_rmse_K": 0.014371890092341607
            }
          },
          "learned": {
            "coefficients_K": [
              6.233074639421888,
              1.3325046514739787,
              0.3467463612123632,
              0.06096016619198206,
              0.014645755952603734,
              -0.0011502976740783092,
              -0.0005310949229082022,
              -0.0010606881859256177
            ],
            "initial_K": [
              0.6377615888297758,
              1.2118562682360068,
              1.6720750861273015,
              1.992189851174585,
              2.1725614044512773,
              2.2326592087450843,
              2.198829276263278,
              2.0955222881838456,
              1.9425903027869975,
              1.7552618648981593,
              1.5440891649312405,
              1.3154998232671093,
              1.073292629991541,
              0.8195980988301836,
              0.5551608547479217,
              0.2808120268681982
            ],
            "metrics": {
              "initial_rmse_K": 0.03620457123835566,
              "observation_residual_rms_K": 0.009736085211406644,
              "future_predictive_rmse_K": 0.01576947808094891
            }
          }
        }
      },
      {
        "split": "train",
        "index": 70,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.245093694265876,
          -0.8208339197142636,
          0.21421614597808197,
          0.2592311603843375,
          0.06369355437158461,
          -0.016109070167473028,
          -0.05800900167360918,
          -0.010577263878233212
        ],
        "initial_K": [
          0.3171896563316251,
          0.6199891014156165,
          0.8649708091067385,
          1.0195791263878555,
          1.119678401379672,
          1.2483105351695922,
          1.4472869925299305,
          1.6718235581069585,
          1.8404597696530738,
          1.9081154263815903,
          1.876518266599084,
          1.7539367645691688,
          1.5343381122471573,
          1.2181041932729755,
          0.8324180825799645,
          0.4179134512982583
        ],
        "observed_K": [
          0.2675330598454578,
          0.4943019367958419,
          0.7184287483183331,
          0.9025519416664141,
          1.1259977421440501,
          1.2856505985012083,
          1.426170473176372,
          1.577300912779268,
          1.6435078046103897,
          1.6657369258068029,
          1.6261464656133646,
          1.517565878084598,
          1.3069393125722157,
          1.0433494910255596,
          0.7597361023315744,
          0.40556810040705615
        ],
        "future_observed_K": [
          0.2835923972712699,
          0.5281137709368253,
          0.7017320783244405,
          0.9142647539325258,
          1.0775615776218312,
          1.2165857218284848,
          1.4055260099713214,
          1.508598559948706,
          1.5490532873264162,
          1.5606186769821266,
          1.5281078598179316,
          1.398352506851397,
          1.246862138132137,
          0.9857840632486415,
          0.6861735354526004,
          0.33589509078590446
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.258338052502825,
              -0.8698442669675253,
              0.19464830696447077,
              0.1349435750940384,
              0.29900196721094613,
              -0.23155082198413768,
              3.223834981086765,
              -4.1028335222502035
            ],
            "initial_K": [
              -0.036995112761736726,
              0.9151759293954024,
              1.446040780955013,
              0.5206961990972274,
              0.04692981196707047,
              1.5820740299828078,
              2.953498514944792,
              1.7757832909501818,
              0.10635805276482369,
              1.262619718332442,
              3.68632890026843,
              3.082035173173384,
              -0.07165174250983908,
              -0.8299460861928888,
              1.8689259277603867,
              3.0609007565646285
            ],
            "metrics": {
              "initial_rmse_K": 1.3142786552965038,
              "observation_residual_rms_K": 0.00976434447942581,
              "future_predictive_rmse_K": 0.022733543284060777
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.1950508214122255,
              -0.8510992690745967,
              0.18378772368338744,
              0.10923957493819893,
              0.12508154149469458,
              -0.017549690582589147,
              0.020186287332323673,
              -0.0013380100833889476
            ],
            "initial_K": [
              0.3154450076802436,
              0.580784444114325,
              0.7817744920116798,
              0.9441336966533875,
              1.106441018088876,
              1.2900726627747294,
              1.4889340985900428,
              1.6764978055127246,
              1.8165698075185293,
              1.8746278022797502,
              1.8329036574744546,
              1.7001628875973527,
              1.4998116289018255,
              1.2415183504882372,
              0.9092790806526522,
              0.48756128507621543
            ],
            "metrics": {
              "initial_rmse_K": 0.04796748408228926,
              "observation_residual_rms_K": 0.019328630848452304,
              "future_predictive_rmse_K": 0.02716817016224344
            }
          },
          "learned": {
            "coefficients_K": [
              5.258037715986815,
              -0.8718617516677757,
              0.19098863603046268,
              0.10349220676998028,
              0.039057656635292655,
              -0.0017357630086600635,
              0.003147923011043793,
              0.00036122457930438354
            ],
            "initial_K": [
              0.29308293273103403,
              0.557018697364556,
              0.7793801323114522,
              0.9685428301423702,
              1.1439357733440745,
              1.321496333137861,
              1.5034684721852447,
              1.6757517700590088,
              1.8120910808042618,
              1.8832590271912784,
              1.8673688013129186,
              1.7555462969253184,
              1.549982638482607,
              1.2581345953021124,
              0.8901632949524781,
              0.4621288484702953
            ],
            "metrics": {
              "initial_rmse_K": 0.04488796164203183,
              "observation_residual_rms_K": 0.013251181420261032,
              "future_predictive_rmse_K": 0.023543547745350807
            }
          }
        }
      },
      {
        "split": "train",
        "index": 71,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.288608665228962,
          0.5489715885836521,
          0.6695802667182214,
          0.0760059690952995,
          -0.2555926561992148,
          0.05907380398292514,
          -0.11685518656688304,
          -0.030607668904301926
        ],
        "initial_K": [
          0.5020023032416576,
          1.046408401468744,
          1.555252643486518,
          1.8950372140491543,
          2.0285315487641946,
          2.0347768239683646,
          1.993664046771823,
          1.9233064630736167,
          1.837464324334768,
          1.7849805896715643,
          1.7808139310614624,
          1.739860782052062,
          1.5418640733152444,
          1.1637846602585586,
          0.7123022133985603,
          0.3154667904504298
        ],
        "observed_K": [
          0.45161885734356516,
          0.8882507882814101,
          1.258557405832929,
          1.5131394830739031,
          1.6898396271118883,
          1.8340185924683332,
          1.883725750797283,
          1.8762618201493944,
          1.8281380159929388,
          1.7328854308325012,
          1.6318577130052077,
          1.489234668532248,
          1.2393375131895932,
          1.0206190569051894,
          0.660178795445886,
          0.34461872921866277
        ],
        "future_observed_K": [
          0.4131084669142277,
          0.7920490666597071,
          1.1397196929289612,
          1.4131288597115366,
          1.6107565181224865,
          1.716538799764114,
          1.7997188606507886,
          1.8424211160439692,
          1.7645522611071764,
          1.7397963358664879,
          1.5622919202633914,
          1.363878578176629,
          1.1921744745520564,
          0.924902394262075,
          0.6559750632121059,
          0.3432597996650202
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.271671894703931,
              0.5703456138486496,
              0.6531271609258791,
              0.1446091331841569,
              -0.0841009965911951,
              1.0076638006664118,
              -1.4199745559480517,
              -8.756025492079184
            ],
            "initial_K": [
              -2.555271705955274,
              0.5986271693903906,
              4.713043812245122,
              3.035564799507194,
              -1.022414065771652,
              0.07117654329535306,
              4.536296177508646,
              4.5126520052833,
              0.066088310078531,
              -1.0625316669830283,
              2.7667133995314925,
              4.496057235932913,
              1.1227870002415854,
              -1.3666257232236323,
              0.7883394382407072,
              2.5987375736101046
            ],
            "metrics": {
              "initial_rmse_K": 2.2187551331338145,
              "observation_residual_rms_K": 0.012434227175680386,
              "future_predictive_rmse_K": 0.01958670291748593
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.196188587133847,
              0.5580547616400058,
              0.6166853236708149,
              0.11706404124990895,
              -0.03518198356014573,
              0.07637281423333822,
              -0.008891278418132108,
              -0.002855502260883147
            ],
            "initial_K": [
              0.6079772162270157,
              1.133530811712648,
              1.526642920768166,
              1.782799718714465,
              1.9283138798246289,
              1.9917713518672324,
              1.9900114742308879,
              1.9395109358808975,
              1.8692769630293302,
              1.8066367465370703,
              1.7456174218114164,
              1.6394300487385758,
              1.4365380009923177,
              1.1276121643513901,
              0.7542130860423896,
              0.37063621850099815
            ],
            "metrics": {
              "initial_rmse_K": 0.06819738069655196,
              "observation_residual_rms_K": 0.023157462142360672,
              "future_predictive_rmse_K": 0.0269906903527054
            }
          },
          "learned": {
            "coefficients_K": [
              6.271313680365558,
              0.5716684524227382,
              0.6408474215110997,
              0.11090500827396231,
              -0.010985840254446873,
              0.0075537004592554835,
              -0.0013865382707208924,
              0.0007709042074463869
            ],
            "initial_K": [
              0.6065456170090363,
              1.1420291775511207,
              1.5553589890413606,
              1.8266153775685203,
              1.9666991094416653,
              2.008172771040816,
              1.9915196129194956,
              1.9509293817157378,
              1.9039816793133186,
              1.8484398178867794,
              1.766246897611725,
              1.6325769198630216,
              1.4273222656686073,
              1.145058052135779,
              0.7978438037124655,
              0.4084605691945529
            ],
            "metrics": {
              "initial_rmse_K": 0.07056124224850925,
              "observation_residual_rms_K": 0.015378785255594427,
              "future_predictive_rmse_K": 0.018721810119686603
            }
          }
        }
      },
      {
        "split": "train",
        "index": 72,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.49909087709581,
          1.2288457085998097,
          0.4185488463619528,
          -0.18114565881429376,
          0.14566618937382295,
          0.046585155402078283,
          -0.024785092062452472,
          0.02749656699718665
        ],
        "initial_K": [
          0.6509748108433617,
          1.2139332188758243,
          1.6559441957767094,
          1.9871542014426349,
          2.215250869857936,
          2.3338211925758863,
          2.339354905039204,
          2.235040430465285,
          2.031137686546825,
          1.767576875929741,
          1.5201124309784977,
          1.3436772818240608,
          1.208153750243505,
          1.0245184346203116,
          0.7407869284308309,
          0.38278270112874635
        ],
        "observed_K": [
          0.486549710711954,
          0.9442501454659867,
          1.3420104816268854,
          1.6675909591471103,
          1.912120620232448,
          2.0321743739103946,
          2.057197065333146,
          2.0053686055860176,
          1.8834836114781868,
          1.7526617485367484,
          1.6092128348501675,
          1.345270104990041,
          1.0905376513921619,
          0.9240814588676228,
          0.6174735924960786,
          0.30523572580709324
        ],
        "future_observed_K": [
          0.4379278748888713,
          0.8388999372871462,
          1.2809298255652677,
          1.5852812795376208,
          1.7930544009525848,
          1.9009322952943062,
          1.963803714289421,
          1.9086727379107786,
          1.8775746250206893,
          1.7183187230070505,
          1.5150304226852533,
          1.3573677268688737,
          1.070059923471949,
          0.8623253516733282,
          0.5542499593137286,
          0.35114807283120775
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.495050415850204,
              1.1706705744345287,
              0.39421577186929,
              -0.22424937862967642,
              -0.06010561349135286,
              -0.8436063628095413,
              3.689089823391977,
              6.665887609062498
            ],
            "initial_K": [
              3.7919681515896846,
              1.9552343968916546,
              -1.4003620097352705,
              0.3249756730494212,
              4.74801099810173,
              4.736734467197941,
              0.6724976739019242,
              -0.5310787514571107,
              2.6510861343843652,
              4.33741035087539,
              1.7497120868703397,
              -0.5886304473546962,
              0.6488494676412757,
              2.2953796218317226,
              1.1889621728081878,
              -0.4297136113324731
            ],
            "metrics": {
              "initial_rmse_K": 1.9154264569166988,
              "observation_residual_rms_K": 0.017289085418975187,
              "future_predictive_rmse_K": 0.02912701576045376
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.416878614701481,
              1.1454428201290467,
              0.37222013631575573,
              -0.1815344434486034,
              -0.02514399105166656,
              -0.0639385795046977,
              0.02309951582715251,
              0.002173869543400683
            ],
            "initial_K": [
              0.5534640781055795,
              1.090563984364508,
              1.5826531012744371,
              1.9827061826331327,
              2.238682614271252,
              2.326355665185881,
              2.2723493673980375,
              2.1373804182799647,
              1.9721048173759865,
              1.7920845258228835,
              1.594581696719387,
              1.38646981609905,
              1.1815250439750211,
              0.9720162327535034,
              0.7199245706000792,
              0.39128689651944876
            ],
            "metrics": {
              "initial_rmse_K": 0.061332692554168206,
              "observation_residual_rms_K": 0.027094924452025586,
              "future_predictive_rmse_K": 0.0395073492091753
            }
          },
          "learned": {
            "coefficients_K": [
              6.49467944296985,
              1.1733857845734526,
              0.3868039426859982,
              -0.17198346082804625,
              -0.007851401231559963,
              -0.006323884777810782,
              0.0036022224502782457,
              -0.00058688280531385
            ],
            "initial_K": [
              0.5817182093173576,
              1.132181123517606,
              1.616803461218126,
              1.9990201072238336,
              2.2479831407111313,
              2.3498073012321097,
              2.315866272409467,
              2.1814058752549883,
              1.9928926080711655,
              1.790509352636663,
              1.595757678922837,
              1.409104548031829,
              1.214878545873831,
              0.9892197509707165,
              0.7109115371268782,
              0.374708414536713
            ],
            "metrics": {
              "initial_rmse_K": 0.04482499696143697,
              "observation_residual_rms_K": 0.020166237730929862,
              "future_predictive_rmse_K": 0.02946496625190714
            }
          }
        }
      },
      {
        "split": "train",
        "index": 73,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.098658487778355,
          -2.1863613725148254,
          0.20217555465863524,
          -0.12905321509168258,
          -0.09908847908059532,
          -0.05217071029868647,
          -0.013076750696024942,
          -0.011874075594050537
        ],
        "initial_K": [
          0.005619577884126092,
          0.09445399478664374,
          0.28101613747258847,
          0.5192541922872994,
          0.7640851084393991,
          1.0066940480530064,
          1.2577585066113652,
          1.5193394778084546,
          1.7763049154539505,
          1.997205311994806,
          2.1356517263245705,
          2.1432374408700365,
          1.9915898981933107,
          1.679847775742001,
          1.2230929133310147,
          0.6472109738627816
        ],
        "observed_K": [
          0.08664200357049348,
          0.23873002265626897,
          0.4333835898905624,
          0.5636129197884913,
          0.7887874426972941,
          1.01652435918067,
          1.2543803520673793,
          1.4541602214656644,
          1.5991623464205242,
          1.7366857183655129,
          1.7862024460453667,
          1.7849424165274257,
          1.572325625979683,
          1.3324592339684729,
          0.9544158032175689,
          0.5329146222622986
        ],
        "future_observed_K": [
          0.12999852641499218,
          0.2866076844574744,
          0.4508370734771492,
          0.6091363780955381,
          0.8224748335949985,
          0.9951253728476832,
          1.202650339157247,
          1.3903029693222084,
          1.555846091534781,
          1.6372239574804222,
          1.7071145643550167,
          1.6072196703375388,
          1.4559449655923826,
          1.1759553390775739,
          0.8488502483881009,
          0.45228307618488295
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.070421865726604,
              -2.191619647152249,
              0.2667702189454421,
              -0.2783303510987776,
              -0.05105029577229301,
              0.015304383003822053,
              1.2940355254677338,
              -30.586189771876974
            ],
            "initial_K": [
              -9.996723632047233,
              -1.5980379223306103,
              10.041735180216886,
              3.8752444985522096,
              -8.547529026099319,
              -4.035199139194859,
              9.835161370268366,
              8.240685340526499,
              -5.6930087507195175,
              -6.298710366821096,
              8.022708891651458,
              11.587350670849434,
              -2.1621041294453276,
              -8.639125232178278,
              3.4519863245524967,
              11.558061522283692
            ],
            "metrics": {
              "initial_rmse_K": 7.650700394588099,
              "observation_residual_rms_K": 0.013275123154565083,
              "future_predictive_rmse_K": 0.015554834459940653
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.009396317893988,
              -2.144390611762741,
              0.25188552652271967,
              -0.22531409313294057,
              -0.021355878519867928,
              0.001159949180801927,
              0.008102701623555307,
              -0.009974723591703066
            ],
            "initial_K": [
              0.03721369679824882,
              0.11966467887178156,
              0.26916411276387153,
              0.48213393395135473,
              0.740085680235346,
              1.0156213370420946,
              1.2791757988950025,
              1.514286793405865,
              1.723725900860348,
              1.9089654434383287,
              2.0441873743139123,
              2.0802632624482578,
              1.9735931658120665,
              1.702894672511249,
              1.2652249768753108,
              0.6788449135639476
            ],
            "metrics": {
              "initial_rmse_K": 0.04387853322213293,
              "observation_residual_rms_K": 0.025257409998896745,
              "future_predictive_rmse_K": 0.023941283308436718
            }
          },
          "learned": {
            "coefficients_K": [
              5.070132262277253,
              -2.1967028089029292,
              0.26175455129562375,
              -0.21345975327986144,
              -0.006668534464850698,
              0.00011472549162541915,
              0.001263564739394579,
              0.0026928910161606425
            ],
            "initial_K": [
              0.04485055337987981,
              0.1263036972981838,
              0.2699713527675811,
              0.4799736987934846,
              0.7372182520689115,
              1.011846178522011,
              1.2801007759509346,
              1.5302742057416538,
              1.7554767624846959,
              1.9437100324471501,
              2.072555702486114,
              2.107930795296204,
              2.008120978521833,
              1.7375625714661305,
              1.2869182552742169,
              0.6859557477782534
            ],
            "metrics": {
              "initial_rmse_K": 0.038150905541892294,
              "observation_residual_rms_K": 0.019663810135087195,
              "future_predictive_rmse_K": 0.01478532412831308
            }
          }
        }
      },
      {
        "split": "train",
        "index": 74,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.926165032182134,
          0.12951406877525157,
          0.663595716072547,
          0.09596959811979028,
          0.06181711459342813,
          0.001877464183825936,
          0.028600168877096616,
          -0.030171158865921976
        ],
        "initial_K": [
          0.5481732600295158,
          1.0249047599195364,
          1.3736172184340736,
          1.5844882146946202,
          1.700709478860216,
          1.7717950440722094,
          1.8119802575336643,
          1.8197986285763779,
          1.8126337840220612,
          1.8063424337489378,
          1.7746463195291735,
          1.669307733896195,
          1.4776862782141504,
          1.221877984217496,
          0.9022712079708397,
          0.49118197444180556
        ],
        "observed_K": [
          0.35917243048556907,
          0.8232010153394764,
          1.0557953228275003,
          1.3190005898404595,
          1.5370325675495258,
          1.6404383415960422,
          1.709440408484546,
          1.7567309298253868,
          1.735405577793944,
          1.7489841061763611,
          1.6110453867615315,
          1.4688383066582142,
          1.2780010584653438,
          1.0394119315168329,
          0.7134345719031066,
          0.35226333014283023
        ],
        "future_observed_K": [
          0.38914274066552795,
          0.7420836134134855,
          1.0331030765505103,
          1.2250004008409843,
          1.4180653993024894,
          1.5625881594717312,
          1.6851453962849088,
          1.705352154564245,
          1.6675182284109868,
          1.6234059461187484,
          1.528304038354215,
          1.3687633469955678,
          1.2123978286494579,
          0.9620103981733404,
          0.6544272531329578,
          0.34415510483485623
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.925246101774552,
              0.10388481656348808,
              0.590675830757922,
              0.16319309501454446,
              0.05420467193071676,
              -0.14537530390236836,
              0.4071141700107996,
              17.127092036563695
            ],
            "initial_K": [
              6.48467268051543,
              2.12631393303845,
              -4.38029088581443,
              -0.632333126944717,
              6.999251894616329,
              4.95770219436468,
              -2.8968584808554865,
              -2.2635618374419737,
              5.731593053088554,
              6.641114781146032,
              -1.140564584449994,
              -3.5948960611632987,
              3.4244763689519804,
              6.74882778215722,
              -0.1124742824291769,
              -5.226187950893271
            ],
            "metrics": {
              "initial_rmse_K": 4.290594280986182,
              "observation_residual_rms_K": 0.021820887522680365,
              "future_predictive_rmse_K": 0.022714068391391357
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.853932235003814,
              0.10164611621040229,
              0.5577185235400356,
              0.1321081371959703,
              0.02267544921042261,
              -0.011018279183699919,
              0.0025491762640183634,
              0.005585462271324221
            ],
            "initial_K": [
              0.5183453573657392,
              0.9704562526576577,
              1.315935519168465,
              1.546466505393199,
              1.6777851898392495,
              1.7417455134184598,
              1.776601837887548,
              1.8083454076965542,
              1.834830837584529,
              1.8316029037926158,
              1.7739800696960095,
              1.6499045028349044,
              1.4544971100075306,
              1.1834927843189715,
              0.8385692566954639,
              0.43505332017871595
            ],
            "metrics": {
              "initial_rmse_K": 0.0372204026801193,
              "observation_residual_rms_K": 0.028514048575889652,
              "future_predictive_rmse_K": 0.026466379753689897
            }
          },
          "learned": {
            "coefficients_K": [
              5.924907673976083,
              0.10412576317423695,
              0.5795702670725393,
              0.12515759657996797,
              0.007080580385630038,
              -0.0010897697219305585,
              0.000397527811261286,
              -0.0015079155861586267
            ],
            "initial_K": [
              0.5211127957272214,
              0.9808961522523084,
              1.3353524494361437,
              1.5703372111356775,
              1.7027114163588342,
              1.767950327017659,
              1.8016323262474196,
              1.8256270198924949,
              1.8432137838251659,
              1.8408047390847841,
              1.7943426685763868,
              1.67962895029864,
              1.4823432631396698,
              1.2017632316720201,
              0.848069787639757,
              0.43916687061152226
            ],
            "metrics": {
              "initial_rmse_K": 0.028701290778083147,
              "observation_residual_rms_K": 0.023320413889122035,
              "future_predictive_rmse_K": 0.022972471082029676
            }
          }
        }
      },
      {
        "split": "train",
        "index": 75,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.8202068433211895,
          0.539907999994188,
          0.40963947115323673,
          0.13491773780528338,
          -0.024680229799970813,
          0.11065259094242469,
          0.02088124150296981,
          0.009707447431205924
        ],
        "initial_K": [
          0.6393106795115904,
          1.1681982374142965,
          1.5560369845158468,
          1.8413473888117737,
          2.05848008325235,
          2.1998185473400245,
          2.2475819402925326,
          2.2159455710841094,
          2.1458498845914376,
          2.0651860701398275,
          1.9623470742002709,
          1.7961449367179894,
          1.5309619209573664,
          1.1709861184750454,
          0.7647222401541898,
          0.3685837453782831
        ],
        "observed_K": [
          0.46237548028667863,
          0.8941464828974326,
          1.2956448955886857,
          1.57295558580864,
          1.8175448395109133,
          1.9668899471085293,
          2.0665787897394514,
          2.1055840888573725,
          2.032792079277869,
          1.9336042362676351,
          1.814468434176612,
          1.5990120797364886,
          1.3587891985273037,
          1.0442140624631593,
          0.7501163721242783,
          0.3687331122451123
        ],
        "future_observed_K": [
          0.4510119906349537,
          0.8211863832941776,
          1.1993056806392826,
          1.466740923523386,
          1.715243372091082,
          1.845188018547734,
          1.9263734542902418,
          1.9985473919122185,
          1.9629717311619292,
          1.8664472555547034,
          1.7215029295032716,
          1.5535507093437417,
          1.274455528790458,
          0.9934460075163913,
          0.686314849851953,
          0.31741797855121934
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.8269380943075575,
              0.5010824325723742,
              0.3693242623758696,
              0.06576370216851991,
              0.14847480494424256,
              0.30107078335374376,
              -0.00920045118035115,
              -14.961252226236502
            ],
            "initial_K": [
              -4.405489646314263,
              0.28432423992162226,
              6.468010063405396,
              3.5843748306468535,
              -2.646690519926862,
              -0.5133064719955893,
              6.443377015089704,
              5.792873105435895,
              -1.277081196268691,
              -2.0931640970849164,
              4.584115693751789,
              6.372941466685165,
              -0.27508354657104417,
              -3.709282336388129,
              1.7288931754855388,
              5.474616611264543
            ],
            "metrics": {
              "initial_rmse_K": 3.7433669715912745,
              "observation_residual_rms_K": 0.009801744270709506,
              "future_predictive_rmse_K": 0.01978015052758127
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.744771827228167,
              0.49028419028988135,
              0.3487174717399256,
              0.05323705753493709,
              0.062111489261365914,
              0.022818744697342914,
              -5.760932312080597e-05,
              -0.004879141751735205
            ],
            "initial_K": [
              0.5834313672528284,
              1.1006735567235346,
              1.5099556034260804,
              1.8066861225845183,
              2.0135168563001176,
              2.1531369142233725,
              2.229762094407271,
              2.2371640332542087,
              2.1780603950051995,
              2.0671398985967158,
              1.9159715158771133,
              1.7227912955498854,
              1.4789249527870383,
              1.1793965746225732,
              0.825846736379978,
              0.42665091007629324
            ],
            "metrics": {
              "initial_rmse_K": 0.046391660609829466,
              "observation_residual_rms_K": 0.022440849654139734,
              "future_predictive_rmse_K": 0.02142822723625174
            }
          },
          "learned": {
            "coefficients_K": [
              6.8265481652497835,
              0.5022446246792479,
              0.3623804297306278,
              0.05043612234254896,
              0.019394781929354413,
              0.002256902066923071,
              -8.98380722106599e-06,
              0.0013172291812427763
            ],
            "initial_K": [
              0.5760138631240301,
              1.0974870285495353,
              1.526241212957328,
              1.8469446685128017,
              2.0632910686863593,
              2.1900406350107837,
              2.2451979982389885,
              2.24341328187653,
              2.1923970674701767,
              2.0939737962896388,
              1.9473373287637183,
              1.7503546970368011,
              1.499335444079819,
              1.1913674529728817,
              0.8295211249175749,
              0.4259579608299876
            ],
            "metrics": {
              "initial_rmse_K": 0.039550862706157056,
              "observation_residual_rms_K": 0.012448581149269758,
              "future_predictive_rmse_K": 0.019930611788050556
            }
          }
        }
      },
      {
        "split": "train",
        "index": 76,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.9004714286049005,
          -0.8676499984421292,
          0.17636734929767037,
          -0.023186999227011434,
          0.10307031935739663,
          -0.059686838068007404,
          0.04750597667006392,
          0.009005431943879759
        ],
        "initial_K": [
          0.3194963146157269,
          0.6036481164855371,
          0.8554882365504465,
          1.0993151162734711,
          1.339211221302246,
          1.5573528888919859,
          1.7458163724385787,
          1.9110013416026792,
          2.040340189558889,
          2.0906118282677877,
          2.0285750370192885,
          1.8702048255833255,
          1.6577516645048576,
          1.3994037379211028,
          1.0520116116856952,
          0.5757253271444698
        ],
        "observed_K": [
          0.2756227822366056,
          0.5487622116461326,
          0.7983151354933922,
          1.0514148552491032,
          1.2840035747607146,
          1.46039697771211,
          1.6343980962929614,
          1.779595821543443,
          1.8588503261569693,
          1.8463663342972843,
          1.772526702081447,
          1.6714872223009603,
          1.4667352374659843,
          1.123922739688835,
          0.8349590682503103,
          0.4633761275159512
        ],
        "future_observed_K": [
          0.26580335706471103,
          0.5079749452423664,
          0.7797465035569509,
          1.018857172259801,
          1.266878672176215,
          1.4109168169206543,
          1.5895909382366225,
          1.6862870872037719,
          1.7630082170134858,
          1.7840944293214998,
          1.7043022749036896,
          1.55652819944325,
          1.3589932375363358,
          1.0756583085939444,
          0.7689684780870116,
          0.3770845156663635
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.89344615479455,
              -0.8722636609430378,
              0.15035477453138443,
              -0.041670776171988375,
              0.2632676740596969,
              -0.4989589533436097,
              0.2645199267198014,
              -12.33624143588026
            ],
            "initial_K": [
              -3.9262387625164585,
              -0.21885610840536407,
              4.908987416206584,
              2.666826942075279,
              -2.394115438425546,
              -0.6847740064946328,
              5.020422970300578,
              4.682338762838564,
              -0.7390602878542607,
              -1.1026371185474433,
              4.343866643470441,
              5.511168598322142,
              -0.1183623561731093,
              -2.734995668901631,
              2.0408706462423343,
              5.042065952070047
            ],
            "metrics": {
              "initial_rmse_K": 3.089012052928089,
              "observation_residual_rms_K": 0.01673922367389668,
              "future_predictive_rmse_K": 0.014885645398722277
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.8225150193303765,
              -0.8534665255161902,
              0.14196559007880827,
              -0.03373334279309414,
              0.1101328088382697,
              -0.037817076914513185,
              0.001656311590766067,
              -0.00402307706194123
            ],
            "initial_K": [
              0.29676406427782476,
              0.5823179124061663,
              0.8455204551283495,
              1.0832661250332856,
              1.305838500159879,
              1.5260130954685347,
              1.739646381782779,
              1.9196042997644809,
              2.0306228590674538,
              2.0507727008580776,
              1.981797598003716,
              1.8417728026503264,
              1.6445450041054004,
              1.3806600607792165,
              1.0210003446429574,
              0.5498219229705357
            ],
            "metrics": {
              "initial_rmse_K": 0.02546220004310459,
              "observation_residual_rms_K": 0.024535365971293664,
              "future_predictive_rmse_K": 0.02519549069923271
            }
          },
          "learned": {
            "coefficients_K": [
              5.893109543289592,
              -0.8742867570964123,
              0.14752788635175962,
              -0.03195854697677646,
              0.03438980188829791,
              -0.003740321397403246,
              0.00025829124911355694,
              0.0010861161191910045
            ],
            "initial_K": [
              0.29106249130789197,
              0.5729769651405939,
              0.8413651050555776,
              1.0963330117568184,
              1.3381366409870659,
              1.5632231003721806,
              1.7626390457432635,
              1.9224466923115096,
              2.0265845766294044,
              2.0618942366632527,
              2.0212867230964986,
              1.9010603904821983,
              1.6953599978343024,
              1.3959848438417992,
              1.0007703517758169,
              0.5240439052057896
            ],
            "metrics": {
              "initial_rmse_K": 0.026397187518194445,
              "observation_residual_rms_K": 0.018657016244646343,
              "future_predictive_rmse_K": 0.014530900795036843
            }
          }
        }
      },
      {
        "split": "train",
        "index": 77,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.667649896433263,
          -0.5502093711299172,
          0.6295078907534664,
          -0.10016852100501583,
          -0.057707207667475835,
          -0.0261362187106961,
          0.0633323774655936,
          -0.021280952508553313
        ],
        "initial_K": [
          0.36935873005338005,
          0.7180841892442725,
          1.028905887189902,
          1.289968850611564,
          1.4891117347502958,
          1.6108393217035664,
          1.6568293158784924,
          1.6708971469915654,
          1.7150324617901305,
          1.8002178326012443,
          1.8601134575472638,
          1.8169591466476744,
          1.6559071398605238,
          1.404276744941251,
          1.0577765088906315,
          0.5825849799675012
        ],
        "observed_K": [
          0.335815602531834,
          0.6485221519432849,
          0.9129324469388387,
          1.1323507996447375,
          1.3205380815605414,
          1.4448192485073086,
          1.5805046846341608,
          1.6317951268012822,
          1.726964973177159,
          1.7045425952842426,
          1.6696709547275823,
          1.5189891409454281,
          1.3940764247096389,
          1.1194435453399547,
          0.7835910272152891,
          0.3901038926558383
        ],
        "future_observed_K": [
          0.24299908768678405,
          0.5995862517300806,
          0.831181709185102,
          1.082923478282291,
          1.271124019955077,
          1.3670991268463888,
          1.5103588237374197,
          1.5792816390153874,
          1.6069917991635139,
          1.6163800370485768,
          1.5291622623352,
          1.4353020403659993,
          1.2884234231048937,
          1.0531597218590234,
          0.6976851966634988,
          0.3678534945124832
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.671349459513245,
              -0.5136988412112174,
              0.5951348060439909,
              0.136755644092633,
              0.18425957836991544,
              0.14561103578341936,
              -2.131798520171159,
              15.454871536610751
            ],
            "initial_K": [
              5.1030712050849125,
              1.5032090216972143,
              -3.4853438823402634,
              -0.03511461584426101,
              5.946228583736458,
              3.556076399223203,
              -2.8343356096130607,
              -1.2135665633890849,
              5.974981196846954,
              5.796234697433297,
              -1.6897680192115652,
              -3.0886289156028957,
              4.224481274209157,
              6.970827922124601,
              -0.3806143776267631,
              -5.478975752490397
            ],
            "metrics": {
              "initial_rmse_K": 3.9089368906689823,
              "observation_residual_rms_K": 0.01232108347078336,
              "future_predictive_rmse_K": 0.027508663499853463
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.6030913900897845,
              -0.5026287174410464,
              0.561928706153834,
              0.11070648173259218,
              0.07708133933918736,
              0.011036145764943063,
              -0.013348418177499528,
              0.005040120161181858
            ],
            "initial_K": [
              0.43971067018138305,
              0.8148063776949617,
              1.0898914125373673,
              1.2697755544163867,
              1.3893122036640186,
              1.4907548990275519,
              1.5994768813909581,
              1.711017202868726,
              1.8001520855731388,
              1.8441939313996654,
              1.8344015079734435,
              1.7629348468599295,
              1.6076811915008788,
              1.3426561119300673,
              0.9647999977856399,
              0.5028840182672747
            ],
            "metrics": {
              "initial_rmse_K": 0.07140965126005337,
              "observation_residual_rms_K": 0.021913919473017605,
              "future_predictive_rmse_K": 0.02478389700784997
            }
          },
          "learned": {
            "coefficients_K": [
              5.671025533337191,
              -0.5148902953508108,
              0.5839454071457345,
              0.10488193591679838,
              0.02406923075077511,
              0.001091536827206126,
              -0.0020816008436925905,
              -0.0013606887627148185
            ],
            "initial_K": [
              0.4290696585259189,
              0.8065811715921497,
              1.0978847860846872,
              1.2971316263842816,
              1.4267897228107125,
              1.5225008728473233,
              1.6127859053978424,
              1.7072272753046582,
              1.797097513276519,
              1.8616430688456211,
              1.8737927183647853,
              1.805733899376962,
              1.6359992408078035,
              1.3558907724724079,
              0.9724709171692958,
              0.5084523099791165
            ],
            "metrics": {
              "initial_rmse_K": 0.05994007624948451,
              "observation_residual_rms_K": 0.015331440755517508,
              "future_predictive_rmse_K": 0.02742982841127273
            }
          }
        }
      },
      {
        "split": "train",
        "index": 78,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          7.185929403838237,
          2.1349977028062526,
          0.38184557309809464,
          -0.016564056830142254,
          0.028790020536396625,
          0.03645611188866309,
          0.007862864471241106,
          0.030393408684568406
        ],
        "initial_K": [
          0.814602300697556,
          1.5181137519728947,
          2.068357052804233,
          2.4697363389455487,
          2.7131328994243353,
          2.7781797038660487,
          2.6799394973344137,
          2.4711258191780323,
          2.1987831925310735,
          1.8904936932005074,
          1.5784673771869229,
          1.2966491635509447,
          1.0450614041262933,
          0.7910210371981006,
          0.5189474684046056,
          0.2500365568868231
        ],
        "observed_K": [
          0.628232915575992,
          1.1756055759460935,
          1.6477622386367157,
          2.0485530567765466,
          2.268552297820152,
          2.351593255622082,
          2.3673263969993315,
          2.249841491670573,
          2.0885479416505714,
          1.822396852791304,
          1.591088278298653,
          1.3437924453752947,
          1.0770100106366924,
          0.772721797660531,
          0.5379998566474972,
          0.2743823646248297
        ],
        "future_observed_K": [
          0.5479300897980033,
          1.0870308746963648,
          1.4792779871921855,
          1.8786827856432484,
          2.0694953884840563,
          2.197525663523063,
          2.24569572061466,
          2.1925730924257123,
          2.0174661401703644,
          1.7923109172350418,
          1.5820346740678262,
          1.3374687554507423,
          1.0370422097510035,
          0.7685591301620365,
          0.5361040905802099,
          0.27962322472715473
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              7.165129679003609,
              2.0976810320233126,
              0.41575090881515747,
              -0.02374590795874154,
              -0.008901827127621506,
              0.11457114243474803,
              -0.7467077260582161,
              -7.303274047340522
            ],
            "initial_K": [
              -1.9268346535078305,
              0.9253603998307922,
              4.646929577678889,
              3.582407675019425,
              0.39617382010084645,
              1.1982867846234444,
              4.59887257290293,
              4.355078078788299,
              0.6681852140811704,
              -0.24957362440034547,
              2.6433101676569204,
              3.5412554319047684,
              0.418314469439915,
              -1.4325177844011134,
              0.8299999000905307,
              2.4825911324401435
            ],
            "metrics": {
              "initial_rmse_K": 1.843275007938965,
              "observation_residual_rms_K": 0.013684628647157042,
              "future_predictive_rmse_K": 0.021314696999173988
            }
          },
          "tikhonov": {
            "coefficients_K": [
              7.078893074726448,
              2.052476358016096,
              0.3925537002712512,
              -0.019222796566096902,
              -0.0037239027877587322,
              0.008683571417255944,
              -0.0046755670807926844,
              -0.00238173307888326
            ],
            "initial_K": [
              0.7661934484959098,
              1.465504547891775,
              2.0380539898534797,
              2.4425263401399935,
              2.6650866506613378,
              2.716801814398977,
              2.6239524293339698,
              2.422172862891366,
              2.1544556889575937,
              1.8637031094326244,
              1.5792287060836165,
              1.3093822628349738,
              1.0481077187321057,
              0.787721891758294,
              0.5256267320107435,
              0.2627481656987057
            ],
            "metrics": {
              "initial_rmse_K": 0.03661298640664247,
              "observation_residual_rms_K": 0.025419748505735747,
              "future_predictive_rmse_K": 0.0316395764133637
            }
          },
          "learned": {
            "coefficients_K": [
              7.164720433712973,
              2.1025463160158897,
              0.4079341877734687,
              -0.0182114370002012,
              -0.0011628167888677555,
              0.0008588540053283954,
              -0.0007291249233205032,
              0.0006430000342417797
            ],
            "initial_K": [
              0.7814510715658173,
              1.4923831129994476,
              2.073355266268277,
              2.484265673715058,
              2.7089313085154187,
              2.7558888112494397,
              2.6545935264476745,
              2.4470364539356853,
              2.177482150805456,
              1.883884180860552,
              1.5924196633107723,
              1.3150820232945692,
              1.051105138146387,
              0.7927321325181852,
              0.5325768241363382,
              0.2678694445171309
            ],
            "metrics": {
              "initial_rmse_K": 0.01821655998803187,
              "observation_residual_rms_K": 0.014227970768898287,
              "future_predictive_rmse_K": 0.02111840961748258
            }
          }
        }
      },
      {
        "split": "train",
        "index": 79,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.866567003501831,
          -1.21895398083289,
          0.13889587068101017,
          0.021978230919151593,
          -0.009328910521206936,
          -0.036760526151233604,
          -0.003816084716771707,
          0.016280699005529354
        ],
        "initial_K": [
          0.23932878579824868,
          0.4825756688048875,
          0.7351545796953478,
          0.991676605062159,
          1.2333260612927242,
          1.4508451597786058,
          1.6583850243774403,
          1.866041886713357,
          2.0459382899015846,
          2.146104140866828,
          2.135875165301388,
          2.018550823534345,
          1.8013143589817984,
          1.4777628775881189,
          1.0489761389048304,
          0.5426931501483561
        ],
        "observed_K": [
          0.2679541292197022,
          0.48533897092302636,
          0.7560466121651145,
          0.9875692169659228,
          1.2054320059642647,
          1.3977159268218378,
          1.6389188674476298,
          1.7443550862688904,
          1.850180148151711,
          1.8991537214769494,
          1.8532742098678003,
          1.7138930361944864,
          1.512786380854795,
          1.2286320724871016,
          0.865299661651412,
          0.4471359742676787
        ],
        "future_observed_K": [
          0.26147244401390973,
          0.46432518749545587,
          0.702256916477417,
          0.9566062781044555,
          1.1480369446244494,
          1.3574336730092813,
          1.5324641041677944,
          1.676120053944036,
          1.7595312267472003,
          1.7842906994088967,
          1.7580160020735323,
          1.613839962518306,
          1.4052044412199804,
          1.1544468844054134,
          0.7862004652366626,
          0.41744747977898844
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.894675433357776,
              -1.1584290141266869,
              0.14453114231964184,
              0.007196555952385267,
              0.1665527231909203,
              -0.10133636900472906,
              0.28779774862648916,
              -3.7924295714075287
            ],
            "initial_K": [
              -0.9300834969425127,
              0.349683564920256,
              1.9716764948077277,
              1.3913808186507337,
              0.06816539771530761,
              0.8437976600159458,
              2.749496931396775,
              2.722051761841074,
              1.1537753433250644,
              1.1653688488498128,
              2.8773812093182505,
              3.1171146446187707,
              1.1750960646264996,
              0.16405645971997806,
              1.4136525530807367,
              2.0063762434762533
            ],
            "metrics": {
              "initial_rmse_K": 0.9562661943050155,
              "observation_residual_rms_K": 0.012523006229860413,
              "future_predictive_rmse_K": 0.019508493542145143
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.823729502793758,
              -1.1334650633902925,
              0.13646689284143243,
              0.005825758749237871,
              0.06967402773695469,
              -0.00768048200199394,
              0.0018020674387656617,
              -0.0012367815997327352
            ],
            "initial_K": [
              0.2694742134157559,
              0.5246933533461604,
              0.7608541508759581,
              0.9858791586829716,
              1.2136930420992025,
              1.450677319375282,
              1.6856117653892964,
              1.8916199581143076,
              2.0381402572939042,
              2.103086117169082,
              2.077369920833631,
              1.9608749528761245,
              1.7540044181595016,
              1.4519155254038598,
              1.0489068931571732,
              0.5532267248332956
            ],
            "metrics": {
              "initial_rmse_K": 0.032438160151769514,
              "observation_residual_rms_K": 0.021008462167745774,
              "future_predictive_rmse_K": 0.02321600130321483
            }
          },
          "learned": {
            "coefficients_K": [
              5.894338751641045,
              -1.16111583164228,
              0.14181374688551293,
              0.00551925096201851,
              0.021756241722230923,
              -0.000759642825894976,
              0.00028102094578132494,
              0.00033389577447974413
            ],
            "initial_K": [
              0.2604366244938062,
              0.5145002267995027,
              0.7603159459846887,
              1.0008372321436934,
              1.2397685102462837,
              1.4762469831297915,
              1.7014970988913227,
              1.898857191908687,
              2.047013517700058,
              2.124901179387245,
              2.1155920860204835,
              2.007317859761592,
              1.7928441294308535,
              1.4704335366155994,
              1.047715276162024,
              0.5458601112734285
            ],
            "metrics": {
              "initial_rmse_K": 0.020810710309807443,
              "observation_residual_rms_K": 0.01305078567687361,
              "future_predictive_rmse_K": 0.019204676794410916
            }
          }
        }
      },
      {
        "split": "train",
        "index": 80,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.2935800224225105,
          -0.15849604653913796,
          0.5708855015953731,
          0.23626709641398957,
          0.004726303374731542,
          -0.07621214961634758,
          -0.03909171662157091,
          -0.07300104141109201
        ],
        "initial_K": [
          0.4117345952458728,
          0.844291913668848,
          1.2053221825080125,
          1.3855753167874125,
          1.41585055423022,
          1.4309561044823191,
          1.5026976421060048,
          1.5955953175854618,
          1.6679081315355333,
          1.7171161502708436,
          1.7188620485992476,
          1.6153570670891932,
          1.3956814866994869,
          1.115536780602649,
          0.8070776728095194,
          0.4384850905872521
        ],
        "observed_K": [
          0.3747870266045387,
          0.6747080082700349,
          0.8927412150246118,
          1.182895745671109,
          1.277336750376193,
          1.4038660422909588,
          1.4622571335969354,
          1.5935668331942223,
          1.5558159822585855,
          1.5447218227198334,
          1.5417538696254267,
          1.3763042544861497,
          1.179231432482635,
          0.9690722836429427,
          0.6350115258483596,
          0.3187764090511143
        ],
        "future_observed_K": [
          0.31718466295251896,
          0.5943739724046144,
          0.8304953439256209,
          1.0662179938670235,
          1.2388462664781614,
          1.3324717197167928,
          1.4429087649685126,
          1.4773955531633638,
          1.4861002084808643,
          1.5285841147842936,
          1.4005775658439599,
          1.2847582862122375,
          1.1495270258766277,
          0.879507943070026,
          0.5910265561432073,
          0.33558240577426773
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.282899218191839,
              -0.13204489201534197,
              0.532644522594232,
              0.43579386424311334,
              -0.05163757596601523,
              0.5622446917621345,
              -0.8026517116646552,
              2.725938237176468
            ],
            "initial_K": [
              1.3381745463014054,
              1.1001794351757384,
              0.45890603803959074,
              1.0814375585647678,
              2.063864185067928,
              1.7082427005537812,
              0.8052987910471345,
              1.2417179644883158,
              2.4231093695372365,
              2.2288185210205045,
              0.9443221750290396,
              0.8942726631672574,
              2.1631878873591526,
              2.1708873839108147,
              0.21212713364575064,
              -1.0377689000356718
            ],
            "metrics": {
              "initial_rmse_K": 0.7445626242616251,
              "observation_residual_rms_K": 0.02563217580718456,
              "future_predictive_rmse_K": 0.02106556173567581
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.219316378839979,
              -0.12919934676477818,
              0.5029251261758318,
              0.3527840170042747,
              -0.021601555538669128,
              0.042613627054213704,
              -0.005025864591239782,
              0.0008889790015260534
            ],
            "initial_K": [
              0.49108915536809117,
              0.8954351948152549,
              1.1665903828982664,
              1.3131001889484484,
              1.3820971064872378,
              1.427800636642718,
              1.4863362100619595,
              1.5670350160721722,
              1.6557658603885748,
              1.7210090904095299,
              1.7204171571988855,
              1.6138924891490798,
              1.3852203707038544,
              1.058760349518589,
              0.6907291167306604,
              0.3332911054572915
            ],
            "metrics": {
              "initial_rmse_K": 0.053619684779872154,
              "observation_residual_rms_K": 0.030175473637450326,
              "future_predictive_rmse_K": 0.02184963333874023
            }
          },
          "learned": {
            "coefficients_K": [
              5.282597478834311,
              -0.1323511520661392,
              0.5226300318036569,
              0.33422316457754425,
              -0.006745248970675096,
              0.004214727157578598,
              -0.0007837515902104587,
              -0.00023999898791744197
            ],
            "initial_K": [
              0.4872464047274878,
              0.8973442395919698,
              1.1823515409240268,
              1.3396930362392983,
              1.407891278946267,
              1.4443032714039503,
              1.496445767569506,
              1.5809757908864028,
              1.6788495799978798,
              1.7464700837794056,
              1.736321950641489,
              1.6180105476391817,
              1.390690099096634,
              1.081032692164951,
              0.7279363195569459,
              0.3631583749240511
            ],
            "metrics": {
              "initial_rmse_K": 0.04038092210881099,
              "observation_residual_rms_K": 0.026578061135405995,
              "future_predictive_rmse_K": 0.02113555773990422
            }
          }
        }
      },
      {
        "split": "train",
        "index": 81,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.2427615831085355,
          0.9482912835077886,
          0.3382467692962171,
          -0.21258704793323047,
          0.01830647373848948,
          0.05577771346849259,
          -0.10863619970461011,
          0.00780135792155406
        ],
        "initial_K": [
          0.511864899671355,
          1.0260672277796263,
          1.497000822817812,
          1.8562920129716463,
          2.0783020727430217,
          2.1921337190359003,
          2.222456336865732,
          2.150258965787549,
          1.961507069385897,
          1.7156263551923479,
          1.5160996220493168,
          1.3968285585099407,
          1.2740771861923355,
          1.0432328906966277,
          0.7015064369672572,
          0.3355358198854246
        ],
        "observed_K": [
          0.4567716298799947,
          0.8334080331959863,
          1.2985005372819654,
          1.5708719545140009,
          1.8069533778425049,
          1.9052805153759322,
          1.9905829614022148,
          1.9527681478521521,
          1.8002033369783175,
          1.719270750589887,
          1.507017157871874,
          1.3552873804711905,
          1.1057092070999497,
          0.9017311000692739,
          0.6398315374019972,
          0.33421535375218697
        ],
        "future_observed_K": [
          0.39143777379346917,
          0.8278089625201386,
          1.1566436235605002,
          1.4029834203879823,
          1.6884144997749526,
          1.7827601202538652,
          1.8612508615333083,
          1.8478611393025715,
          1.778725905407089,
          1.6521406881368366,
          1.5016423560382535,
          1.320338971290549,
          1.0904180682112867,
          0.8571744171512301,
          0.5992198813610651,
          0.2921533590406983
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.254952471205395,
              0.9753732462559942,
              0.39046853378692453,
              -0.4016315896442519,
              0.11163997559486549,
              -0.7913806071560383,
              -0.7731119469031865,
              -18.49213902935622
            ],
            "initial_K": [
              -6.290400125472081,
              -0.5017365466060648,
              7.795303858338237,
              4.629617871359041,
              -3.4270126453046217,
              -1.431547428457343,
              6.975322432783473,
              6.494780279166112,
              -1.9880718879788448,
              -3.2062292374631873,
              4.643667966017339,
              6.77424701318964,
              -1.0906928368647573,
              -4.884779292221576,
              2.0860197230886803,
              6.770864678197217
            ],
            "metrics": {
              "initial_rmse_K": 4.6331351272391315,
              "observation_residual_rms_K": 0.020596998556494488,
              "future_predictive_rmse_K": 0.01859652369244793
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.179670391857628,
              0.9543541165793366,
              0.3686819788665704,
              -0.32512895929959323,
              0.04670236911847532,
              -0.0599802871336878,
              -0.004840899112949934,
              -0.006030629405391712
            ],
            "initial_K": [
              0.4898782150614457,
              0.9861116854544569,
              1.4584530046240802,
              1.8479278407286073,
              2.1064707238596525,
              2.221679045658778,
              2.209160103223268,
              2.095599550704024,
              1.9136056004960726,
              1.7025297288104977,
              1.5017511030994382,
              1.3353508905270666,
              1.195952087424113,
              1.0388535735992697,
              0.8007362808510106,
              0.4445906161635422
            ],
            "metrics": {
              "initial_rmse_K": 0.051708479738620326,
              "observation_residual_rms_K": 0.029144748160654176,
              "future_predictive_rmse_K": 0.022627305110912974
            }
          },
          "learned": {
            "coefficients_K": [
              6.2545952118176835,
              0.977635490977357,
              0.38312715812314546,
              -0.3080231088575561,
              0.014583167710332974,
              -0.005932387421049596,
              -0.0007549074012929164,
              0.0016280980217919785
            ],
            "initial_K": [
              0.5158129973285314,
              1.0164705604570832,
              1.4778888172304707,
              1.8639900285149245,
              2.1344503796216077,
              2.2613998423635846,
              2.244336583054953,
              2.1127803938946763,
              1.9161119979142895,
              1.7070771928820898,
              1.5238540243735486,
              1.3744220251190011,
              1.2315143883602242,
              1.0464945647502515,
              0.7780980573737757,
              0.4184295532131492
            ],
            "metrics": {
              "initial_rmse_K": 0.04154958651482849,
              "observation_residual_rms_K": 0.023583291891496026,
              "future_predictive_rmse_K": 0.01846899825115908
            }
          }
        }
      },
      {
        "split": "train",
        "index": 82,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.05118471161086,
          -0.09954842440484497,
          0.09118551132956253,
          -0.2547661369122044,
          -0.02874381639746912,
          0.010722267457048483,
          -0.032373199996876566,
          0.011391502759690269
        ],
        "initial_K": [
          0.31527443700262664,
          0.6560788767006482,
          1.0229596631274191,
          1.3833660335540596,
          1.68957142917087,
          1.9079704792440295,
          2.0302053438513337,
          2.0612350234372934,
          2.0120421569823974,
          1.9086212751246707,
          1.787599443960148,
          1.6612106591791747,
          1.4933754888281008,
          1.2324257797226452,
          0.8688022588490532,
          0.4433185641407087
        ],
        "observed_K": [
          0.3309420734373576,
          0.6588710378451063,
          0.9596774009463789,
          1.2688321732620762,
          1.4708343898692113,
          1.665670382343632,
          1.7788741309690306,
          1.8453830877116622,
          1.8492345242950314,
          1.7996823532807316,
          1.6950552448323672,
          1.4889867344592809,
          1.2920264075792318,
          1.0604884640133097,
          0.7197267073491208,
          0.3662260019924119
        ],
        "future_observed_K": [
          0.29407925624322717,
          0.6269909853562387,
          0.9479134883321271,
          1.1580348207128668,
          1.4144356047991506,
          1.557347026289635,
          1.7008276815101577,
          1.7872666338549867,
          1.7847528976945009,
          1.7017774081137313,
          1.606960153873891,
          1.4471293236201943,
          1.2096633040047169,
          0.9704953127661313,
          0.637241143002695,
          0.34478759452081503
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.021646468167324,
              -0.1118097558271642,
              0.11963477156373767,
              -0.18508175586291284,
              0.07084169124178852,
              -0.7240217944067283,
              -0.9705383275985153,
              8.831886710277406
            ],
            "initial_K": [
              2.837791566645043,
              0.9003785849290429,
              -1.5918264267572937,
              0.8040952358690865,
              4.453256373137205,
              3.0289678014400883,
              -0.78495521196391,
              0.14885215359440052,
              4.460215252646067,
              4.471210837958989,
              -0.04197686220125485,
              -1.297875006555271,
              2.614711594114434,
              4.314230103194761,
              0.3615608422437498,
              -2.637139274761028
            ],
            "metrics": {
              "initial_rmse_K": 2.2253896252076664,
              "observation_residual_rms_K": 0.010864501624079747,
              "future_predictive_rmse_K": 0.01884986853217925
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.949172365557011,
              -0.10940027436366527,
              0.11295963824177911,
              -0.14982745436520833,
              0.029635216200309074,
              -0.05487503070820237,
              -0.0060770993747738715,
              0.0028802420107016387
            ],
            "initial_K": [
              0.33741154537057544,
              0.6892041793501181,
              1.0457743653994571,
              1.3730827537249342,
              1.6364119429308517,
              1.8237865547109626,
              1.9443840957559193,
              2.006436734688884,
              2.0042461599417116,
              1.9309462981264007,
              1.7973773582374966,
              1.6273586302669474,
              1.4312033267092996,
              1.1899587341677524,
              0.871783481449019,
              0.46549505678347025
            ],
            "metrics": {
              "initial_rmse_K": 0.04363546495799611,
              "observation_residual_rms_K": 0.020849937893059917,
              "future_predictive_rmse_K": 0.0233241246321926
            }
          },
          "learned": {
            "coefficients_K": [
              6.021302534342066,
              -0.11206908324965378,
              0.11738546406645527,
              -0.14194465600727812,
              0.009253820226651343,
              -0.005427448874618862,
              -0.0009476849629311407,
              -0.0007775832346310292
            ],
            "initial_K": [
              0.35429408507828497,
              0.7090823416051575,
              1.0560279650488271,
              1.3767925656653053,
              1.6491348162624493,
              1.8542511256340282,
              1.9814954254507007,
              2.0305784648760485,
              2.0111302819157353,
              1.9380835742137106,
              1.8235714107001306,
              1.669787568439587,
              1.467461894317911,
              1.2013553307668712,
              0.8609022712079699,
              0.4515298301218281
            ],
            "metrics": {
              "initial_rmse_K": 0.03288723049008318,
              "observation_residual_rms_K": 0.013069899373015188,
              "future_predictive_rmse_K": 0.018591123919930497
            }
          }
        }
      },
      {
        "split": "train",
        "index": 83,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          4.717948505863349,
          -1.754826584098173,
          0.4921012254153009,
          0.07247496267167385,
          0.029072507462543196,
          -0.004355419885806371,
          -0.03639783846444896,
          -0.03866124129463096
        ],
        "initial_K": [
          0.16693161868858583,
          0.3543158401940449,
          0.5260447165717669,
          0.642288117755827,
          0.737262409316381,
          0.8866704444688829,
          1.110059737063016,
          1.3564513542006464,
          1.5793147522073196,
          1.7700950804993587,
          1.9101849782896907,
          1.9430101414603302,
          1.8193641005467043,
          1.537909961933291,
          1.1230636759234902,
          0.5973831504830824
        ],
        "observed_K": [
          0.14554060735734586,
          0.3315803395876605,
          0.4966865446363957,
          0.6601349580000742,
          0.8182318804856573,
          0.9523305597804039,
          1.1683862786025,
          1.2956215683577352,
          1.468801020973089,
          1.5581107830944045,
          1.6328536745768831,
          1.5965119800153382,
          1.4472537146906985,
          1.2147263343559167,
          0.8476130798783752,
          0.43489485042502934
        ],
        "future_observed_K": [
          0.16344607702944608,
          0.30476204761070813,
          0.5017114322305144,
          0.6372345991275759,
          0.7706874625648138,
          0.95303669671268,
          1.157599590449977,
          1.2817388657470044,
          1.3716707872304381,
          1.489277419056419,
          1.5015668064601286,
          1.4418494238054833,
          1.3077714969856016,
          1.0717585073184872,
          0.7750681351019354,
          0.38287802858220793
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              4.720669088894807,
              -1.7344290306833001,
              0.5407433169967244,
              0.08198207211296803,
              -0.259885101883631,
              0.20900053354445977,
              -2.7504719465365977,
              -6.690554829095292
            ],
            "initial_K": [
              -3.0002042948296674,
              -0.5686859624084915,
              3.3244032248983717,
              2.3031124955898843,
              -1.4150092008078903,
              -1.147952312418581,
              2.6395915774326806,
              3.5712253318704708,
              0.6426424977520326,
              -0.489119139143394,
              2.219991956247185,
              3.9640906715263275,
              1.9574269096496373,
              -0.04353357108281908,
              0.9058212311985052,
              1.8334775405633956
            ],
            "metrics": {
              "initial_rmse_K": 1.7983635570004168,
              "observation_residual_rms_K": 0.0112644045311588,
              "future_predictive_rmse_K": 0.018530398448829487
            }
          },
          "tikhonov": {
            "coefficients_K": [
              4.6638530240948395,
              -1.6970523763093666,
              0.5105720408139619,
              0.06636615862542868,
              -0.10871777687060076,
              0.015840560028556414,
              -0.01722228877656969,
              -0.0021819139812151987
            ],
            "initial_K": [
              0.15987462909146435,
              0.33038030985879674,
              0.5038407980484977,
              0.6620003458125566,
              0.7997094659322249,
              0.934204401920567,
              1.090857127568068,
              1.2839420746668764,
              1.5075747557348258,
              1.732452069111451,
              1.9038821423556707,
              1.952063791364964,
              1.8227480175596944,
              1.5101874486756335,
              1.0609461905053346,
              0.5415125946071289
            ],
            "metrics": {
              "initial_rmse_K": 0.041634684931961936,
              "observation_residual_rms_K": 0.019827890647660752,
              "future_predictive_rmse_K": 0.019265227982265397
            }
          },
          "learned": {
            "coefficients_K": [
              4.720399462010183,
              -1.738451801386006,
              0.5305765571063686,
              0.06287446847791091,
              -0.03394794746229118,
              0.0015667203934242211,
              -0.0026857063039914773,
              0.0005890545741976306
            ],
            "initial_K": [
              0.18293942863591,
              0.35632917376427603,
              0.5131071196236897,
              0.6525846332062268,
              0.7841674115155607,
              0.9265446930248133,
              1.099366342435145,
              1.3102391015045214,
              1.5446602633754565,
              1.765034599806278,
              1.9191186168162282,
              1.95427815010969,
              1.83331975375726,
              1.5468167481548571,
              1.1158776384490723,
              0.5833227403002021
            ],
            "metrics": {
              "initial_rmse_K": 0.023090047094772755,
              "observation_residual_rms_K": 0.013907784272208236,
              "future_predictive_rmse_K": 0.01820997191289886
            }
          }
        }
      },
      {
        "split": "train",
        "index": 84,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.365450688879013,
          1.9244174798089329,
          0.2825711321028386,
          0.23244685247205027,
          -0.011621844537338184,
          0.04572505651320541,
          -0.012784385806567274,
          -0.003848685832625317
        ],
        "initial_K": [
          0.7496922001664869,
          1.4056758580792859,
          1.9002806345389276,
          2.211565589002983,
          2.3616643217913826,
          2.3899809237823684,
          2.3251543861172057,
          2.182359499029464,
          1.9790957545662047,
          1.7395905185878247,
          1.4799156682268704,
          1.19935899816735,
          0.8969733512230792,
          0.5945149072041863,
          0.3329802401199071,
          0.1399273804019383
        ],
        "observed_K": [
          0.5493280253787262,
          1.0380274035005475,
          1.4727053130583874,
          1.8285998110650175,
          2.0053308463824493,
          2.081521880486187,
          2.0746984317749484,
          2.0059035069985915,
          1.8733715871670817,
          1.668556121225306,
          1.4097962708624998,
          1.175569662114414,
          0.9268376524933123,
          0.6670567791024413,
          0.44386097013332987,
          0.23653800087882576
        ],
        "future_observed_K": [
          0.5054228298670405,
          0.972035421936173,
          1.400677852289285,
          1.6708623159779916,
          1.8583036756747306,
          1.9627154146365733,
          1.9432368971081346,
          1.8741860151422796,
          1.7824895644008731,
          1.6442445799209244,
          1.4250830646508441,
          1.1692445105411775,
          0.9393682664095884,
          0.7027742445536803,
          0.45312470332854976,
          0.21434994873289534
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.356029757053975,
              1.8857900099384362,
              0.27040217267244104,
              0.19406759679735577,
              0.06415405649462572,
              -1.2384030205020822,
              -2.3648935496220354,
              0.5661028704844
            ],
            "initial_K": [
              -0.2216001619248232,
              0.6634622757529474,
              2.3178664057484126,
              3.251970410056264,
              2.6493692526191737,
              1.5129119227090029,
              1.4484263223543046,
              2.4889870731999117,
              3.0082220310170458,
              2.042402568596912,
              0.7110629396149344,
              0.5552350197852634,
              1.2625640288134692,
              1.2710232792768024,
              0.2659680426126814,
              -0.40481791175674076
            ],
            "metrics": {
              "initial_rmse_K": 0.6853462212010938,
              "observation_residual_rms_K": 0.009382647725622225,
              "future_predictive_rmse_K": 0.024805369666675698
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.27953115235473,
              1.8451515518773893,
              0.2553148320143434,
              0.15710167578298803,
              0.026837576870603744,
              -0.09386099189854831,
              -0.014807960389751863,
              0.00018461664233652105
            ],
            "initial_K": [
              0.6805023328062572,
              1.316981453039931,
              1.843196445301634,
              2.191657535670113,
              2.3424546028758386,
              2.3423330398005358,
              2.2653245653147773,
              2.152572951291602,
              1.992902132097613,
              1.759672961461701,
              1.4590817180664861,
              1.138253478798576,
              0.8496063091943257,
              0.6124189288516405,
              0.4082905026081918,
              0.2081628159436359
            ],
            "metrics": {
              "initial_rmse_K": 0.050663602579543505,
              "observation_residual_rms_K": 0.023038110095301705,
              "future_predictive_rmse_K": 0.035006277290693256
            }
          },
          "learned": {
            "coefficients_K": [
              6.355666724511405,
              1.8901638417120241,
              0.26531821901646296,
              0.14883616238200886,
              0.008380236202795547,
              -0.009283379494751526,
              -0.0023092071607879495,
              -4.984123048735801e-05
            ],
            "initial_K": [
              0.7157341498771566,
              1.3563680402032,
              1.8614901142029927,
              2.198462757952722,
              2.3683516241977327,
              2.399097635870575,
              2.328131556565903,
              2.185374417556303,
              1.98732964908551,
              1.743248414535979,
              1.464876868137228,
              1.1706977950128703,
              0.8824537488991202,
              0.6181028284652064,
              0.38624928777384054,
              0.1842830560785914
            ],
            "metrics": {
              "initial_rmse_K": 0.02750865777676654,
              "observation_residual_rms_K": 0.013970293780026776,
              "future_predictive_rmse_K": 0.025908125763549478
            }
          }
        }
      },
      {
        "split": "train",
        "index": 85,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.409159894876527,
          1.1382221283570848,
          0.020498636190383585,
          0.028802994416232068,
          0.10950987345954093,
          0.050997130263288816,
          0.010721102556134893,
          0.05549382209409446
        ],
        "initial_K": [
          0.6234520111320048,
          1.1287925504429561,
          1.511200853671967,
          1.830403332442935,
          2.0956715987142855,
          2.2633115977313993,
          2.316804469126896,
          2.2774259358157614,
          2.148319393800215,
          1.9189909227291366,
          1.6265349985693756,
          1.344557258745598,
          1.096689729125592,
          0.8395205579750671,
          0.5481745092699997,
          0.25885592198963814
        ],
        "observed_K": [
          0.44724372375247184,
          0.9083990331317199,
          1.3139951576807254,
          1.6158971762042158,
          1.8329323855107253,
          1.9637146785364241,
          2.0700921972142825,
          2.0422657633805463,
          1.976893105993399,
          1.7502159237507728,
          1.5850392622155838,
          1.3225221377022542,
          1.138123619986911,
          0.7995531631612905,
          0.5283825786640727,
          0.2590882457223324
        ],
        "future_observed_K": [
          0.44295636980888975,
          0.848916256116783,
          1.2129170807224023,
          1.5169374470221133,
          1.721272220560599,
          1.8421660558264024,
          1.94239078945585,
          1.9482229506620459,
          1.8652340452294645,
          1.7150376816526618,
          1.5184170755457573,
          1.31473501447144,
          1.0161053711192616,
          0.7797311131246705,
          0.5334916228233475,
          0.29640148274942546
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.431307529571496,
              1.137045407291634,
              0.007189957342017664,
              0.10083655932860737,
              0.10638900309459938,
              0.76038045907937,
              -7.230124892374605,
              -10.117114624568305
            ],
            "initial_K": [
              -5.007174006265473,
              -0.6036542555026944,
              6.514076570766546,
              5.086205891077773,
              -1.6559061053594133,
              -1.9743279987473858,
              4.434185057262364,
              6.740102570322946,
              1.6715305152661752,
              -1.9723714199641702,
              0.9349045737097208,
              4.194376291598346,
              2.291400765230998,
              -0.8188540049499569,
              -0.3390049910807711,
              1.108198547176899
            ],
            "metrics": {
              "initial_rmse_K": 3.126708589278104,
              "observation_residual_rms_K": 0.01656835731327538,
              "future_predictive_rmse_K": 0.020108429114417032
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.353902912033646,
              1.1125422696918992,
              0.006788786986527889,
              0.08162925038566128,
              0.04450572893979662,
              0.057630725158057054,
              -0.045271975576386216,
              -0.0032993786633219056
            ],
            "initial_K": [
              0.5722106965475786,
              1.09639924998254,
              1.5269780898939915,
              1.8424668222286735,
              2.059925129342039,
              2.2088563464918427,
              2.2882100384278363,
              2.2650637998020113,
              2.122718146978966,
              1.8953929623386145,
              1.640581028080248,
              1.384000931787288,
              1.1094428639265306,
              0.8041922559419711,
              0.4953447512196202,
              0.22565081526798678
            ],
            "metrics": {
              "initial_rmse_K": 0.03312171796847454,
              "observation_residual_rms_K": 0.029173676858153,
              "future_predictive_rmse_K": 0.0256663596777255
            }
          },
          "learned": {
            "coefficients_K": [
              6.4309401974453495,
              1.1396826284584736,
              0.007054775699229766,
              0.0773345306787463,
              0.013897250213435483,
              0.005700002539694472,
              -0.007059876406500845,
              0.0008907381823354048
            ],
            "initial_K": [
              0.5691990212221002,
              1.0936825415478257,
              1.5374049473821245,
              1.8797469282246027,
              2.116922355609869,
              2.255784356157272,
              2.3037052109450347,
              2.263327176532151,
              2.137186360915519,
              1.9362156959187313,
              1.6811735254176703,
              1.394966900581487,
              1.0954997135183135,
              0.7965226678025192,
              0.5109192154971274,
              0.24692563052555316
            ],
            "metrics": {
              "initial_rmse_K": 0.033075505974015915,
              "observation_residual_rms_K": 0.023142075467649473,
              "future_predictive_rmse_K": 0.020044763689949764
            }
          }
        }
      },
      {
        "split": "train",
        "index": 86,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.647361560273765,
          -0.8106967154470668,
          0.3981351305839409,
          -0.17628519976729276,
          -0.0922705372748036,
          -0.046849655665098806,
          0.039938464502543514,
          -0.018126907865511497
        ],
        "initial_K": [
          0.2539769831316511,
          0.5372437703269104,
          0.8467948936691352,
          1.1480537016029815,
          1.3987834789076719,
          1.571003535883426,
          1.6669220106785667,
          1.7246346481931383,
          1.7916801115983594,
          1.8735140112163289,
          1.9166492990119743,
          1.8595047034672418,
          1.6886318893532017,
          1.4232640912334238,
          1.06025524450164,
          0.5774971805363416
        ],
        "observed_K": [
          0.24824030423384907,
          0.5682507050876007,
          0.7710539738493096,
          1.0389523769551559,
          1.2699871750607628,
          1.396772611943259,
          1.54563162496037,
          1.6631200486960993,
          1.7294707300502272,
          1.7416836881840436,
          1.695775392252959,
          1.6452025186976922,
          1.4455106893730514,
          1.1285428190554458,
          0.8027578145932569,
          0.43892100057995725
        ],
        "future_observed_K": [
          0.24508206515046743,
          0.5019034913674392,
          0.7738158785165291,
          1.0129689235569792,
          1.2098819520772146,
          1.3602257445187134,
          1.4904622370376321,
          1.6220515277946015,
          1.6490466043070202,
          1.6414428208666347,
          1.5948654208545718,
          1.4513829529641398,
          1.304789797853492,
          1.0847400498071615,
          0.7693506930951146,
          0.3982933198700622
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.652133013594062,
              -0.8483510710692839,
              0.39210092997515295,
              -0.06218189981572221,
              -0.40394786367803065,
              0.1619271150037666,
              -1.1186243667460092,
              -6.529001526029494
            ],
            "initial_K": [
              -2.352218985537044,
              -0.09897329836226332,
              3.2291655755088833,
              2.2916899719642734,
              -0.6475864214247953,
              0.051465641790386485,
              3.3183077905582232,
              3.4753686191116944,
              0.49103110569710506,
              -0.09832524767415851,
              2.792542755594565,
              3.973849989861918,
              1.3679000224104378,
              -0.503310491237803,
              1.06991119890606,
              2.2470644917935263
            ],
            "metrics": {
              "initial_rmse_K": 1.6562190226361284,
              "observation_residual_rms_K": 0.019341088502665808,
              "future_predictive_rmse_K": 0.02193175259976019
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.584106225545339,
              -0.8300692479389244,
              0.37022329399159065,
              -0.05033751551332106,
              -0.16898357540467415,
              0.01227277338467884,
              -0.0070043513444541985,
              -0.002129228453680493
            ],
            "initial_K": [
              0.2587857859026126,
              0.5427820140371012,
              0.8467046710881966,
              1.1338965493384143,
              1.3633698480342014,
              1.518395815676193,
              1.6154969685566398,
              1.6916864902674293,
              1.7784274435777763,
              1.8747995863094515,
              1.9373195967008734,
              1.8998563334864338,
              1.7148054166789226,
              1.3841297148125986,
              0.954333466864133,
              0.48166656301901867
            ],
            "metrics": {
              "initial_rmse_K": 0.045317165428592966,
              "observation_residual_rms_K": 0.025805635322225035,
              "future_predictive_rmse_K": 0.02320747500910251
            }
          },
          "learned": {
            "coefficients_K": [
              5.651810184989209,
              -0.8503187052439507,
              0.38472886289167435,
              -0.047689132502931775,
              -0.05276639851324342,
              0.0012138462472909574,
              -0.0010922840050600225,
              0.0005748309836915331
            ],
            "initial_K": [
              0.29506414739064735,
              0.5884013500126428,
              0.8712299663204545,
              1.1272761325656975,
              1.3406065496162936,
              1.506135179361434,
              1.6335514006305805,
              1.739863089002906,
              1.8350561938827212,
              1.910827302368228,
              1.939655643916171,
              1.8846387776567834,
              1.715056260036237,
              1.4200300836589728,
              1.0132152895135491,
              0.5266829590837697
            ],
            "metrics": {
              "initial_rmse_K": 0.03889916726379955,
              "observation_residual_rms_K": 0.021111511383155996,
              "future_predictive_rmse_K": 0.021689808674611236
            }
          }
        }
      },
      {
        "split": "train",
        "index": 87,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.295157439633047,
          0.608264336354427,
          0.21898672717997125,
          -0.08818182745945685,
          0.07267465480894061,
          -0.001108203272923499,
          0.0717935314658582,
          -0.04285218936279906
        ],
        "initial_K": [
          0.5198889001147298,
          0.9916109082981643,
          1.3807204607123973,
          1.6872930243023456,
          1.9336230440287563,
          2.1144896392947135,
          2.1879249448231946,
          2.139392966049251,
          2.021464249546165,
          1.891410507829331,
          1.739071099059401,
          1.526243335024747,
          1.2715721435999539,
          1.0270593339469614,
          0.7767431162321846,
          0.43985991062852764
        ],
        "observed_K": [
          0.42295301999188273,
          0.80526552340777,
          1.2198030952651864,
          1.472240458810877,
          1.6763261761967818,
          1.8308321935181888,
          1.9540975707039618,
          1.9298663850274027,
          1.8935323509569033,
          1.7758877565671167,
          1.6276973414535358,
          1.4114593928131285,
          1.2055891772887863,
          0.9119228081230878,
          0.6725852550603912,
          0.3482820077432196
        ],
        "future_observed_K": [
          0.3799911715150541,
          0.7543066100785053,
          1.0964612763517039,
          1.3808297145494954,
          1.5936853572157532,
          1.725630381302006,
          1.8618479054795483,
          1.8387419911774425,
          1.7975814810803221,
          1.7115461249958368,
          1.5826135770891634,
          1.407901457826605,
          1.201309595769826,
          0.8756292326803947,
          0.5744838655998388,
          0.32850592036444626
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.267927153760653,
              0.5980232861442552,
              0.23189739371621848,
              -0.050506824444051024,
              0.406902986572414,
              -0.584532684701063,
              -0.25944235582179376,
              -22.10037419092292
            ],
            "initial_K": [
              -7.202378496553091,
              -0.49672594083887067,
              8.818957853428866,
              4.650271918816324,
              -4.8551313930568085,
              -2.155377351658652,
              7.980838384524878,
              7.305417558474751,
              -2.785106894519187,
              -3.9653899662551746,
              5.609868465671594,
              8.033237002245272,
              -1.6142188921441412,
              -6.176286690406623,
              2.3671673083568674,
              8.12777396915652
            ],
            "metrics": {
              "initial_rmse_K": 5.517577135983011,
              "observation_residual_rms_K": 0.014089535202978632,
              "future_predictive_rmse_K": 0.023232872855328324
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.192488916378731,
              0.5851359847451475,
              0.21895846300370594,
              -0.04088630399707052,
              0.1702197924449285,
              -0.044302877718207984,
              -0.0016245179953436129,
              -0.007207341792875315
            ],
            "initial_K": [
              0.5228666426197164,
              0.9990368900925349,
              1.3880312722110697,
              1.6734052519543858,
              1.8723307111678624,
              2.014503739059418,
              2.1079049726844388,
              2.131029508585299,
              2.0598086249040564,
              1.897804104442844,
              1.6807840455014709,
              1.4554398986937829,
              1.2478539482585433,
              1.0407554745376895,
              0.781705055340105,
              0.42888839050569555
            ],
            "metrics": {
              "initial_rmse_K": 0.04426780191040215,
              "observation_residual_rms_K": 0.025241526373719743,
              "future_predictive_rmse_K": 0.029467838238310475
            }
          },
          "learned": {
            "coefficients_K": [
              6.267569153307815,
              0.5994103192903097,
              0.22753738584001137,
              -0.038735172941847945,
              0.053152416626771386,
              -0.004381803539986426,
              -0.00025333324029368356,
              0.0019457768213825047
            ],
            "initial_K": [
              0.5152057601542946,
              0.98813752943817,
              1.3891319229278891,
              1.7045264367517121,
              1.9319196805269536,
              2.074331918775599,
              2.136529477833058,
              2.1232486275894815,
              2.0405749687784467,
              1.9003366180849048,
              1.7210189898347223,
              1.5192162608889026,
              1.2975620733089346,
              1.0429843680699307,
              0.7397314559796448,
              0.3859292266458987
            ],
            "metrics": {
              "initial_rmse_K": 0.026157020206837356,
              "observation_residual_rms_K": 0.01930060331461997,
              "future_predictive_rmse_K": 0.022135559370152314
            }
          }
        }
      },
      {
        "split": "train",
        "index": 88,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          7.198238705827468,
          1.1550105611197363,
          0.6102823772139508,
          0.10396921815451816,
          -0.042805709538251274,
          0.10875037470348965,
          0.013420751457136865,
          0.038202106806510344
        ],
        "initial_K": [
          0.770153473566716,
          1.4021570622987554,
          1.8634090862407762,
          2.1944091646559776,
          2.410236171655452,
          2.488367477798733,
          2.4359845644311613,
          2.311014325434036,
          2.1695707149676395,
          2.0293505764095348,
          1.8839282263684916,
          1.712498633249939,
          1.4735740690949293,
          1.136141424362579,
          0.7330000560504799,
          0.34300535309154495
        ],
        "observed_K": [
          0.5601443919266109,
          1.091906454001338,
          1.4510736839589593,
          1.824597031282591,
          2.1111543510847115,
          2.1583606574105367,
          2.2186688401233923,
          2.159405261637235,
          2.077907856090833,
          1.9472972938645712,
          1.8030143844400937,
          1.567725532129563,
          1.2948875542391012,
          1.0177338492124857,
          0.6856506953716305,
          0.33385432622278605
        ],
        "future_observed_K": [
          0.5036237943010067,
          0.9991435118689761,
          1.3698263925496008,
          1.686342537640427,
          1.9101945483618072,
          2.0504794212039954,
          2.10025797767403,
          2.096424280977685,
          2.0519911403671793,
          1.932091044220249,
          1.6950592032616865,
          1.5179996890041512,
          1.2527617852521753,
          0.9931795427925036,
          0.6711647270965192,
          0.33042773139586074
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              7.161040036704543,
              1.1376243361141953,
              0.6073576612327093,
              0.16621056836178258,
              -0.4068830575623302,
              0.15604850032029352,
              3.6253999480674564,
              17.828702056667105
            ],
            "initial_K": [
              7.962042259833417,
              3.0801783164736936,
              -4.884488558229349,
              -1.0802127228311666,
              8.186147848763852,
              6.987778486255399,
              -2.0266857081810086,
              -2.9123932533155057,
              5.168602391845607,
              7.318019829870833,
              -0.002470667288656081,
              -3.3805180353800592,
              2.6428493369624806,
              6.109104602089522,
              0.10813602999187233,
              -4.67072839207237
            ],
            "metrics": {
              "initial_rmse_K": 4.539332551241772,
              "observation_residual_rms_K": 0.018282373129743373,
              "future_predictive_rmse_K": 0.01949393194906483
            }
          },
          "tikhonov": {
            "coefficients_K": [
              7.074852653708835,
              1.113108722695545,
              0.5734695757718588,
              0.13455084338342627,
              -0.17021145553890407,
              0.011827221657135045,
              0.022700716840540848,
              0.005814270307627438
            ],
            "initial_K": [
              0.6849723392137285,
              1.3074013484213414,
              1.8229252754764045,
              2.1995818291440465,
              2.40910696379274,
              2.44599754647991,
              2.3557124745080493,
              2.2229129461238015,
              2.1143632586105445,
              2.0314648071921964,
              1.920389513322262,
              1.7251559292122294,
              1.4315370994782557,
              1.0710601131358826,
              0.693861684422014,
              0.33571593087864093
            ],
            "metrics": {
              "initial_rmse_K": 0.053637505239705424,
              "observation_residual_rms_K": 0.029821745128323775,
              "future_predictive_rmse_K": 0.03073758405735067
            }
          },
          "learned": {
            "coefficients_K": [
              7.160631024998912,
              1.1402629000271864,
              0.5959384549009215,
              0.12747178586506472,
              -0.053149813364859105,
              0.0011697786779241014,
              0.0035400322869228672,
              -0.0015696872332345226
            ],
            "initial_K": [
              0.7160909371506825,
              1.360562238359844,
              1.8745271861390367,
              2.2235578663250535,
              2.40461387982666,
              2.4444387587269945,
              2.3892806895966974,
              2.288354093043184,
              2.175063542001052,
              2.054117281499279,
              1.9046023419160165,
              1.6997988399462618,
              1.4289956384785332,
              1.103647226131833,
              0.7460737277507642,
              0.3749652908429375
            ],
            "metrics": {
              "initial_rmse_K": 0.03137471045580185,
              "observation_residual_rms_K": 0.02266650618425742,
              "future_predictive_rmse_K": 0.01879392860126598
            }
          }
        }
      },
      {
        "split": "train",
        "index": 89,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.439610727773125,
          -2.217739168051031,
          0.294342971133427,
          0.10187326929490026,
          0.18973728392052752,
          -0.04983217936799072,
          0.015513956386056555,
          -0.0038874494072350073
        ],
        "initial_K": [
          0.18515871468701406,
          0.3382077366234601,
          0.45403095977342456,
          0.5644142383050105,
          0.7218508712052898,
          0.9655544367696298,
          1.2927316873324926,
          1.6542209736577913,
          1.9752139675879998,
          2.1880913568991045,
          2.260592609904685,
          2.201277205662801,
          2.0325967111151844,
          1.7512780753653796,
          1.321322535565354,
          0.7209113893949071
        ],
        "observed_K": [
          0.1740267284637125,
          0.3289929628649909,
          0.4908840611568239,
          0.630456265548117,
          0.816376637757693,
          1.0455427984188643,
          1.3258669753420165,
          1.5459379875545203,
          1.7025252304013143,
          1.8879007180754095,
          1.8898359053077942,
          1.8662069460426423,
          1.656889526000137,
          1.3988617593563988,
          0.9880039599548817,
          0.5234075740610021
        ],
        "future_observed_K": [
          0.19419112220360063,
          0.33391562851187123,
          0.4745364972322947,
          0.6797416578876526,
          0.899990254218934,
          1.052432235672979,
          1.3290842417001814,
          1.5126967372583497,
          1.6510611890625264,
          1.768070566252074,
          1.7749208895151507,
          1.669335239859503,
          1.4888692805238117,
          1.2402753543592484,
          0.90474694171106,
          0.45211245145697904
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.388577463011921,
              -2.24644295020044,
              0.32787707056610227,
              0.19905763397701698,
              0.6129494568854201,
              0.9059582307052146,
              1.2036480072048563,
              -10.464523609889962
            ],
            "initial_K": [
              -2.5644905404838276,
              0.3252232338718447,
              3.6427072178504143,
              1.0977074621981227,
              -2.8173165929385804,
              -0.5545472900517638,
              4.596708952925722,
              4.006387699726769,
              -0.824479662183468,
              -0.817278281442646,
              4.361117237522135,
              5.5815002777589156,
              0.6116360123331777,
              -1.8771434443588384,
              2.050561585209578,
              4.491858381179313
            ],
            "metrics": {
              "initial_rmse_K": 2.6450804913772563,
              "observation_residual_rms_K": 0.014192776809121337,
              "future_predictive_rmse_K": 0.02319401084462215
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.323722723026362,
              -2.1980324818359187,
              0.3095828645369136,
              0.16114121260459754,
              0.2564152458283807,
              0.0686643497673077,
              0.007536733320086182,
              -0.0034126751748424014
            ],
            "initial_K": [
              0.2489080977464607,
              0.40634503705944,
              0.4630641332355453,
              0.5035310453949011,
              0.6373067243849652,
              0.9114890998157749,
              1.2798936961721432,
              1.6474548167717573,
              1.9380777612900875,
              2.1238504981387027,
              2.2053084891370083,
              2.1796056409499376,
              2.0290842069853836,
              1.7310143432602283,
              1.2749392983356056,
              0.6792962102950177
            ],
            "metrics": {
              "initial_rmse_K": 0.047509581994445854,
              "observation_residual_rms_K": 0.024740831129267983,
              "future_predictive_rmse_K": 0.030318012839951006
            }
          },
          "learned": {
            "coefficients_K": [
              5.388269687710041,
              -2.2516532670975264,
              0.3217125053366831,
              0.15266316903443747,
              0.0800675983677723,
              0.006791290010436485,
              0.001175305585213264,
              0.0009213250106551049
            ],
            "initial_K": [
              0.17867812344924883,
              0.3267920392467928,
              0.4421669116877369,
              0.5565892263818617,
              0.7157742929746059,
              0.9503562109934843,
              1.2570854929616313,
              1.5985913270397722,
              1.918219440751856,
              2.1598362627896814,
              2.281703250525524,
              2.2591347739619274,
              2.080087430744999,
              1.742746024793756,
              1.2592834932946175,
              0.6613065315219384
            ],
            "metrics": {
              "initial_rmse_K": 0.037564238527846176,
              "observation_residual_rms_K": 0.020135384904051604,
              "future_predictive_rmse_K": 0.02435890501631928
            }
          }
        }
      },
      {
        "split": "train",
        "index": 90,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.0383193620128734,
          0.2902370161732293,
          0.1518794692235485,
          -0.0364171489291275,
          -0.13717361618235874,
          -0.030516279219700425,
          -0.011331865431015251,
          -0.03787019546488964
        ],
        "initial_K": [
          0.3719503328172022,
          0.791399216243369,
          1.2213643515350225,
          1.5767193259103938,
          1.8154982700512468,
          1.9530893568983958,
          2.0104487934378823,
          1.9992153148689058,
          1.947124651432244,
          1.8833859298522055,
          1.7914133558722511,
          1.6199986371107642,
          1.353538671405249,
          1.0342388927225479,
          0.7036204320925814,
          0.3614642727939968
        ],
        "observed_K": [
          0.4209130570601274,
          0.7255989773297046,
          1.04949432449694,
          1.302453520422616,
          1.6253934462340158,
          1.685599235299835,
          1.7823559325864964,
          1.8745567956952172,
          1.82238174942081,
          1.7211996842102069,
          1.642790020230781,
          1.4307687608865114,
          1.2025467042086626,
          0.9792917411301885,
          0.6956162956776316,
          0.3310287515398323
        ],
        "future_observed_K": [
          0.35470675745176045,
          0.6588578742527704,
          0.993105296634069,
          1.2583278037047225,
          1.5198126796461788,
          1.6194999853762153,
          1.7355784647930237,
          1.7768686165296788,
          1.7146619015455256,
          1.6634628100710507,
          1.580515452759392,
          1.3974343895349777,
          1.1754069443879647,
          0.9061255823724412,
          0.606581205939512,
          0.2972707442159319
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.010469026143364,
              0.24338330167324915,
              0.21971627996231813,
              -0.08723993994648581,
              0.19772552670251128,
              -0.3820339920817935,
              2.307876808573863,
              19.78793861437944
            ],
            "initial_K": [
              7.884935894425162,
              2.463160368157929,
              -5.801658576694516,
              -1.5434579577840126,
              8.010303365805811,
              6.1951935790194606,
              -3.245530753793478,
              -3.2060476816761536,
              6.02464192034314,
              7.706575665390965,
              -1.046940876634066,
              -4.509662111837127,
              2.9528666005425963,
              7.104707135041034,
              0.12511813170450048,
              -5.416968372746608
            ],
            "metrics": {
              "initial_rmse_K": 4.9917888932550385,
              "observation_residual_rms_K": 0.026872874189652597,
              "future_predictive_rmse_K": 0.022141734351543877
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.9381294507067155,
              0.2381384323899877,
              0.2074570058183301,
              -0.07062250982121143,
              0.08271455169173585,
              -0.028955104955429974,
              0.014450945739714437,
              0.0064532136758500905
            ],
            "initial_K": [
              0.4456222584662206,
              0.8527467958778978,
              1.2034629169253228,
              1.4952038862631665,
              1.7237235608959163,
              1.882040135639949,
              1.971102656493626,
              1.9981132466174583,
              1.9640335864382437,
              1.8650472145118215,
              1.7099224396926003,
              1.5237498860576324,
              1.3239355781157658,
              1.0964969007709533,
              0.8059683752013781,
              0.43262020625781933
            ],
            "metrics": {
              "initial_rmse_K": 0.06518900963414466,
              "observation_residual_rms_K": 0.033265058949497966,
              "future_predictive_rmse_K": 0.028629548100980083
            }
          },
          "learned": {
            "coefficients_K": [
              6.010125730731605,
              0.24394779592362115,
              0.2155852947200306,
              -0.06690688235620373,
              0.025828243880852822,
              -0.00286382257607246,
              0.0022535329987377066,
              -0.0017421837280299666
            ],
            "initial_K": [
              0.43882321200883123,
              0.8524303105677902,
              1.2188690320909688,
              1.5227081893509893,
              1.7557974620487138,
              1.9147300499158055,
              1.998942029559677,
              2.012403912579344,
              1.9653028985092342,
              1.8707617661341334,
              1.7383776258807677,
              1.570423278723744,
              1.3621876418827972,
              1.104183009505919,
              0.7871788082104937,
              0.4122403191534788
            ],
            "metrics": {
              "initial_rmse_K": 0.047925521533306974,
              "observation_residual_rms_K": 0.0290668306235873,
              "future_predictive_rmse_K": 0.02125169899432977
            }
          }
        }
      },
      {
        "split": "train",
        "index": 91,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.3812368290779045,
          0.5171940196966862,
          0.3828278262638978,
          -0.06812387883301835,
          0.10033802439426084,
          0.03166729484697111,
          -0.07665161220630441,
          0.02119943909706419
        ],
        "initial_K": [
          0.5387874090101897,
          1.0337188245771602,
          1.4442819361312313,
          1.744024915862111,
          1.937107902924156,
          2.0575835186887783,
          2.1328727968715384,
          2.146758320625793,
          2.0630450263399296,
          1.894239888607264,
          1.714001439398537,
          1.5728751517814326,
          1.4254810467040429,
          1.1819576606880624,
          0.8212221188992815,
          0.40817842552794087
        ],
        "observed_K": [
          0.45044586242980333,
          0.8590035256895641,
          1.2233640195719433,
          1.48489645350498,
          1.7136570397796713,
          1.8575848058321944,
          1.9760347087104668,
          1.9608213674171968,
          1.8997545163125786,
          1.8144632278862238,
          1.657161311376198,
          1.5155478215487146,
          1.2564775510636208,
          1.0390193390931375,
          0.6671598830338542,
          0.33765726206977686
        ],
        "future_observed_K": [
          0.38617283507602446,
          0.7745216609401829,
          1.0971944418406057,
          1.4197497920743987,
          1.5994158857692793,
          1.7551213191725021,
          1.8454556175813128,
          1.8186239182030666,
          1.8569506741261665,
          1.7327595032253709,
          1.5823700691909186,
          1.4291218224793416,
          1.2165005894822336,
          0.9444498297228837,
          0.6776029216836128,
          0.32638180396211297
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.415777596818691,
              0.51372123930154,
              0.3962957194334226,
              -0.012750884262348041,
              0.16174867799949924,
              1.586436987742151,
              -1.5166077625339398,
              0.09665153446990345
            ],
            "initial_K": [
              0.6006674628182573,
              1.2508206363769423,
              1.6866746206162915,
              1.6667572277083158,
              1.4892562917161494,
              1.7484047604381674,
              2.4593341237827753,
              2.823330496311414,
              2.2271740310454664,
              1.2352503196228983,
              1.030724242817568,
              1.8195173218529879,
              2.388151284924324,
              1.641934059942989,
              0.14145872226090161,
              -0.5609587850645327
            ],
            "metrics": {
              "initial_rmse_K": 0.5306069329903065,
              "observation_residual_rms_K": 0.01448055387945947,
              "future_predictive_rmse_K": 0.021911513779689983
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.3385598912734,
              0.5026506328562835,
              0.3741840312715054,
              -0.010322100744213988,
              0.0676643507319563,
              0.12023916833928058,
              -0.009496354572907548,
              3.151985743375207e-05
            ],
            "initial_K": [
              0.5792682965442848,
              1.0664138944197252,
              1.426814525881014,
              1.6891563869231436,
              1.8975460818495204,
              2.0596132503451674,
              2.142723431546613,
              2.119426481140249,
              2.010101542211775,
              1.872748629178249,
              1.7478261361416145,
              1.6177154312605422,
              1.4264553816434047,
              1.1389761197693102,
              0.7753367596475508,
              0.38561931573373287
            ],
            "metrics": {
              "initial_rmse_K": 0.03474824367911354,
              "observation_residual_rms_K": 0.025443400243457696,
              "future_predictive_rmse_K": 0.0200463364508135
            }
          },
          "learned": {
            "coefficients_K": [
              6.415411151703963,
              0.5149127453904376,
              0.3888447842144122,
              -0.009779029121315385,
              0.021128704889289033,
              0.011892329361204185,
              -0.0014808960453673234,
              -8.509462957411437e-06
            ],
            "initial_K": [
              0.5450303120836608,
              1.0398925815649158,
              1.4488355439241114,
              1.7568405094487038,
              1.9657681362723287,
              2.085521617162388,
              2.1278035927934025,
              2.105506128414428,
              2.0338788532833996,
              1.9277204140039605,
              1.794243969726738,
              1.6279949157062856,
              1.4141972757860315,
              1.1394863075141968,
              0.8020954696936915,
              0.41465231842159683
            ],
            "metrics": {
              "initial_rmse_K": 0.032957352192783215,
              "observation_residual_rms_K": 0.018850595567981982,
              "future_predictive_rmse_K": 0.021542080113820247
            }
          }
        }
      },
      {
        "split": "train",
        "index": 92,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.365176728731818,
          -0.902301380563681,
          0.18620605825639588,
          -0.0007016841715675164,
          -0.06333037862386101,
          -0.01909050012487801,
          -0.032236048457401405,
          0.007671961380660211
        ],
        "initial_K": [
          0.22859315571556535,
          0.48174889119106445,
          0.7533983577374495,
          1.0091993913589747,
          1.2204344677368575,
          1.3914799021006283,
          1.5476487312431284,
          1.6983379948148223,
          1.8223399687881294,
          1.8903054879432653,
          1.8869287947918787,
          1.8019919128325055,
          1.6149261896919818,
          1.3105206000876906,
          0.9087117886730236,
          0.4589990740108425
        ],
        "observed_K": [
          0.26241188849448716,
          0.4903276550592207,
          0.6900399271315794,
          0.9229091466313527,
          1.141604442618617,
          1.313276862887661,
          1.4436226124128593,
          1.5921019352455072,
          1.6905686702572742,
          1.6781986276057224,
          1.6494929336361557,
          1.5313694082089184,
          1.3540198350843664,
          1.0952843438833317,
          0.7616721956367842,
          0.4063062260247387
        ],
        "future_observed_K": [
          0.21243918872553863,
          0.5070108503198201,
          0.6976782250052238,
          0.9447929754637845,
          1.0998059653510135,
          1.2527242121548299,
          1.432880576542512,
          1.5322199956174787,
          1.594445451276145,
          1.6332959322011429,
          1.579059885857527,
          1.415891571796599,
          1.2354656272560423,
          0.9732942463637531,
          0.6989028963792825,
          0.3640618355759456
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.340017799472326,
              -0.922152901704107,
              0.19025836391760517,
              0.007293678947196854,
              0.15661211621049706,
              -0.0061500670466137,
              0.4618205870755127,
              15.19295621624371
            ],
            "initial_K": [
              5.640584337705453,
              1.6003914170107518,
              -4.3510733091495695,
              -1.0789891063004378,
              5.821554029752443,
              4.236872429269887,
              -2.544609757386085,
              -1.8881481296418172,
              5.25356466759364,
              6.114247207069637,
              -0.7385964976283113,
              -2.8998556197381227,
              3.310889315667371,
              6.23484956313103,
              0.10986106696189335,
              -4.508313725630694
            ],
            "metrics": {
              "initial_rmse_K": 3.7987382725845102,
              "observation_residual_rms_K": 0.010114001552404179,
              "future_predictive_rmse_K": 0.022528254210307814
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.275747503966644,
              -0.9022806615160288,
              0.1796427215908164,
              0.005904381793443934,
              0.06551557200469843,
              -0.00046612563412814037,
              0.002891724645144858,
              0.004954704718965
            ],
            "initial_K": [
              0.2749473389453744,
              0.5246900891377476,
              0.7443936351934737,
              0.9473032186151511,
              1.1470276252434406,
              1.3463028250971059,
              1.5372154808815066,
              1.7030792933236425,
              1.8207341083926827,
              1.8697121515390573,
              1.8424650837952865,
              1.7412329303743164,
              1.563798291379386,
              1.298441519352922,
              0.9372778921570296,
              0.4927143922164988
            ],
            "metrics": {
              "initial_rmse_K": 0.04052298299465151,
              "observation_residual_rms_K": 0.01944765906661113,
              "future_predictive_rmse_K": 0.028706463823212996
            }
          },
          "learned": {
            "coefficients_K": [
              5.3397127977160075,
              -0.9242917091218594,
              0.18668123029009162,
              0.005593737450568676,
              0.020457732492310546,
              -4.610244433087177e-05,
              0.00045094605076178185,
              -0.0013376290282898476
            ],
            "initial_K": [
              0.2622922058925946,
              0.5139974131891972,
              0.7485346441539082,
              0.965999861694709,
              1.171408638239889,
              1.3680707280077142,
              1.5515359406912574,
              1.7096182600526209,
              1.8269109182351129,
              1.8880591400643616,
              1.8782459072997393,
              1.7840828941104023,
              1.5962869666455117,
              1.3121702818845156,
              0.9375330641149663,
              0.48969754116317515
            ],
            "metrics": {
              "initial_rmse_K": 0.024627973718265386,
              "observation_residual_rms_K": 0.012602183815295088,
              "future_predictive_rmse_K": 0.022609142451898826
            }
          }
        }
      },
      {
        "split": "train",
        "index": 93,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.944585510145798,
          -0.46773431538602284,
          0.08563057169226695,
          0.3698508564571831,
          0.2526071604331949,
          -0.07815941932786918,
          -0.050847538654435115,
          -0.03104372008733126
        ],
        "initial_K": [
          0.4353995304780918,
          0.8318941273970698,
          1.1184669389454054,
          1.2602824744825851,
          1.3357093215153792,
          1.478750065513667,
          1.7347610631188743,
          2.011261332163922,
          2.1757511870285096,
          2.1671843725480984,
          2.009413974174981,
          1.7608294696839484,
          1.4738936401373792,
          1.172887441148357,
          0.8421252284023705,
          0.449582428301898
        ],
        "observed_K": [
          0.3412267335308498,
          0.5997429245844238,
          0.94420584470611,
          1.1342601747575793,
          1.3585498302726338,
          1.5234624320476058,
          1.7167721341212494,
          1.7584585670633295,
          1.9082921133333264,
          1.8626665997706315,
          1.7659724595711042,
          1.585470873345884,
          1.3898632583452024,
          1.0562514490606503,
          0.7484683755933286,
          0.3510998283760954
        ],
        "future_observed_K": [
          0.3261445948568439,
          0.5948855227548281,
          0.8778152449564393,
          1.1211194635594572,
          1.3230260177076918,
          1.4743069812560572,
          1.608910693254717,
          1.7536709366367416,
          1.755672169088443,
          1.7646412687859283,
          1.6607443176572025,
          1.5090183511264303,
          1.2813151458055003,
          1.0380663078633048,
          0.6878089042870658,
          0.37032589225012313
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.964740603337615,
              -0.4961487782632449,
              0.08204006931950573,
              0.40981476938286154,
              0.14407565972569608,
              -0.23916411081498304,
              -2.086416410319972,
              9.403173417791294
            ],
            "initial_K": [
              2.913158594132392,
              0.9875423111185311,
              -1.5222162220885953,
              0.7855367777924065,
              4.166837385268505,
              2.4776036981483536,
              -1.1715186161011566,
              0.32734462903491846,
              4.923499794006966,
              4.57030756980091,
              -0.3168842861997512,
              -1.2426061048816357,
              3.2451783262856453,
              4.73224248187833,
              -0.11744694706392855,
              -3.42942915850188
            ],
            "metrics": {
              "initial_rmse_K": 2.413355014922029,
              "observation_residual_rms_K": 0.02351021659245603,
              "future_predictive_rmse_K": 0.015794127195884418
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.892951396711913,
              -0.48545685540267736,
              0.07746256736675063,
              0.3317534101166525,
              0.060271194127766985,
              -0.01812671666331008,
              -0.013064254653442747,
              0.0030665491984084464
            ],
            "initial_K": [
              0.40957235885622917,
              0.7678335507891,
              1.0428856892879983,
              1.2367581421432357,
              1.3862680778271468,
              1.5420746073740759,
              1.7318376095972694,
              1.9334859070986836,
              2.084853319630274,
              2.124933033877781,
              2.03010858796969,
              1.816121437201068,
              1.515340085297872,
              1.1591184645022619,
              0.7751146366452407,
              0.38558952999831897
            ],
            "metrics": {
              "initial_rmse_K": 0.05459306168803402,
              "observation_residual_rms_K": 0.02962084678495253,
              "future_predictive_rmse_K": 0.024146142111461804
            }
          },
          "learned": {
            "coefficients_K": [
              5.964399919761582,
              -0.4972995274343392,
              0.08049759683775223,
              0.314299030693434,
              0.01882013586586026,
              -0.0017928341302980227,
              -0.002037287350995731,
              -0.0008278808641752839
            ],
            "initial_K": [
              0.405099812647726,
              0.7614620803848549,
              1.0409808932005957,
              1.2481469840627706,
              1.4153273850883448,
              1.5810025479906766,
              1.763326570186424,
              1.9464069181597055,
              2.0872432847940474,
              2.1366912992734535,
              2.0613618028681633,
              1.85663153710979,
              1.5468305533532387,
              1.1735304561464264,
              0.7776879552951235,
              0.3847481789112358
            ],
            "metrics": {
              "initial_rmse_K": 0.0652699831141185,
              "observation_residual_rms_K": 0.02494219368082156,
              "future_predictive_rmse_K": 0.016596637344518394
            }
          }
        }
      },
      {
        "split": "train",
        "index": 94,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.658327684045523,
          2.1190523916325708,
          0.18977702027544863,
          0.14519587031963846,
          -0.14109690589164986,
          0.04839334107691082,
          -0.050291363609852736,
          9.74249257058888e-05
        ],
        "initial_K": [
          0.7097039299963912,
          1.380141954373166,
          1.9485041766354454,
          2.348343855392097,
          2.552748737125713,
          2.585965018175878,
          2.492175253515989,
          2.306160292879877,
          2.0576010592789027,
          1.7830817839772182,
          1.509694652892798,
          1.2293229799670762,
          0.9145392579869239,
          0.5739219152494143,
          0.27513576949416885,
          0.08769585299008126
        ],
        "observed_K": [
          0.5717789984289033,
          1.12097110813122,
          1.5192323652184252,
          1.8985861521473713,
          2.1202134658137513,
          2.2185733942070462,
          2.1963247690006225,
          2.1057932116223066,
          1.9537632030695153,
          1.728791901852062,
          1.4211782028299216,
          1.21547576255455,
          0.9593190913160483,
          0.6403583452385807,
          0.4175198030365168,
          0.2001125123453774
        ],
        "future_observed_K": [
          0.5363482964122658,
          0.9681641638934946,
          1.428483149931297,
          1.7371748031880099,
          1.979323678271664,
          2.040585272173947,
          2.093674684341263,
          2.0095421269183604,
          1.901959036756178,
          1.6635691539401418,
          1.4430439806255717,
          1.2004541597596947,
          0.955335907337802,
          0.659340755525108,
          0.4869671419068672,
          0.23628221078402456
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.624129349050717,
              2.0925011754692346,
              0.16830375207810683,
              0.17987511120962718,
              -0.18991846058439268,
              0.6380510611579314,
              -1.9611525797628728,
              13.075796448448404
            ],
            "initial_K": [
              4.711475336780182,
              1.999382770485796,
              -1.979042291650768,
              1.1085318324204316,
              6.3004344631984655,
              4.35083891707963,
              -1.1470904921924416,
              -0.11136438335300491,
              5.482026853121575,
              4.930023101040485,
              -1.5561581434563898,
              -2.749923178964494,
              3.3178379812704897,
              5.34545938115032,
              -1.0880470929451624,
              -5.213667072090498
            ],
            "metrics": {
              "initial_rmse_K": 3.306989884664715,
              "observation_residual_rms_K": 0.017617354936156494,
              "future_predictive_rmse_K": 0.022414678818228798
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.544404006042794,
              2.0474081265009807,
              0.1589130877334294,
              0.1456125693780364,
              -0.07944862045484755,
              0.04835914035313358,
              -0.012279905674413833,
              0.00426425966383591
            ],
            "initial_K": [
              0.7189970542639204,
              1.3675916777586705,
              1.8929915073009078,
              2.265820673555274,
              2.4766586803014277,
              2.5326684426673163,
              2.45610197607237,
              2.280421509080409,
              2.042934437484776,
              1.7754416822022376,
              1.4943973265994872,
              1.1980802262782362,
              0.8819114727015251,
              0.5649212175537774,
              0.2949048448895506,
              0.11172531618317033
            ],
            "metrics": {
              "initial_rmse_K": 0.038992793259683134,
              "observation_residual_rms_K": 0.027772738972227633,
              "future_predictive_rmse_K": 0.03296536678622876
            }
          },
          "learned": {
            "coefficients_K": [
              6.623751003666598,
              2.0973544454936293,
              0.16513939704635627,
              0.13795152669630395,
              -0.024808432169863715,
              0.0047829907063344675,
              -0.0019149731205914018,
              -0.0011512285462097007
            ],
            "initial_K": [
              0.7326867901433552,
              1.3958884014462658,
              1.9315918540396022,
              2.30443401599714,
              2.5074080018804388,
              2.557374014760664,
              2.4835384286758346,
              2.3168869079681587,
              2.0844394224784635,
              1.8069374210274889,
              1.4994599980202832,
              1.1762947391517935,
              0.8572799085070542,
              0.5679786065644172,
              0.32988957159454024,
              0.14703668529884723
            ],
            "metrics": {
              "initial_rmse_K": 0.03543704519799491,
              "observation_residual_rms_K": 0.01996530288307837,
              "future_predictive_rmse_K": 0.022052853090943493
            }
          }
        }
      },
      {
        "split": "train",
        "index": 95,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.4280678508184605,
          -1.3423666030473942,
          0.07907781940880058,
          -0.22421865572603122,
          0.09459850352638363,
          0.014251039484927515,
          -0.0015668925995722571,
          0.019467523014159552
        ],
        "initial_K": [
          0.17464926154684743,
          0.34613053566593943,
          0.5383573397161506,
          0.7796305743193741,
          1.0634675351492882,
          1.3510691949944205,
          1.6042317412895286,
          1.7985091046028183,
          1.9160028368475652,
          1.9522351720823719,
          1.9274251913802138,
          1.8628299594773832,
          1.7390484495047414,
          1.5000601054365466,
          1.1094083045119194,
          0.5888748668281933
        ],
        "observed_K": [
          0.17822474813831585,
          0.4156523099492115,
          0.61537798758539,
          0.8366673180255598,
          1.0721368456399438,
          1.2606440433889385,
          1.4869816878383444,
          1.6417417937494665,
          1.7245204942752972,
          1.7360948026354008,
          1.7584054874931712,
          1.631698994339683,
          1.4688893092224922,
          1.1884223402995846,
          0.8517686094096453,
          0.45476632839690256
        ],
        "future_observed_K": [
          0.19938463309117754,
          0.41373823597379256,
          0.6507988889201434,
          0.8139812614638473,
          1.0383638889622056,
          1.2191261495091144,
          1.3983869342735957,
          1.53060555944125,
          1.6450868453523426,
          1.6585317600662557,
          1.653022777643195,
          1.5093204772239577,
          1.3197624693108556,
          1.1093767057887607,
          0.7469126306008584,
          0.38089232694258957
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.447401622346038,
              -1.332627772453193,
              0.09723238481937295,
              -0.2791842448972204,
              0.16758679806688642,
              0.2795575544770326,
              -0.9527963769556337,
              -16.01211429358614
            ],
            "initial_K": [
              -5.520055425958497,
              -0.7478818114540248,
              6.036996946613939,
              2.9666797156814515,
              -3.9843514050815716,
              -1.8269484717970694,
              5.99052625444489,
              5.841739788114353,
              -1.5604430451437539,
              -2.656216614987928,
              4.431540805166713,
              6.755972247053298,
              0.12864276468593894,
              -3.52149745668393,
              1.924001219277781,
              5.704901293188995
            ],
            "metrics": {
              "initial_rmse_K": 4.015563373893474,
              "observation_residual_rms_K": 0.011419715973046144,
              "future_predictive_rmse_K": 0.0192288872817014
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.3818388985586925,
              -1.3039098677255117,
              0.09180721349670691,
              -0.22600533756987837,
              0.07010661244772862,
              0.021188214919976946,
              -0.005966006804709264,
              -0.005221847356225249
            ],
            "initial_K": [
              0.1639288277813977,
              0.3440556425268452,
              0.5513659463378492,
              0.7919977271370966,
              1.0643046688479545,
              1.3477471242854735,
              1.6005702171023848,
              1.781807895224856,
              1.880095909751643,
              1.915334231223394,
              1.9090686410396134,
              1.8560150471555397,
              1.723831180065734,
              1.4750156306611482,
              1.090095470851702,
              0.5820547565827269
            ],
            "metrics": {
              "initial_rmse_K": 0.0177801866047766,
              "observation_residual_rms_K": 0.021109964472729347,
              "future_predictive_rmse_K": 0.01822786844760809
            }
          },
          "learned": {
            "coefficients_K": [
              5.447090487229156,
              -1.3357186201418556,
              0.09540427473654187,
              -0.214114629612332,
              0.021891319567428423,
              0.00209563351014986,
              -0.0009303607838037392,
              0.0014097499248037087
            ],
            "initial_K": [
              0.15236390208175984,
              0.330150770830615,
              0.5497425958979728,
              0.8105828773497881,
              1.0932025369017042,
              1.3666187586812586,
              1.6011204993961279,
              1.7782666241692,
              1.8934704971310483,
              1.9513453036146091,
              1.9555355434337223,
              1.8972986620406262,
              1.7516909908369949,
              1.488384841160567,
              1.092384929097017,
              0.5800715244263539
            ],
            "metrics": {
              "initial_rmse_K": 0.020210266103135883,
              "observation_residual_rms_K": 0.014536419957387867,
              "future_predictive_rmse_K": 0.01857398384774221
            }
          }
        }
      },
      {
        "split": "train",
        "index": 96,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.698634446729098,
          -0.133622201740806,
          0.02440843127510992,
          -0.19891144649343964,
          -0.05804617980493765,
          -0.15751202483745172,
          0.023166519618334946,
          -0.017371687913866028
        ],
        "initial_K": [
          0.23850608993867556,
          0.5555957555754791,
          0.9449488785639,
          1.3228082084850683,
          1.6070233744594153,
          1.775880496610252,
          1.861476390461171,
          1.9058590612889579,
          1.9222639836136493,
          1.8856659226414227,
          1.763093294918488,
          1.561228593986834,
          1.3309218705399446,
          1.10457781160598,
          0.841636852575486,
          0.4721367244214232
        ],
        "observed_K": [
          0.26758321511235744,
          0.5803478813736064,
          0.883486144610337,
          1.1696361570226712,
          1.3773820574447881,
          1.5608805968968764,
          1.6784291603876687,
          1.7763517985356532,
          1.7407908395904732,
          1.720670324738145,
          1.6017615871125135,
          1.4599435368731044,
          1.2234906529685043,
          0.9628450972204838,
          0.7018183176255666,
          0.2988653983696992
        ],
        "future_observed_K": [
          0.2554774481362973,
          0.6160856880205995,
          0.8738860649850884,
          1.0965818710709794,
          1.3034070614919437,
          1.4325703450555112,
          1.6339264167944971,
          1.6805820550773252,
          1.6607209817516915,
          1.6466393832083337,
          1.5219678694412802,
          1.3754031521834413,
          1.1550679967940776,
          0.9037998633337841,
          0.6602527021579111,
          0.3108533846974283
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.685560672232711,
              -0.17588747512212366,
              -0.02906091535255191,
              -0.17886246959651828,
              -0.365915758411513,
              -0.49160790833494544,
              -3.2252928110790746,
              -8.234209932175617
            ],
            "initial_K": [
              -3.8374339319958066,
              -0.7628036411822896,
              4.361150844511272,
              3.4732982971319304,
              -0.9660159641746349,
              -0.8063322305769762,
              3.568816321307348,
              4.5469042449701425,
              0.8968336702490374,
              -0.6493964077123577,
              2.2673812969938885,
              3.914684555282683,
              1.2511034967148496,
              -0.9278817361016243,
              0.7477132170331153,
              2.2152247129778093
            ],
            "metrics": {
              "initial_rmse_K": 2.2119072751498865,
              "observation_residual_rms_K": 0.016628239608537362,
              "future_predictive_rmse_K": 0.024177958889554915
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.617131562397913,
              -0.17209712956745227,
              -0.027439434558123456,
              -0.14479281534896418,
              -0.1530735986329549,
              -0.03725992680701073,
              -0.020195415645428746,
              -0.0026853285316704397
            ],
            "initial_K": [
              0.2333676748579961,
              0.5338318192334733,
              0.90134595563829,
              1.2690346451231413,
              1.5622695885676903,
              1.7504391360133462,
              1.8486937233882457,
              1.8870088614090281,
              1.8850354590413112,
              1.8459101607840394,
              1.7593189985076114,
              1.6079607866681873,
              1.3795901776288837,
              1.0798230806335871,
              0.7330059765489199,
              0.3676459459894787
            ],
            "metrics": {
              "initial_rmse_K": 0.04957745937264546,
              "observation_residual_rms_K": 0.024606206377986363,
              "future_predictive_rmse_K": 0.027385068153808992
            }
          },
          "learned": {
            "coefficients_K": [
              5.685235934365572,
              -0.1762954220426243,
              -0.02851452792750836,
              -0.13717490198382895,
              -0.04779838802664697,
              -0.0036852161211977977,
              -0.003149346513365067,
              0.0007249621517723199
            ],
            "initial_K": [
              0.28461869216713254,
              0.5907853438065869,
              0.9199361901101287,
              1.2477821464624186,
              1.5364252546778185,
              1.7540263518463468,
              1.8875935333410352,
              1.9423471049261833,
              1.932241947835583,
              1.8699371856579199,
              1.7606791632199292,
              1.6010599870489721,
              1.3832430822951796,
              1.1033033387357005,
              0.7678863420799819,
              0.3934697952781932
            ],
            "metrics": {
              "initial_rmse_K": 0.04568949706527887,
              "observation_residual_rms_K": 0.019837620728192853,
              "future_predictive_rmse_K": 0.02352896651963312
            }
          }
        }
      },
      {
        "split": "train",
        "index": 97,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.88754816391905,
          0.9570959741249767,
          0.01739565914712307,
          0.10583745919535849,
          0.02282883620528129,
          0.033085176001695575,
          0.06334626252750682,
          0.013956434455832641
        ],
        "initial_K": [
          0.6223497977408513,
          1.144955627322771,
          1.5539257716389234,
          1.893641787276562,
          2.176873275531567,
          2.3636830035458374,
          2.425295268493563,
          2.386220121446145,
          2.2863065993046416,
          2.129692856719084,
          1.8963282624211182,
          1.5903157647755348,
          1.2518275833023387,
          0.9216350081355532,
          0.6104669838612222,
          0.306409126848173
        ],
        "observed_K": [
          0.4702437594926559,
          0.9408007150128636,
          1.3514971698289802,
          1.6778993759221388,
          1.9338919790397793,
          2.071896180962109,
          2.1808106879920133,
          2.1640234152256776,
          2.045632004070282,
          1.9194237711677422,
          1.7269162886268785,
          1.4964951454218516,
          1.2077679129872203,
          0.9242139017524444,
          0.5955771937216194,
          0.3202139006512783
        ],
        "future_observed_K": [
          0.4375980200956262,
          0.8546827507697826,
          1.2524073097858586,
          1.552175974713961,
          1.7979280540236695,
          1.9394606296760566,
          2.021062858678267,
          2.066221542740408,
          1.998243210309323,
          1.892088796685324,
          1.662935953633846,
          1.4567877980111892,
          1.2232068448113183,
          0.9128777752365534,
          0.6099918330968773,
          0.28767316187802416
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.858213958012328,
              1.0143654377361848,
              0.07516747645528819,
              0.055519326638316914,
              -0.16886732995352144,
              0.37900978825644094,
              -0.5384621388608452,
              -15.79604241609436
            ],
            "initial_K": [
              -4.918048150634237,
              0.08145233263939733,
              6.881453714462263,
              3.9832706847255004,
              -2.7026900066892634,
              -0.589797368742065,
              6.787030609855,
              6.1886222848934835,
              -1.3625161018984904,
              -2.4513942245418696,
              4.502029556559106,
              6.523219776139156,
              -0.38094801989050087,
              -4.146401883387309,
              1.3583640980952556,
              5.361953959005804
            ],
            "metrics": {
              "initial_rmse_K": 3.9566767783101544,
              "observation_residual_rms_K": 0.009175791760380875,
              "future_predictive_rmse_K": 0.02154185254691555
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.775671267280812,
              0.9925060328805173,
              0.07097343721188218,
              0.04494402670596432,
              -0.07064229755979483,
              0.028725894620787947,
              -0.0033716215365832496,
              -0.005151382310726103
            ],
            "initial_K": [
              0.5598298398721104,
              1.089648358136471,
              1.5566418593429459,
              1.9318790771168886,
              2.1984253775198725,
              2.3505591822873173,
              2.3906801661367507,
              2.333302441169268,
              2.2065790163370256,
              2.037414276917302,
              1.8316224835314197,
              1.5762326719805944,
              1.2659416934989536,
              0.9227848468757769,
              0.5851842486199399,
              0.2789850691689728
            ],
            "metrics": {
              "initial_rmse_K": 0.04604423252579479,
              "observation_residual_rms_K": 0.022591661041406214,
              "future_predictive_rmse_K": 0.029929199118452862
            }
          },
          "learned": {
            "coefficients_K": [
              6.857822242594711,
              1.0167181195078656,
              0.07375421870310868,
              0.04257940867639433,
              -0.022058591292110585,
              0.0028411523860652965,
              -0.0005257829161356486,
              0.0013907263712953349
            ],
            "initial_K": [
              0.5764869630025156,
              1.1153372991396866,
              1.5840472546856263,
              1.9578261206088237,
              2.2212471068042783,
              2.370734268711008,
              2.4150207836302924,
              2.3702138881283754,
              2.2522237153545057,
              2.0728215592164982,
              1.8410347704762782,
              1.566245137007808,
              1.2601905634148283,
              0.9376703610222804,
              0.6146443163357875,
              0.3021615314238638
            ],
            "metrics": {
              "initial_rmse_K": 0.03426315087847799,
              "observation_residual_rms_K": 0.012401161270488952,
              "future_predictive_rmse_K": 0.021779772072434273
            }
          }
        }
      },
      {
        "split": "train",
        "index": 98,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.9604544380608395,
          -0.1753010148613023,
          -0.02205915969603404,
          0.20072700581679864,
          -0.09163935977379,
          0.05418219976201592,
          0.015452256506651598,
          0.020055046759604175
        ],
        "initial_K": [
          0.3998403272797104,
          0.7484562055058785,
          1.0448760367890206,
          1.3155004581120464,
          1.5605810413384198,
          1.7540633916279151,
          1.8873424953145443,
          1.9798385656304043,
          2.041379241407714,
          2.047879401519457,
          1.9618010831678852,
          1.7614593464563002,
          1.4506607354044725,
          1.062701487327099,
          0.6601724082302121,
          0.303544358486108
        ],
        "observed_K": [
          0.3178259231936126,
          0.6563481576610144,
          0.922727097843108,
          1.231376292715786,
          1.420134834931439,
          1.6028900083150737,
          1.7399753180204334,
          1.8210003865116315,
          1.847500050581489,
          1.8220354699657342,
          1.7266154358730335,
          1.5125099651607272,
          1.2725808498098112,
          1.0177090786924654,
          0.6825737545682729,
          0.3503507985119933
        ],
        "future_observed_K": [
          0.33127026717353825,
          0.594895406127354,
          0.8983120405467608,
          1.1591428858311787,
          1.3986646855937868,
          1.5349863490872762,
          1.7133773332296482,
          1.714594234697072,
          1.7861000054417067,
          1.7138694689873095,
          1.6230089614242562,
          1.4370997062158208,
          1.2194549206274439,
          0.953427575008499,
          0.6348603355795792,
          0.3283956795195271
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.949141336226023,
              -0.19909311020948176,
              7.716575169498285e-05,
              0.19843696790101253,
              -0.08475128891754488,
              -0.8513739578122749,
              0.5272378255985499,
              0.8640760322943859
            ],
            "initial_K": [
              0.5805937325889013,
              0.6475822827680824,
              0.7036816750286442,
              1.3464614461209237,
              2.0510936529075305,
              1.9568359782592613,
              1.398447399146558,
              1.470942047991418,
              2.2520027579523525,
              2.64677339792227,
              2.0956920910917507,
              1.330045268690433,
              1.1098263798578965,
              1.180115484611684,
              0.9612018971256862,
              0.47080945114416917
            ],
            "metrics": {
              "initial_rmse_K": 0.33499669812242394,
              "observation_residual_rms_K": 0.011629183504123949,
              "future_predictive_rmse_K": 0.019599784580227975
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.877539876073196,
              -0.1948026871152606,
              7.286021682647906e-05,
              0.16063877076344996,
              -0.035454020454620795,
              -0.06452730075258936,
              0.0033013396474822375,
              0.00028179121520643973
            ],
            "initial_K": [
              0.355099749698137,
              0.7093828164333131,
              1.0442772241546836,
              1.3284101612649055,
              1.5428376879189183,
              1.6996857881149192,
              1.8305663503693594,
              1.9516683664459282,
              2.039464257994073,
              2.0437907083687303,
              1.9282069633422574,
              1.699386827004194,
              1.3987192158084572,
              1.0680139192028153,
              0.7249729476046135,
              0.3685665656428316
            ],
            "metrics": {
              "initial_rmse_K": 0.04118509817549236,
              "observation_residual_rms_K": 0.020895913370642383,
              "future_predictive_rmse_K": 0.027721363378803127
            }
          },
          "learned": {
            "coefficients_K": [
              5.948801543621528,
              -0.19955487942384145,
              7.571492346542852e-05,
              0.1521871619194029,
              -0.011070785830665161,
              -0.006382112617195957,
              0.000514822902918833,
              -7.607559496622103e-05
            ],
            "initial_K": [
              0.3805352172069988,
              0.7376625092378185,
              1.0534916093573898,
              1.3200369368904916,
              1.5402527712267091,
              1.7236069287807223,
              1.8769600706812888,
              1.9955843685053767,
              2.0607215578222395,
              2.0467976203870197,
              1.9348734839870625,
              1.7239769524608468,
              1.4329333130490127,
              1.0918663688293535,
              0.729436277275945,
              0.36362442301513803
            ],
            "metrics": {
              "initial_rmse_K": 0.029956039735494502,
              "observation_residual_rms_K": 0.013461539999394563,
              "future_predictive_rmse_K": 0.019711706874962796
            }
          }
        }
      },
      {
        "split": "train",
        "index": 99,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.383901973099747,
          -1.7014035230488904,
          -0.028007066469606802,
          -0.010013514062165578,
          0.048735969535430856,
          -0.04115573386430503,
          0.03084867291270156,
          -0.055230956306927266
        ],
        "initial_K": [
          0.11315764820258956,
          0.26882179396283135,
          0.4571652791727172,
          0.6568536957945628,
          0.8885592685965402,
          1.176631548309172,
          1.4864562799625312,
          1.7538852852997129,
          1.9552051597177877,
          2.0926109788466705,
          2.1315772313537504,
          2.022436836316067,
          1.7794486206610025,
          1.4658102239658084,
          1.0914597491924658,
          0.6024090569977837
        ],
        "observed_K": [
          0.15806797983901275,
          0.3213149007694371,
          0.5534702342172666,
          0.7648991131060177,
          0.9599533318530977,
          1.1740063324411047,
          1.410170020881757,
          1.5979054033354663,
          1.7410939810034125,
          1.8154944666002146,
          1.7990685514850238,
          1.725497103080167,
          1.5107892117845516,
          1.2368097246811,
          0.8744402502352485,
          0.4421796110287052
        ],
        "future_observed_K": [
          0.1799499062959797,
          0.366747313283078,
          0.5219239378213688,
          0.7991626008599759,
          0.9653185339087531,
          1.1363713388194434,
          1.355995417297048,
          1.507231384954034,
          1.6249257537802737,
          1.692290681300053,
          1.6658674317381976,
          1.6111039402377902,
          1.3617708086733569,
          1.11966395022514,
          0.7980228919021054,
          0.4162980391069421
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.39454134024731,
              -1.6820868734409127,
              0.020187283958573204,
              -0.00961548541734589,
              -0.07051384947445456,
              -0.5004151502719513,
              -3.5385178959214514,
              -9.923247110840684
            ],
            "initial_K": [
              -4.596444796761336,
              -1.1419502507311199,
              4.576042422555963,
              3.170797930726147,
              -2.204226698623128,
              -1.8482078305261878,
              3.576615203413737,
              4.880504658282483,
              0.6848229295635266,
              -0.912356473388475,
              2.7738664008143696,
              4.764523247698164,
              1.5317350408460177,
              -0.9962682250502473,
              1.1667780046330232,
              2.9103825850188603
            ],
            "metrics": {
              "initial_rmse_K": 2.6261434348045003,
              "observation_residual_rms_K": 0.007162161964355419,
              "future_predictive_rmse_K": 0.021689993971823914
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.329614821446273,
              -1.6458381837665,
              0.019060915678930365,
              -0.007783931462341403,
              -0.029498070100545972,
              -0.03792744493351102,
              -0.022156698279128632,
              -0.003236154872543566
            ],
            "initial_K": [
              0.10548351438216078,
              0.2589283696882846,
              0.4663071676811038,
              0.6992041300905392,
              0.9360578004896476,
              1.1812337623039348,
              1.4423913741015084,
              1.7020980923490447,
              1.9198300451780839,
              2.056107574855018,
              2.087655253899606,
              2.00364128837995,
              1.7985779734604608,
              1.4743236267844235,
              1.0460424863312665,
              0.542436482904303
            ],
            "metrics": {
              "initial_rmse_K": 0.03526593904258746,
              "observation_residual_rms_K": 0.019630453898072036,
              "future_predictive_rmse_K": 0.021547745239995995
            }
          },
          "learned": {
            "coefficients_K": [
              5.394233224311166,
              -1.6859882436752534,
              0.01980773369434592,
              -0.007374399294758674,
              -0.009210995320518858,
              -0.0037512374146295327,
              -0.003455196055291396,
              0.000873669561172185
            ],
            "initial_K": [
              0.12843049618636287,
              0.277709635915364,
              0.4606969041746316,
              0.6794642022287858,
              0.9281324710130326,
              1.1965781803158282,
              1.4703044279066668,
              1.7276711919914338,
              1.940122916182913,
              2.0776766722909223,
              2.11529606840627,
              2.0356259751778296,
              1.8297797988057543,
              1.5001640375826908,
              1.0638721101033408,
              0.5513496637627451
            ],
            "metrics": {
              "initial_rmse_K": 0.02706360239311062,
              "observation_residual_rms_K": 0.011635083678390017,
              "future_predictive_rmse_K": 0.021844854343291104
            }
          }
        }
      },
      {
        "split": "train",
        "index": 100,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          7.119686803319521,
          2.00048712037886,
          -0.13493821363870281,
          -0.16264418851133086,
          -0.021981567662437147,
          -0.00260474952396288,
          0.01864596864272599,
          -0.003045676531695724
        ],
        "initial_K": [
          0.6329388390627151,
          1.2426581663167708,
          1.8033230466014272,
          2.280716029155857,
          2.6297492809673457,
          2.8063228152847133,
          2.7920147871277243,
          2.6107465078850787,
          2.3178111215481962,
          1.9698157674611216,
          1.6056171454999375,
          1.2517448590758482,
          0.9322753770053818,
          0.6615692939271176,
          0.4310371302710455,
          0.2160448088068652
        ],
        "observed_K": [
          0.5582105405463126,
          1.1143101528115833,
          1.5147789466495336,
          1.9804507862415464,
          2.2148599427244227,
          2.35647125890092,
          2.3549342255413928,
          2.336273151423525,
          2.151052707770027,
          1.869814488366262,
          1.6058813017766342,
          1.269588369474534,
          1.0184515250930957,
          0.7566693157526111,
          0.4352959757911881,
          0.26465937238121023
        ],
        "future_observed_K": [
          0.49274797879841953,
          1.0164939954418986,
          1.414491823644765,
          1.8104681147818826,
          2.0135216172515666,
          2.1781923631099875,
          2.248662277547939,
          2.205512985180249,
          2.039384497288891,
          1.8363638038491454,
          1.5757784210723498,
          1.325513644209223,
          1.0380402300134994,
          0.8113595459090774,
          0.4780985831713503,
          0.2672411051523382
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              7.112072226126907,
              2.034900310325886,
              -0.13032391638465263,
              -0.10830589969739894,
              0.17439816585110043,
              -0.5397184547695064,
              -3.3118207145131944,
              13.250477072845591
            ],
            "initial_K": [
              3.9667465253173413,
              1.421356626749249,
              -1.7156453947137957,
              1.8175393076643855,
              6.54625867244931,
              3.938908842400732,
              -1.4334834789052815,
              0.4144125443330857,
              6.449706566902242,
              5.387589187698573,
              -1.8979188723589289,
              -3.2217393532018637,
              3.3687033570050477,
              5.768784412477486,
              -0.81987176655953,
              -5.2070162031394815
            ],
            "metrics": {
              "initial_rmse_K": 3.419421971609098,
              "observation_residual_rms_K": 0.024639354794253956,
              "future_predictive_rmse_K": 0.023726695481661772
            }
          },
          "tikhonov": {
            "coefficients_K": [
              7.026474199903831,
              1.9910485503294004,
              -0.12305237228809486,
              -0.08767583368084159,
              0.0729560130389151,
              -0.04090631940648798,
              -0.020737216677811577,
              0.004321226254254116
            ],
            "initial_K": [
              0.6491135402984352,
              1.272370810223297,
              1.829021050565713,
              2.2706043557101254,
              2.565263526056746,
              2.7108340108506415,
              2.7198006402947095,
              2.596417376118151,
              2.3404860712193924,
              1.977241985130816,
              1.5715910851071195,
              1.1983350522853846,
              0.8957149913609853,
              0.6520557597841876,
              0.4339423626522665,
              0.21839976522550006
            ],
            "metrics": {
              "initial_rmse_K": 0.04079266517881347,
              "observation_residual_rms_K": 0.033690839482240595,
              "future_predictive_rmse_K": 0.03202792682423887
            }
          },
          "learned": {
            "coefficients_K": [
              7.111666011278663,
              2.0396199830288277,
              -0.12787363743675473,
              -0.08306298805319812,
              0.022781066436367372,
              -0.004045864838019256,
              -0.0032338369354603753,
              -0.0011666079016523006
            ],
            "initial_K": [
              0.6621803584481338,
              1.290596385244943,
              1.848158756640125,
              2.2980551634885966,
              2.611212696696011,
              2.7702165930936284,
              2.769471424545719,
              2.6173206971705034,
              2.340562409211476,
              1.9840224036319771,
              1.600274977144657,
              1.2343073518364092,
              0.9123675981558617,
              0.6398670248071898,
              0.40708272845734683,
              0.19841168464851106
            ],
            "metrics": {
              "initial_rmse_K": 0.025576865478496927,
              "observation_residual_rms_K": 0.02671046262631918,
              "future_predictive_rmse_K": 0.024337995940518317
            }
          }
        }
      },
      {
        "split": "train",
        "index": 101,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.114250738274133,
          0.9489751419798083,
          -0.11281325507419918,
          -0.05147432415629458,
          0.005115707205669783,
          0.10589867914987217,
          -0.029077891068741132,
          0.006742864027111931
        ],
        "initial_K": [
          0.4972974328362676,
          0.950500849383945,
          1.3412252324726424,
          1.6750713680783076,
          1.9559847497739775,
          2.164378833092692,
          2.2613788978200224,
          2.218722946129496,
          2.0512208076271428,
          1.8184220798011212,
          1.5822354523207087,
          1.3560560469454854,
          1.1048888349695376,
          0.8044579687946379,
          0.48826850324935944,
          0.21628530909487861
        ],
        "observed_K": [
          0.4342701887627973,
          0.817668817821867,
          1.2259079917375102,
          1.4932173377377158,
          1.707262283019649,
          1.877318001339451,
          1.988623049526814,
          1.9780070698275258,
          1.9127526039767504,
          1.7332318993302498,
          1.5588070652713524,
          1.3102324181783798,
          1.0739573721876106,
          0.8016984933922023,
          0.5449650155657662,
          0.2607028786684116
        ],
        "future_observed_K": [
          0.3678139518218706,
          0.7513561401035798,
          1.0641141854163396,
          1.3821244601577751,
          1.6005077393922036,
          1.723620773444791,
          1.834568876336105,
          1.8539514260161905,
          1.8177693466966516,
          1.6792239511486418,
          1.506287254758305,
          1.2287201469106244,
          1.0528678458536347,
          0.7420992755248624,
          0.5435206198776943,
          0.27636087024148354
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.191496636938219,
              0.92954660895113,
              -0.11483740780502628,
              0.06070645632237947,
              0.377996521533532,
              0.33567981022671556,
              -2.7104293668418835,
              -11.626031113676571
            ],
            "initial_K": [
              -4.159643970619433,
              -0.03813527007158918,
              5.868229730953611,
              3.8143024122653113,
              -1.9709391174878268,
              -0.928037128486155,
              5.203220551811376,
              5.808612320495698,
              0.21227515319401657,
              -1.688979689061236,
              2.7184686809641003,
              4.732075104016424,
              0.5121468828386,
              -2.3644395597586083,
              0.7725181991112586,
              3.317186451834689
            ],
            "metrics": {
              "initial_rmse_K": 2.986656247422888,
              "observation_residual_rms_K": 0.010769312841918444,
              "future_predictive_rmse_K": 0.030981660236198097
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.116978286359355,
              0.9095150356133954,
              -0.10842994785482045,
              0.049143113927726696,
              0.1581273462314392,
              0.02544183066948762,
              -0.016971559125707573,
              -0.003791464307662506
            ],
            "initial_K": [
              0.5341964822558007,
              1.007409311170379,
              1.383347335654479,
              1.6662685609302343,
              1.8899499619585165,
              2.077851393864604,
              2.2097956812097084,
              2.2348277431536174,
              2.1214204622846657,
              1.8920665568757165,
              1.607440200192443,
              1.3216788781762006,
              1.0546605256607573,
              0.7986377766097406,
              0.5400577383179977,
              0.2730648263538169
            ],
            "metrics": {
              "initial_rmse_K": 0.051143806585637046,
              "observation_residual_rms_K": 0.022267015458659754,
              "future_predictive_rmse_K": 0.025174934256137857
            }
          },
          "learned": {
            "coefficients_K": [
              6.191143001909382,
              0.9317025650606832,
              -0.11267829771547591,
              0.04655757138204077,
              0.04937645890796407,
              0.002516340008438743,
              -0.002646606610991666,
              0.0010235872782169853
            ],
            "initial_K": [
              0.5098196503555624,
              0.9802758676117709,
              1.3844641058988723,
              1.7118630716347711,
              1.96233125748777,
              2.1358676620197867,
              2.225817761546902,
              2.220713927963948,
              2.114373514777775,
              1.9167839425509927,
              1.6555465752884058,
              1.3649351121966522,
              1.071492173998568,
              0.787832334170274,
              0.5163796785938827,
              0.2551736284051295
            ],
            "metrics": {
              "initial_rmse_K": 0.042719490567049,
              "observation_residual_rms_K": 0.015078670989209736,
              "future_predictive_rmse_K": 0.03126494477390877
            }
          }
        }
      },
      {
        "split": "train",
        "index": 102,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.018466921718724,
          -0.7984016013748554,
          -0.06834118741952261,
          0.10127957726710717,
          0.01211175466580313,
          -0.04010480147229347,
          -0.024593178702003542,
          -0.026878602944097628
        ],
        "initial_K": [
          0.20213725755206768,
          0.43781194293564996,
          0.6839779073253156,
          0.8965666701256263,
          1.0788200925978642,
          1.2721999345268138,
          1.4875178826899238,
          1.683074197097539,
          1.8108727284859254,
          1.8507177062541715,
          1.7957431411130922,
          1.6401570983305018,
          1.396040651566684,
          1.096023968561454,
          0.7629563829041668,
          0.3961697994219848
        ],
        "observed_K": [
          0.25032156470949873,
          0.43585596208293403,
          0.6431654452623996,
          0.8712084550469464,
          1.0843314293150148,
          1.2419331771416862,
          1.377694919747012,
          1.5243405586719927,
          1.6094352805807437,
          1.576513401729074,
          1.5139713593472561,
          1.4218879532362954,
          1.252709894960406,
          0.9593624835085512,
          0.681976103384306,
          0.33576783123757975
        ],
        "future_observed_K": [
          0.21904194245376435,
          0.4237113721270396,
          0.6299259963476622,
          0.8198330337970666,
          1.0735150691852122,
          1.1831744925520953,
          1.3510697903711022,
          1.4364577141663801,
          1.4881401094511482,
          1.5145783774327513,
          1.4394389582119727,
          1.3485170440456276,
          1.1358082975529042,
          0.9395593862805207,
          0.6342086098281529,
          0.3201331986790292
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.0028243847028415,
              -0.7745706778056398,
              -0.004698183318509334,
              0.038271162445214224,
              -0.0017141388815910964,
              0.4613028397280129,
              -2.491072100653539,
              15.618590505468905
            ],
            "initial_K": [
              4.880962918520046,
              1.1127901439091357,
              -3.931905701296244,
              -0.4296253263133214,
              5.638831788967598,
              3.3386509254959345,
              -2.9263733874577613,
              -1.1878327428245976,
              5.970850125439075,
              5.611914952064129,
              -1.9667190358635254,
              -3.214104946730328,
              4.269444650557068,
              6.886191588840047,
              -0.7766571711782659,
              -5.89661296733152
            ],
            "metrics": {
              "initial_rmse_K": 3.9617282826352676,
              "observation_residual_rms_K": 0.014632723177044666,
              "future_predictive_rmse_K": 0.018186233449687533
            }
          },
          "tikhonov": {
            "coefficients_K": [
              4.94261241282521,
              -0.7578788097612499,
              -0.004436043811640772,
              0.030981286178260303,
              -0.0007170759966744357,
              0.03496304626658131,
              -0.015598036960432774,
              0.005093511952485666
            ],
            "initial_K": [
              0.23109657761531777,
              0.4533434985219227,
              0.6663601916707199,
              0.8767677594539218,
              1.0894562554318559,
              1.3002763640795725,
              1.493820446570116,
              1.647114600489638,
              1.7400513315662915,
              1.7654439540030835,
              1.7251040460436133,
              1.6137286280763918,
              1.4148763861932574,
              1.122563717267339,
              0.762653876382754,
              0.37963906664830227
            ],
            "metrics": {
              "initial_rmse_K": 0.038180991372848715,
              "observation_residual_rms_K": 0.022165786245453525,
              "future_predictive_rmse_K": 0.022975590778399335
            }
          },
          "learned": {
            "coefficients_K": [
              5.002538642167669,
              -0.7763671884582688,
              -0.004609850647131265,
              0.029351282966584118,
              -0.00022391239926243084,
              0.0034580417297960585,
              -0.0024324145726506794,
              -0.001375103024304818
            ],
            "initial_K": [
              0.22477049598177629,
              0.44939514784180734,
              0.6721370798350315,
              0.89121424166711,
              1.1059877933068825,
              1.313475046965995,
              1.5034655150725018,
              1.659029313573229,
              1.7622805015792724,
              1.7987436863209283,
              1.7574916871837583,
              1.6312824299012996,
              1.4197669455190571,
              1.1323469354594549,
              0.7864256867117878,
              0.40241289467920904
            ],
            "metrics": {
              "initial_rmse_K": 0.028685804649860713,
              "observation_residual_rms_K": 0.017300433450348,
              "future_predictive_rmse_K": 0.01807723348919294
            }
          }
        }
      },
      {
        "split": "train",
        "index": 103,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.202493369767598,
          0.6653590927894562,
          -0.2651443870654024,
          0.06843040254329104,
          -0.02947472835390516,
          -0.03380683533186023,
          -0.053186224777962296,
          -0.008634688215085824
        ],
        "initial_K": [
          0.40235064097128653,
          0.8351041230310603,
          1.266034533062518,
          1.6261016015394674,
          1.8839026785218882,
          2.063558123252897,
          2.188991749964717,
          2.240689304239971,
          2.1819958711427554,
          2.009097931402976,
          1.755963826195145,
          1.4592848490666515,
          1.138544616140034,
          0.810033014436691,
          0.5004603360202701,
          0.23250104954939027
        ],
        "observed_K": [
          0.3949048675600972,
          0.7937698312331062,
          1.1338381163865248,
          1.4298411199913323,
          1.640326051607508,
          1.8511290951223942,
          1.9756505935261768,
          1.9619640477928868,
          1.9304845261381665,
          1.8144401123212364,
          1.6433138292950953,
          1.3610925007768973,
          1.1331273284264463,
          0.8271276255624835,
          0.5361748751832504,
          0.3152669584662402
        ],
        "future_observed_K": [
          0.3733951394273949,
          0.7413445512616263,
          1.0515877583925533,
          1.3214266337322236,
          1.5973421968386317,
          1.7380649424546266,
          1.859475634699536,
          1.870022969367658,
          1.8239793646001126,
          1.7041358119173378,
          1.5551478928972369,
          1.348726433207692,
          1.0833741253024727,
          0.8070159627537995,
          0.5262674089180887,
          0.2597763615254235
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.214118885318973,
              0.6604039638412447,
              -0.2441521645312417,
              0.1778070385381287,
              0.17414253215674708,
              -0.010096598219767964,
              2.6686920968151298,
              -12.54354462693857
            ],
            "initial_K": [
              -2.8885931653926002,
              0.6543202643823682,
              4.833805365848934,
              2.3125619151258268,
              -1.883871255194642,
              0.6505025537225855,
              5.942709722314463,
              4.442156315699966,
              -1.390396550044704,
              -1.0464768890615241,
              4.938638269395884,
              5.44263647697278,
              -1.2760260045807366,
              -3.94666191985991,
              1.8143145487987702,
              5.439872679934522
            ],
            "metrics": {
              "initial_rmse_K": 3.207288326622391,
              "observation_residual_rms_K": 0.01621882179921138,
              "future_predictive_rmse_K": 0.015395227481353538
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.139328262503755,
              0.6461723693124415,
              -0.2305294674859891,
              0.1439384223916507,
              0.07284907375404696,
              -0.0007652409660017822,
              0.016710218042752138,
              -0.004090682476211756
            ],
            "initial_K": [
              0.48245448176981615,
              0.9149690087657076,
              1.274173628833076,
              1.567785882323368,
              1.814156657890254,
              2.0169622467627337,
              2.1586569602775145,
              2.2143332163438285,
              2.166937638738443,
              2.0119776609873985,
              1.759863152259269,
              1.4419463840314348,
              1.1067439851719496,
              0.7957815760972564,
              0.5189543677861983,
              0.25906946377762896
            ],
            "metrics": {
              "initial_rmse_K": 0.04162757724420459,
              "observation_residual_rms_K": 0.025003154301576357,
              "future_predictive_rmse_K": 0.01998537613210932
            }
          },
          "learned": {
            "coefficients_K": [
              6.213763958192291,
              0.6619356804296396,
              -0.2395617491613652,
              0.13636546078405198,
              0.022747673836473803,
              -7.568663135377187e-05,
              0.00260585213270535,
              0.001104367653788349
            ],
            "initial_K": [
              0.46933743470208117,
              0.9039155772313143,
              1.2825903936355718,
              1.5999262354326178,
              1.8576377960870618,
              2.0549827542799917,
              2.1843804451739617,
              2.2320687528897474,
              2.1829614197632865,
              2.0297311096152453,
              1.7822106100622128,
              1.469420478263602,
              1.1308138618492372,
              0.8021788106536332,
              0.5047564194607729,
              0.24157395752659513
            ],
            "metrics": {
              "initial_rmse_K": 0.027929558887428162,
              "observation_residual_rms_K": 0.01839276573469571,
              "future_predictive_rmse_K": 0.015287426758767536
            }
          }
        }
      },
      {
        "split": "train",
        "index": 104,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.419310716040784,
          1.0785908917325022,
          -0.18957046954293727,
          -0.03601190487615462,
          0.03664665165314709,
          0.026233481730039417,
          -0.07528742978315434,
          0.05098097783729995
        ],
        "initial_K": [
          0.5063318034958806,
          0.983004555998304,
          1.4191338448489643,
          1.7990914623340377,
          2.0882533982295532,
          2.2683074370767664,
          2.355356990263063,
          2.352209511108422,
          2.2214150569028255,
          1.9537214716760598,
          1.629176155433608,
          1.344404270164578,
          1.0968224862709821,
          0.8134545892512308,
          0.4883435030176685,
          0.20475657723438923
        ],
        "observed_K": [
          0.451532342436712,
          0.8617814211999408,
          1.225051244851628,
          1.5664453499051287,
          1.8541337099211832,
          1.9930745417473337,
          2.0539630634024357,
          2.051577086105141,
          1.9467335888072164,
          1.7871837875115448,
          1.578020922662654,
          1.3509992828174922,
          1.077977368383396,
          0.7834342653413915,
          0.539698349575225,
          0.2476980351840582
        ],
        "future_observed_K": [
          0.4249944080684637,
          0.8074498057520298,
          1.1741653089204616,
          1.4641670778922682,
          1.700812678959685,
          1.8385260838003061,
          1.940070046734051,
          1.9542425702321178,
          1.8794477975089015,
          1.7221681668838142,
          1.5504790093135987,
          1.2841451721195039,
          1.0712053398436923,
          0.8089036486998609,
          0.5467267069933262,
          0.24627534134449913
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.399403352745993,
              1.0929766928167048,
              -0.16587332178567948,
              -0.06747552812294431,
              -0.29495033066522214,
              0.24355291455916706,
              1.3692652734980717,
              8.790964187321078
            ],
            "initial_K": [
              3.9413938952459473,
              1.7421590162059855,
              -1.8524975056246697,
              0.2656284599599985,
              4.933757019339769,
              4.450066816398818,
              0.1955940893177579,
              -0.13517224240243775,
              3.6851379757572884,
              4.405573739696161,
              0.5721808199905634,
              -1.0975341700769308,
              1.8667408546623097,
              3.344308553458169,
              0.04168825672733567,
              -2.4526591052768056
            ],
            "metrics": {
              "initial_rmse_K": 2.2168865848015478,
              "observation_residual_rms_K": 0.010357839381977693,
              "future_predictive_rmse_K": 0.015372541026339556
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.322382720982992,
              1.06942322861409,
              -0.15661826555910704,
              -0.05462281554156455,
              -0.12338661972062526,
              0.018459352700090876,
              0.00857375839866567,
              0.002866896417209643
            ],
            "initial_K": [
              0.46577903536928617,
              0.9298241250812167,
              1.3821331917374702,
              1.7930833622238038,
              2.1131072049201896,
              2.296070723220885,
              2.3306437294927194,
              2.247586045774695,
              2.0939066981292753,
              1.8998613052405078,
              1.66898045413891,
              1.394538939952054,
              1.082369887580803,
              0.759545913302127,
              0.46243310510914365,
              0.21271580699474663
            ],
            "metrics": {
              "initial_rmse_K": 0.05357823996216626,
              "observation_residual_rms_K": 0.02162369052054269,
              "future_predictive_rmse_K": 0.023781221131647167
            }
          },
          "learned": {
            "coefficients_K": [
              6.399037842866574,
              1.0955117026330887,
              -0.16275466237408118,
              -0.051748972142964055,
              -0.03852840450197058,
              0.0018257337033858925,
              0.0013370230448999977,
              -0.0007739803048365816
            ],
            "initial_K": [
              0.48788793809143755,
              0.9663538229488077,
              1.4171114637013444,
              1.8110462501026372,
              2.1147041692597774,
              2.301387666793638,
              2.3609459666643278,
              2.3029523850595246,
              2.151020976165978,
              1.9318757348091338,
              1.6673486286191361,
              1.374508905653065,
              1.070273100140508,
              0.7724316491204564,
              0.4945077145802474,
              0.2397328695096873
            ],
            "metrics": {
              "initial_rmse_K": 0.032075064033158254,
              "observation_residual_rms_K": 0.012802840679546072,
              "future_predictive_rmse_K": 0.014616093246694137
            }
          }
        }
      },
      {
        "split": "train",
        "index": 105,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          4.252293994058688,
          -2.242974267257158,
          -0.0938272400843066,
          -0.6020727791787794,
          -0.03411313744991353,
          -0.0038999303091044506,
          -0.013042775454878221,
          -0.008715736971705253
        ],
        "initial_K": [
          -0.18379285731149647,
          -0.24107971823577506,
          -0.1157999395511512,
          0.16545246250046342,
          0.5301042648133868,
          0.8975868264836402,
          1.201672823097893,
          1.410897756483528,
          1.5418080876453355,
          1.6398505623807165,
          1.732332268448739,
          1.7961578127687199,
          1.7687153390577828,
          1.5849124603731897,
          1.2100042198193626,
          0.6586350850087259
        ],
        "observed_K": [
          0.020264471488045256,
          0.04819381509271148,
          0.20919736353845517,
          0.33524779768514357,
          0.5471625353857263,
          0.8170251779694503,
          1.0582038268848448,
          1.2523476912778204,
          1.3579024104997681,
          1.5149805210544434,
          1.5519813775989324,
          1.5020505512066349,
          1.3970434540078718,
          1.1603991327725698,
          0.8635716688333246,
          0.44886854920414765
        ],
        "future_observed_K": [
          0.04125824980760461,
          0.12800282640219307,
          0.2993997735462034,
          0.42374200121100697,
          0.5707578154675169,
          0.7923341895309426,
          1.0237225848403895,
          1.1835444881740107,
          1.3079716863797177,
          1.451661048730016,
          1.4063444883132166,
          1.4131402564105884,
          1.2609306929029744,
          1.0512866572722421,
          0.7334482164843125,
          0.397249917131361
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              4.214931880840129,
              -2.228376460752166,
              -0.10830421846366428,
              -0.6625650115963947,
              0.028787827303878914,
              0.34854906663297436,
              1.7194001619964205,
              -15.99055661639433
            ],
            "initial_K": [
              -4.962301872522752,
              -0.8446646863725817,
              4.718153497230198,
              1.4746988929395504,
              -4.366954629580611,
              -1.353953626619043,
              5.927409244941559,
              4.7130963735614255,
              -2.686133772082243,
              -2.666602116461263,
              5.117060928699329,
              6.844586583139275,
              -0.6522919243851201,
              -4.0574857531655875,
              2.462579232065171,
              6.604718595380066
            ],
            "metrics": {
              "initial_rmse_K": 4.019905558359441,
              "observation_residual_rms_K": 0.015186628206606292,
              "future_predictive_rmse_K": 0.022194409773686315
            }
          },
          "tikhonov": {
            "coefficients_K": [
              4.164202664629523,
              -2.1803553222016143,
              -0.10226128388765499,
              -0.5363598836422896,
              0.012042816470541302,
              0.02641721683319261,
              0.010766154568371654,
              -0.0052148169979860815
            ],
            "initial_K": [
              -0.13693174666372215,
              -0.18962628533829118,
              -0.10022187435185437,
              0.14223633301238925,
              0.4935459740581516,
              0.8683865821021548,
              1.1809455969565863,
              1.3917183986183694,
              1.5216893758506025,
              1.618070417303054,
              1.7034328582995042,
              1.753875248779189,
              1.715314053098357,
              1.5321955578411917,
              1.1705938713995128,
              0.6386008769185856
            ],
            "metrics": {
              "initial_rmse_K": 0.03508841993610786,
              "observation_residual_rms_K": 0.0232344117684526,
              "future_predictive_rmse_K": 0.027165654250288825
            }
          },
          "learned": {
            "coefficients_K": [
              4.214691139764969,
              -2.2335448749001823,
              -0.1062679418244111,
              -0.5081406441981675,
              0.0037604604564950932,
              0.0026128111806312383,
              0.0016789132715832663,
              0.0014078519284964834
            ],
            "initial_K": [
              -0.14485474854392613,
              -0.197725200751169,
              -0.10069192002966376,
              0.1477370016580729,
              0.49401631009305025,
              0.8573290519328546,
              1.1686685024555525,
              1.397550699482196,
              1.5528764306975764,
              1.6622159338348337,
              1.7436197397279416,
              1.7845631529110757,
              1.7395245862568316,
              1.5503088934499356,
              1.1799974995377382,
              0.6409112067848192
            ],
            "metrics": {
              "initial_rmse_K": 0.027700344677826373,
              "observation_residual_rms_K": 0.019103901229342395,
              "future_predictive_rmse_K": 0.02185615887406794
            }
          }
        }
      },
      {
        "split": "train",
        "index": 106,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.148962014208787,
          0.448605546676099,
          -0.3708110436171712,
          0.056163223063203156,
          0.01334535951569124,
          -0.07879949830617596,
          0.0012651123746685743,
          -0.04950180002778658
        ],
        "initial_K": [
          0.35211796969824294,
          0.7508189906242422,
          1.1594116059876922,
          1.505463540804076,
          1.7735211061334544,
          1.9942476837647936,
          2.165642085777685,
          2.244687701983205,
          2.20763775590772,
          2.0648523204563904,
          1.8231258984121768,
          1.4917908614892497,
          1.127696520633013,
          0.8105931510495672,
          0.5545093936380383,
          0.29719528608838075
        ],
        "observed_K": [
          0.33988414717087206,
          0.7331675112706357,
          1.019332499276408,
          1.3420068657290982,
          1.6205713116463358,
          1.8047372870951857,
          1.9132119547214068,
          2.014260407082938,
          1.9254926621256767,
          1.8324017410960418,
          1.6559047075659907,
          1.4109898041382054,
          1.1335093459210057,
          0.8555047828771895,
          0.5412890571261468,
          0.32758152915020067
        ],
        "future_observed_K": [
          0.33832017808485493,
          0.6943536067571396,
          1.02450568763301,
          1.2964022588080253,
          1.5240385152655875,
          1.6640975000984253,
          1.7898404820796476,
          1.8232926479745455,
          1.815879924151161,
          1.7355731367091052,
          1.5810140830677193,
          1.3690405597332092,
          1.1070579265020872,
          0.8387986284694935,
          0.5683998685440101,
          0.29696387228394333
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.163378902795929,
              0.4414186063744159,
              -0.4327041571907421,
              0.017487245418013192,
              -0.010270320344043942,
              -0.32028013526703936,
              1.981089686487529,
              -8.30150526165528
            ],
            "initial_K": [
              -1.9137733478159769,
              0.4822427859541273,
              3.4052518362360606,
              1.9854720866621776,
              -0.5706262130800834,
              1.175060139493338,
              4.615344233483194,
              3.588440222496362,
              -0.1837572503839917,
              0.14090955205587097,
              4.022237069320674,
              4.0941830169901205,
              -0.5867680364835972,
              -2.3931488133296965,
              1.4880423472400315,
              3.8359263931568806
            ],
            "metrics": {
              "initial_rmse_K": 2.1224944517135613,
              "observation_residual_rms_K": 0.019260043578675796,
              "future_predictive_rmse_K": 0.020798143801777778
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.089198965898468,
              0.4319061095280156,
              -0.4085610263897184,
              0.014156281653072356,
              -0.004296384777197913,
              -0.02427465912460199,
              0.012404743380834972,
              -0.002707274786355272
            ],
            "initial_K": [
              0.36132842027467243,
              0.7276827418507049,
              1.0954680614664427,
              1.448949157456146,
              1.7630569599591144,
              2.010651123321794,
              2.1706135427002713,
              2.2314491903126314,
              2.188030126213658,
              2.038431743634896,
              1.7905440586628616,
              1.4736384661547088,
              1.1354560177720683,
              0.8176486990568173,
              0.5320370864287662,
              0.26451129629250486
            ],
            "metrics": {
              "initial_rmse_K": 0.028104876880359585,
              "observation_residual_rms_K": 0.02637866205831499,
              "future_predictive_rmse_K": 0.019938790820268323
            }
          },
          "learned": {
            "coefficients_K": [
              6.163026873746439,
              0.4424424164040789,
              -0.4245686904518278,
              0.01341148415089208,
              -0.0013415786166019713,
              -0.0024009001844236687,
              0.001934440766237155,
              0.0007308870149062032
            ],
            "initial_K": [
              0.36946936941289066,
              0.7393838804781702,
              1.1066354842225252,
              1.4602179963897077,
              1.7792240726425024,
              2.0365300358983403,
              2.2062182289350374,
              2.2696295558748036,
              2.2183875023183046,
              2.056715001979671,
              1.8035014502569309,
              1.490582374391654,
              1.154906193206083,
              0.8277794821097049,
              0.526969751442453,
              0.25460478563373634
            ],
            "metrics": {
              "initial_rmse_K": 0.029079226924565087,
              "observation_residual_rms_K": 0.020159960753820597,
              "future_predictive_rmse_K": 0.020694570704266183
            }
          }
        }
      },
      {
        "split": "train",
        "index": 107,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.869035773220383,
          0.49345895489862845,
          -0.24963910426473318,
          0.32107106876309516,
          -0.11919938221196434,
          0.04090053578421984,
          0.04024585127794416,
          0.03140197234198751
        ],
        "initial_K": [
          0.5271156776113473,
          0.9792582477134137,
          1.3574325134795606,
          1.6994874096140258,
          1.997502196883143,
          2.2059651569644667,
          2.3171721102952305,
          2.3721985305678674,
          2.3893040856965935,
          2.325384576157153,
          2.1261974979216265,
          1.7874817918682007,
          1.356718184880048,
          0.904519903529852,
          0.5055434743377886,
          0.20988254036473084
        ],
        "observed_K": [
          0.41444355833190544,
          0.8250893488863358,
          1.2461942331344875,
          1.5121852989530813,
          1.790889344344948,
          1.9981537532778282,
          2.1239593103581185,
          2.171845166029291,
          2.140896094024885,
          2.002576929211841,
          1.8385785249538267,
          1.6141692281767566,
          1.2531809049370006,
          0.9747666390817673,
          0.6578528964924226,
          0.28557526283156565
        ],
        "future_observed_K": [
          0.4222876737626139,
          0.7972914091886922,
          1.2010281201368014,
          1.4512668990379474,
          1.7435669013940196,
          1.8685942410176772,
          2.0486028529461966,
          2.068307970505803,
          2.0472313345327455,
          1.9170574362625832,
          1.7710358413655558,
          1.5098419881291096,
          1.2745700542037741,
          0.9641950946666741,
          0.6525983394312699,
          0.3429115787129973
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.856656402416557,
              0.5227708593818398,
              -0.24079884367517257,
              0.2515415440084693,
              -0.10103852354924928,
              0.306272623582382,
              -0.9792736800201159,
              -13.501653424369824
            ],
            "initial_K": [
              -4.356394249031368,
              0.005075870937321425,
              6.03389807944928,
              3.6036922464282357,
              -2.2695143129399993,
              -0.5305406180643801,
              6.007377166548097,
              5.835230224714525,
              -0.5187432791598106,
              -1.6274316855462851,
              4.149192818553772,
              5.908995409918994,
              0.07113669976368286,
              -3.294704903890748,
              1.1258908207691154,
              4.4322803370250785
            ],
            "metrics": {
              "initial_rmse_K": 3.393557181893768,
              "observation_residual_rms_K": 0.018337809539893123,
              "future_predictive_rmse_K": 0.025867292205898874
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.774132457794541,
              0.5115052351434232,
              -0.22736324828517443,
              0.203628007688655,
              -0.04226746196279017,
              0.02321300236263818,
              -0.0061317964467288676,
              -0.00440313951961711
            ],
            "initial_K": [
              0.4883524221130778,
              0.948305979780901,
              1.3544749311758988,
              1.6930364940702294,
              1.965340945872096,
              2.176833345159335,
              2.322895686579271,
              2.389521469718358,
              2.3650888438733086,
              2.2449528376505365,
              2.0270101921963777,
              1.7148141033106639,
              1.332201050233365,
              0.9289189988854887,
              0.5606687457003355,
              0.2562425489347075
            ],
            "metrics": {
              "initial_rmse_K": 0.04561089185936578,
              "observation_residual_rms_K": 0.027272862214991745,
              "future_predictive_rmse_K": 0.03871256351334431
            }
          },
          "learned": {
            "coefficients_K": [
              6.856264775960664,
              0.5239833548256696,
              -0.23627147560871598,
              0.19291462721084138,
              -0.013198334434165685,
              0.002295896365317091,
              -0.0009562146231212117,
              0.0011887221481647425
            ],
            "initial_K": [
              0.49614247425837654,
              0.9601233947579052,
              1.3690408840755317,
              1.7125332279824588,
              1.9897177221349747,
              2.2030308660380404,
              2.3513913107453237,
              2.4250648422693355,
              2.4065425257274424,
              2.279712393302096,
              2.0424720634375295,
              1.7139881087796156,
              1.3321092793904776,
              0.9427402331069129,
              0.5847832494432307,
              0.2749166961480653
            ],
            "metrics": {
              "initial_rmse_K": 0.04543855425570622,
              "observation_residual_rms_K": 0.01987006439883133,
              "future_predictive_rmse_K": 0.025773256536142358
            }
          }
        }
      },
      {
        "split": "train",
        "index": 108,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.627914922579983,
          -0.934106455203038,
          -0.10193079768415782,
          0.07638337600168088,
          0.09831595769755852,
          0.016676936135249783,
          0.013753973256568713,
          0.0005314678544326512
        ],
        "initial_K": [
          0.2749576833319634,
          0.5157841304168306,
          0.7232682400653517,
          0.9308160800966121,
          1.169470975706302,
          1.4376714395038572,
          1.7015539592542663,
          1.9167253215006874,
          2.047622124772796,
          2.07469207521464,
          1.9951079348150813,
          1.8207661012607814,
          1.5703813676894336,
          1.257519341029706,
          0.8861111590227849,
          0.4605337249430831
        ],
        "observed_K": [
          0.21579114667578997,
          0.4672700351153122,
          0.7163737444001995,
          0.9259381317521469,
          1.1564954962721539,
          1.4012081693426282,
          1.56902264334003,
          1.6911434499187157,
          1.8192922005875685,
          1.8272991995239871,
          1.7467513973305346,
          1.5795734004315594,
          1.3662511502910584,
          1.1174388452792017,
          0.7602974338388827,
          0.3988792138016107
        ],
        "future_observed_K": [
          0.26824763934619905,
          0.46163024314645784,
          0.7204821249954888,
          0.9268934540225702,
          1.1537374556055469,
          1.2921933486746466,
          1.503601833172889,
          1.6550410127991275,
          1.6993504158817063,
          1.6808462455131266,
          1.6138094477734308,
          1.5046154650538683,
          1.2919002763656642,
          1.0183769061083396,
          0.6707853464267659,
          0.3753369749097467
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.614103625268688,
              -0.9687816584068489,
              -0.14751172897499554,
              0.027418279423193123,
              0.19540162372735156,
              -0.778174536761174,
              0.5577795562585006,
              7.686694103890834
            ],
            "initial_K": [
              2.8373317511527003,
              0.8724625012888512,
              -1.918119761172606,
              0.025523756881845383,
              3.70219276492678,
              2.8956992491049114,
              -0.58547763010948,
              -0.107780736757209,
              3.8545680035704164,
              4.520728761157105,
              0.8610826495455037,
              -0.7285529518887668,
              2.0752041014588176,
              3.6354213889226505,
              0.7585414901157201,
              -1.7079419103916045
            ],
            "metrics": {
              "initial_rmse_K": 1.9368166975205026,
              "observation_residual_rms_K": 0.012571053042690248,
              "future_predictive_rmse_K": 0.022216737669147644
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.54653454356428,
              -0.9479045763415115,
              -0.139281174892848,
              0.02219565612989828,
              0.08174239298278657,
              -0.05897937317771127,
              0.0034925790112664144,
              0.002506773468422759
            ],
            "initial_K": [
              0.21837684742330749,
              0.44463284774513157,
              0.6811829344399483,
              0.9245176289500924,
              1.1709027146867208,
              1.420446106722833,
              1.6687874414698431,
              1.890700357469064,
              2.0381427990256396,
              2.0663927926060173,
              1.967717775717328,
              1.7755554942678904,
              1.530909336405998,
              1.2453381714838252,
              0.899518540299163,
              0.47752465609343775
            ],
            "metrics": {
              "initial_rmse_K": 0.03283697623160982,
              "observation_residual_rms_K": 0.0212365114980809,
              "future_predictive_rmse_K": 0.023382583859619374
            }
          },
          "learned": {
            "coefficients_K": [
              5.613782968759634,
              -0.9710286148425484,
              -0.1447382941818863,
              0.021027886962123016,
              0.025524679976895333,
              -0.00583339140676321,
              0.0005446454643419833,
              -0.0006767573748389893
            ],
            "initial_K": [
              0.21736509335893336,
              0.440815111012942,
              0.6754584784219733,
              0.9245096280179688,
              1.1869720434273883,
              1.4534876326344652,
              1.7035312343799593,
              1.9080334183986405,
              2.0374374323214446,
              2.0707251603304893,
              2.00062728941215,
              1.8329769311285102,
              1.5811210031259957,
              1.2590515278586083,
              0.8784925771662933,
              0.45232179571215375
            ],
            "metrics": {
              "initial_rmse_K": 0.027884696768142554,
              "observation_residual_rms_K": 0.014669258286934491,
              "future_predictive_rmse_K": 0.022151434958625798
            }
          }
        }
      },
      {
        "split": "train",
        "index": 109,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.911401959918765,
          -0.38461710452571063,
          -0.450048081107491,
          -0.22597347536011514,
          -0.07620782676642301,
          -0.13866198732970034,
          0.038683704083616356,
          -0.04051024404197967
        ],
        "initial_K": [
          0.12692598964295476,
          0.36955238965604337,
          0.7374612046181447,
          1.1498408617919196,
          1.524277070811635,
          1.8189912867935738,
          2.0178421234990336,
          2.121512034021493,
          2.1453480925853357,
          2.0905124272666136,
          1.9294366327150598,
          1.6572379997516502,
          1.339515737993654,
          1.0531441208220507,
          0.7826738034292526,
          0.4394921937730657
        ],
        "observed_K": [
          0.22303323868051567,
          0.5320459576199681,
          0.8224106098226949,
          1.0658282306653855,
          1.372237659591247,
          1.6175452949083624,
          1.778021684351674,
          1.8616479160463124,
          1.9521006995505856,
          1.8150995713122133,
          1.7158160754333156,
          1.570781119484267,
          1.2881641197920632,
          1.0229775667428567,
          0.6732529247811532,
          0.349270015256693
        ],
        "future_observed_K": [
          0.26851060250217806,
          0.5290829905666143,
          0.8076775855959675,
          1.037125766143031,
          1.3064158800549166,
          1.4964051940613885,
          1.6931654096920015,
          1.757261859424189,
          1.765778545500508,
          1.767978253275955,
          1.6294441626869474,
          1.4554495433830308,
          1.1963573765445927,
          0.9953356403445446,
          0.6661966438263021,
          0.3246915619472023
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.93752958308393,
              -0.43124270543158494,
              -0.45186076035312595,
              -0.2689609026195535,
              -0.2368657345644021,
              0.4639544693784727,
              -2.203943192311591,
              -3.29535615800756
            ],
            "initial_K": [
              -1.597904527521588,
              -0.15135523445933746,
              2.249592582661072,
              2.058816516167156,
              0.29849849302949516,
              0.5866946622165128,
              2.8403852790948667,
              3.5588667494357042,
              1.8560731521735205,
              0.7100502955710606,
              1.7203877050569365,
              2.7239251856457036,
              1.8767864724780954,
              0.5458305776990059,
              0.3930610838167312,
              0.5993108975779727
            ],
            "metrics": {
              "initial_rmse_K": 1.0005330667133052,
              "observation_residual_rms_K": 0.021529580891431383,
              "future_predictive_rmse_K": 0.020100816046147312
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.866067877297811,
              -0.4219494975418125,
              -0.42664876906586274,
              -0.21772933358760818,
              -0.09908808120210905,
              0.035164018474351647,
              -0.013800157515854903,
              -0.001074676743245906
            ],
            "initial_K": [
              0.1688357511458004,
              0.3983484955993736,
              0.7133885717707531,
              1.0915532417939022,
              1.4774107639655212,
              1.806679527308693,
              2.028835291213716,
              2.1245498919259087,
              2.1105862261402835,
              2.022903398140702,
              1.8856843619366437,
              1.694098526638629,
              1.4301536219745619,
              1.0954141414716374,
              0.7229624278094243,
              0.35316352593355893
            ],
            "metrics": {
              "initial_rmse_K": 0.04944257169078609,
              "observation_residual_rms_K": 0.027941490790751467,
              "future_predictive_rmse_K": 0.01979876425335393
            }
          },
          "learned": {
            "coefficients_K": [
              5.937190453699153,
              -0.4322429138520369,
              -0.4433651216462094,
              -0.20627404696774695,
              -0.030941002213393146,
              0.003477919010388263,
              -0.00215204671790372,
              0.0002901320844189491
            ],
            "initial_K": [
              0.18490462927866963,
              0.41956034661404573,
              0.7277955765909021,
              1.0950216742249188,
              1.4745432967137886,
              1.8075252900775907,
              2.045328590364557,
              2.1639860541072418,
              2.1662321497263424,
              2.072539286332295,
              1.9070826331855109,
              1.6866776959016423,
              1.4186407103249552,
              1.106777509443422,
              0.758280709461282,
              0.3850145822586568
            ],
            "metrics": {
              "initial_rmse_K": 0.04253752840629318,
              "observation_residual_rms_K": 0.02293454336569415,
              "future_predictive_rmse_K": 0.019792105841025552
            }
          }
        }
      },
      {
        "split": "train",
        "index": 110,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.178131943554102,
          2.0975387784564523,
          -0.29134628683523955,
          -0.14666182418212548,
          0.044436348042564806,
          0.021180356243108295,
          0.04380146014599747,
          0.013938833753297455
        ],
        "initial_K": [
          0.6006557083155155,
          1.1398909963277264,
          1.6093803705416696,
          2.024819979896232,
          2.360401402959608,
          2.5476368512319834,
          2.5409289564524635,
          2.3587869128186973,
          2.056838553110153,
          1.6865471987651626,
          1.2923191644799448,
          0.924695849358257,
          0.6279743548504553,
          0.4134847584096646,
          0.25733863570182836,
          0.12611759912956866
        ],
        "observed_K": [
          0.49464865199755553,
          0.9635086690915652,
          1.3789418853982882,
          1.7006938457634235,
          1.980049841737155,
          2.142307997042712,
          2.1235591278034294,
          2.0529249722312755,
          1.8705067742305401,
          1.6155989519632044,
          1.305321930626623,
          1.0314331094726534,
          0.8004383778892589,
          0.565481523029651,
          0.38609665798441506,
          0.13200232473998974
        ],
        "future_observed_K": [
          0.45274581010626,
          0.921476085307522,
          1.2710894450100403,
          1.5755129383383586,
          1.8243881882758044,
          1.9515299836275408,
          1.969253162110802,
          1.9096139125182157,
          1.7910389342028463,
          1.5748985017051242,
          1.3124031515499197,
          1.050884850657563,
          0.8181005518617752,
          0.554316408843448,
          0.36148503931633763,
          0.1603201127868612
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.172239649317089,
              2.0492807686280776,
              -0.30705068858877954,
              -0.31808904718778325,
              0.24988953850539672,
              0.42100761448902696,
              -1.2795206395698195,
              22.999092121962978
            ],
            "initial_K": [
              8.144498026904467,
              2.451566027339662,
              -5.735623906367098,
              -0.6187898240161711,
              9.183239650015835,
              6.290576922624182,
              -3.71936977303597,
              -2.433662405318535,
              7.706222208627842,
              7.648181465901285,
              -3.451129143561565,
              -6.21240449825259,
              3.9986902792671764,
              8.408122440567018,
              -1.4077714594434325,
              -8.184803558638388
            ],
            "metrics": {
              "initial_rmse_K": 5.757074579309281,
              "observation_residual_rms_K": 0.01343498416958782,
              "future_predictive_rmse_K": 0.018816371034917137
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.0979530680565,
              2.00511911216988,
              -0.289918509907456,
              -0.2574995681200479,
              0.10453633121952448,
              0.03190899217668314,
              -0.00801181556423461,
              0.0075004303735678466
            ],
            "initial_K": [
              0.5592492566056221,
              1.0841864035682947,
              1.5575432293475102,
              1.970448394261017,
              2.2999080442089275,
              2.502780868260622,
              2.5342858779544355,
              2.3749007936096818,
              2.05028542096485,
              1.6343636854779713,
              1.224591892689956,
              0.8940667804418919,
              0.6561862389824414,
              0.47618115134386496,
              0.3149939721089311,
              0.15664711849502302
            ],
            "metrics": {
              "initial_rmse_K": 0.04590089256046394,
              "observation_residual_rms_K": 0.02575311401185224,
              "future_predictive_rmse_K": 0.023185360129971275
            }
          },
          "learned": {
            "coefficients_K": [
              6.1718871141750435,
              2.0540337948354446,
              -0.30127768959474954,
              -0.24395186966021343,
              0.03264225945647297,
              0.00315597861986571,
              -0.0012493916369905233,
              -0.0020249023829712683
            ],
            "initial_K": [
              0.5415199997298448,
              1.074821885394629,
              1.5802244568835961,
              2.0235545908762043,
              2.361128481913468,
              2.548756756054977,
              2.5550682619988097,
              2.3783875184392658,
              2.0569450615225606,
              1.6602266250952689,
              1.2632941772783024,
              0.9204664859010543,
              0.6528407696400362,
              0.4514992806974335,
              0.29071055909591786,
              0.14469825210722978
            ],
            "metrics": {
              "initial_rmse_K": 0.029837126658557367,
              "observation_residual_rms_K": 0.018454402016328843,
              "future_predictive_rmse_K": 0.018001332276729527
            }
          }
        }
      },
      {
        "split": "train",
        "index": 111,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.567407311996764,
          -1.461224514613055,
          -0.08901652498895718,
          0.12764601204412107,
          -0.19386393653502354,
          0.056168411162228545,
          0.022825957939954615,
          0.02220609470230994
        ],
        "initial_K": [
          0.16255518396998556,
          0.3253783684071576,
          0.5210009909580404,
          0.7778291931056479,
          1.0692453728712326,
          1.3365070311493943,
          1.5579537895176252,
          1.7621545046662297,
          1.9679539381411693,
          2.137819074425788,
          2.198716284791695,
          2.091790257315953,
          1.80241818444222,
          1.3701591808489049,
          0.8799467400024537,
          0.41600906630619494
        ],
        "observed_K": [
          0.19333362870072535,
          0.38358826606748253,
          0.6227447054907408,
          0.8168752625086514,
          1.0623966134335923,
          1.301415665266498,
          1.4960816069914133,
          1.6759925563735587,
          1.7972927557691276,
          1.8561445111362398,
          1.8604759790867855,
          1.7103821054834996,
          1.5123174597755604,
          1.1871766348422574,
          0.8166348264519351,
          0.4418293963079877
        ],
        "future_observed_K": [
          0.1798794097485291,
          0.40980495059305505,
          0.6049382910804313,
          0.821913575038765,
          1.058316504429833,
          1.2196838185198418,
          1.4604942274143276,
          1.6006061599772017,
          1.6987769671565702,
          1.727969004534162,
          1.6960633191050072,
          1.5859339355272821,
          1.4005423996752917,
          1.1179836696787955,
          0.7650776003109926,
          0.3734425773244223
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.602217010609707,
              -1.456063834280106,
              -0.09065470678100672,
              0.11338688383043254,
              -0.31160069839370963,
              0.20111536115859688,
              1.5352848472295548,
              -7.255125513803699
            ],
            "initial_K": [
              -1.8124153238166592,
              0.14078259294017403,
              2.552009414137556,
              1.1970426827640244,
              -1.049532194796971,
              0.6011072737025307,
              3.7965451312785965,
              3.0343260623883666,
              -0.1796321643396417,
              0.2829136918469015,
              4.043222862888705,
              4.500287292048321,
              0.5121473188641122,
              -1.3775587308964434,
              1.5406726935195485,
              3.3282534038943377
            ],
            "metrics": {
              "initial_rmse_K": 1.8588202432839291,
              "observation_residual_rms_K": 0.010198089056232968,
              "future_predictive_rmse_K": 0.016616890770877628
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.534790991394113,
              -1.4246859031468666,
              -0.08559654312075446,
              0.09178899391521012,
              -0.13035197075613675,
              0.015242927360373746,
              0.009613302555793674,
              -0.0023660309493614834
            ],
            "initial_K": [
              0.149426206934213,
              0.3244002867380585,
              0.5392920810902209,
              0.7905825700416913,
              1.05865825640526,
              1.31941126795762,
              1.5591244917915896,
              1.7780378597862192,
              1.9737691983574648,
              2.1182788781352575,
              2.1569747386323908,
              2.040321091102855,
              1.7616408918073116,
              1.364270586685594,
              0.9120764686947254,
              0.45231266590412533
            ],
            "metrics": {
              "initial_rmse_K": 0.025228140495120174,
              "observation_residual_rms_K": 0.02007791116593072,
              "future_predictive_rmse_K": 0.018208148994695875
            }
          },
          "learned": {
            "coefficients_K": [
              5.60189703301943,
              -1.459440975016446,
              -0.08895026660060468,
              0.08695974460588658,
              -0.040703388003439714,
              0.0015076111644998418,
              0.0014991333388508503,
              0.000638760906898045
            ],
            "initial_K": [
              0.1662982689861641,
              0.3465449507416509,
              0.5511279285563857,
              0.7834597762849564,
              1.0389840399317471,
              1.307660697754975,
              1.5763764221541405,
              1.827043276773707,
              2.032307692810052,
              2.1561434432200755,
              2.163382575615388,
              2.033641559191282,
              1.7705488677746182,
              1.4003436547212904,
              0.960722383049688,
              0.4864112814622821
            ],
            "metrics": {
              "initial_rmse_K": 0.04345546472786821,
              "observation_residual_rms_K": 0.012698132672002283,
              "future_predictive_rmse_K": 0.01656240315375724
            }
          }
        }
      },
      {
        "split": "train",
        "index": 112,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.464077326976059,
          -0.10854189270472792,
          -0.5018624031742223,
          0.16557936083498992,
          0.13840931813588175,
          -0.03523237176638141,
          -0.011413173010279568,
          -0.028571325464807305
        ],
        "initial_K": [
          0.29211445601024355,
          0.5865607603569559,
          0.8586453089762119,
          1.0922877258981996,
          1.319103110486806,
          1.5795716445446932,
          1.8512448250451765,
          2.0502387471356673,
          2.104471923632934,
          2.00054612585669,
          1.767290593880885,
          1.4517776971883123,
          1.1152309387144959,
          0.8113617569503906,
          0.5465104753592576,
          0.28364100671873127
        ],
        "observed_K": [
          0.2981550149012334,
          0.5813917243510554,
          0.7849297350726748,
          1.0582398693879018,
          1.2841849065192683,
          1.5285807080790739,
          1.6514092067759443,
          1.7674892225520031,
          1.7513295908255337,
          1.6795840962932236,
          1.5432572136521978,
          1.377682281579118,
          1.1158795579949405,
          0.8181600133063833,
          0.5442058196390652,
          0.27677752989095256
        ],
        "future_observed_K": [
          0.2893124022163057,
          0.510585105595931,
          0.7654333078220006,
          1.0474006291569167,
          1.2710304934387773,
          1.4157380904816568,
          1.549455646197064,
          1.6740029423542966,
          1.6179965681844994,
          1.5629342215107713,
          1.5046524846401346,
          1.297629951294288,
          1.04376377348184,
          0.8183039088318026,
          0.5754029033152243,
          0.2790919343661066
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.452457706171355,
              -0.08545032448433448,
              -0.491892421113459,
              0.16145416048243155,
              0.07280562650633522,
              1.7786008871455994,
              2.696976146270684,
              0.2048192861156033
            ],
            "initial_K": [
              1.8072678606395671,
              1.5706936920609702,
              0.04062735088902364,
              -0.34708390479664986,
              1.1711515652512614,
              2.7901084561105645,
              2.737594291459328,
              1.5570542279325224,
              1.0601875493387407,
              1.7648181415230813,
              2.4286946530264584,
              1.982046225811517,
              0.9152224355203445,
              0.3640505570739061,
              0.5004138916155394,
              0.5217237038282128
            ],
            "metrics": {
              "initial_rmse_K": 0.8171950299572971,
              "observation_residual_rms_K": 0.012747733458630159,
              "future_predictive_rmse_K": 0.023706345435300775
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.386834129403037,
              -0.08360888434011989,
              -0.4644468260905772,
              0.13070043424308062,
              0.030456789558426765,
              0.13480364687050053,
              0.016887320764380587,
              6.6795366813933e-05
            ],
            "initial_K": [
              0.3308081534793093,
              0.6001699971582459,
              0.8155051858710796,
              1.0421564141747497,
              1.3252745736164895,
              1.632678269133744,
              1.8792645130404133,
              2.0006001369931625,
              1.994877269805391,
              1.8976747779691874,
              1.7312560002790982,
              1.4898987533076724,
              1.171752966393707,
              0.8123336670378477,
              0.4757279798183192,
              0.2082984224064834
            ],
            "metrics": {
              "initial_rmse_K": 0.056674336883485506,
              "observation_residual_rms_K": 0.023698420708194848,
              "future_predictive_rmse_K": 0.025636447934538505
            }
          },
          "learned": {
            "coefficients_K": [
              5.452146282269959,
              -0.08564851481428812,
              -0.4826441290307728,
              0.12382395641198314,
              0.009510362716763093,
              0.013332838124361281,
              0.002633470174772945,
              -1.803284487642467e-05
            ],
            "initial_K": [
              0.2820360051326823,
              0.5571172661167562,
              0.8269569074229126,
              1.0993803646407134,
              1.375764163120864,
              1.640494693253998,
              1.8622097569112397,
              2.005189719802173,
              2.041847379224185,
              1.960060291599457,
              1.7657841256026807,
              1.483164993149351,
              1.151068606157931,
              0.8134348025058766,
              0.5048230703914153,
              0.23786005560282084
            ],
            "metrics": {
              "initial_rmse_K": 0.03772054435472992,
              "observation_residual_rms_K": 0.018902201753683165,
              "future_predictive_rmse_K": 0.02316575220697558
            }
          }
        }
      },
      {
        "split": "train",
        "index": 113,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.489050422574091,
          0.9631172753515335,
          -0.31408283772597506,
          -0.03965940760588328,
          -0.10013797470209096,
          -0.07112381153774057,
          -0.0430565665628501,
          0.025022805882630565
        ],
        "initial_K": [
          0.407528725413385,
          0.8578962606329686,
          1.343051579144178,
          1.791594547150456,
          2.1177528780363226,
          2.293029195079951,
          2.3566326203455352,
          2.3478779174739866,
          2.2538971399639043,
          2.0467494147940415,
          1.7482059464513418,
          1.4197233294097094,
          1.097991969907791,
          0.7808794026876253,
          0.4756618695097954,
          0.21377075106143467
        ],
        "observed_K": [
          0.43264321925257876,
          0.8231251464771908,
          1.2467277402388108,
          1.5490734647145812,
          1.8210749722419715,
          2.031486424591409,
          2.0912801275579813,
          2.0571259827888344,
          1.9493507908076713,
          1.8671088940989358,
          1.6390683856798087,
          1.3656343189205686,
          1.1016815074039434,
          0.7855448272637433,
          0.557280407652297,
          0.24364127106492892
        ],
        "future_observed_K": [
          0.4171693634006708,
          0.7854067344427861,
          1.1373511899311588,
          1.47322365987189,
          1.6824029924353776,
          1.8291560014362969,
          1.9640321381387928,
          1.9385989637745045,
          1.9245057279715176,
          1.7888845896160885,
          1.5689123516336985,
          1.2954925812252722,
          1.0754682698259712,
          0.8116433704653664,
          0.46381455660069604,
          0.2884352931856514
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.475189382955788,
              1.0153700720945182,
              -0.2609061839883679,
              -0.024156105437144852,
              -0.5098311034595546,
              -0.22563403819001704,
              4.680367768443392,
              -1.0206489053732517
            ],
            "initial_K": [
              1.4678745910508992,
              1.4994038301725445,
              0.5914748151703904,
              0.6260106004418067,
              2.287249473589312,
              3.7945338969744014,
              3.137329327149356,
              1.1220271219530904,
              0.5978412441005079,
              2.351199700960897,
              3.647246834128764,
              2.131057645754735,
              -0.46631295388271543,
              -0.7206893031255297,
              1.2988233787996408,
              2.0631490555675884
            ],
            "metrics": {
              "initial_rmse_K": 1.2145441335694849,
              "observation_residual_rms_K": 0.01772180033038328,
              "future_predictive_rmse_K": 0.029957572096938098
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.397256621170062,
              0.9934890175371222,
              -0.2463486808487565,
              -0.019554859786967343,
              -0.2132777282955871,
              -0.01710124594334702,
              0.029306477890160377,
              -0.00033285253217886274
            ],
            "initial_K": [
              0.4232143078407048,
              0.8701340040348917,
              1.3386588455535635,
              1.7840936168549297,
              2.1303427870179226,
              2.315230313541868,
              2.3372352759259347,
              2.2546729711325293,
              2.1306186096956443,
              1.9779480093507025,
              1.7628149793971317,
              1.4600710265537877,
              1.096571958206715,
              0.7369099088497346,
              0.4337527462013431,
              0.1967842018210908
            ],
            "metrics": {
              "initial_rmse_K": 0.04739397021458481,
              "observation_residual_rms_K": 0.027725557181766867,
              "future_predictive_rmse_K": 0.030744001354270557
            }
          },
          "learned": {
            "coefficients_K": [
              6.474819544463023,
              1.017725083978064,
              -0.25600076871435024,
              -0.01852602954172721,
              -0.06659758250642929,
              -0.0016914093140712465,
              0.004570158672781681,
              8.986069492254892e-05
            ],
            "initial_K": [
              0.4664647634086519,
              0.9309009806463036,
              1.3798701508173647,
              1.7836904644021383,
              2.10310065187241,
              2.3055910375352977,
              2.3804411330988446,
              2.3402396289775416,
              2.2080156493021437,
              2.002738730993671,
              1.7366154925965547,
              1.4240714064221194,
              1.089756508601326,
              0.7648965227490478,
              0.4741270577353065,
              0.2238016813760197
            ],
            "metrics": {
              "initial_rmse_K": 0.03146471253987285,
              "observation_residual_rms_K": 0.022175519554388592,
              "future_predictive_rmse_K": 0.029597403361274695
            }
          }
        }
      },
      {
        "split": "train",
        "index": 114,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.678317279842282,
          -0.24995903439403,
          -0.0379987532256793,
          -0.14159263962415602,
          0.06258974282662298,
          0.10206045117002854,
          -0.08222363662796633,
          0.026238403744819814
        ],
        "initial_K": [
          0.31763200453475227,
          0.6211772421011649,
          0.9084890839722747,
          1.1844498972059652,
          1.4505655131548156,
          1.6989888609972157,
          1.901849830073516,
          2.0077535516292864,
          1.9794422120657376,
          1.8498182299834758,
          1.7076344180497864,
          1.595411925055714,
          1.4468791562031678,
          1.169673091470713,
          0.7742346877303328,
          0.36441593899584174
        ],
        "observed_K": [
          0.31757907548561837,
          0.5685573437416003,
          0.821397440006836,
          1.137841112977689,
          1.3496847662618043,
          1.5898688261202296,
          1.6793557198740194,
          1.7337047381887898,
          1.7589865409929526,
          1.68485590225498,
          1.6216639313903196,
          1.4829436843336241,
          1.20550239862421,
          0.9809734789173764,
          0.6768692163173372,
          0.37491705777284773
        ],
        "future_observed_K": [
          0.28513980263002514,
          0.5949863771655394,
          0.830947421591173,
          1.0910023777946607,
          1.2916811606410996,
          1.4478750267450453,
          1.6001290660892913,
          1.660817178576087,
          1.6901076422308334,
          1.6573282178883946,
          1.531225402061689,
          1.3987767741432156,
          1.2168906927720737,
          0.9398965348796061,
          0.6540540264447553,
          0.35255195406252476
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.661075066790681,
              -0.23669232244798233,
              -0.040477151391637455,
              -0.28528466430214966,
              -0.2889912307117796,
              0.19335347384011636,
              6.74773511048282,
              -2.596775875757573
            ],
            "initial_K": [
              1.573712966282589,
              1.5492032980567576,
              0.10705927822379202,
              -0.5634286183267585,
              1.1999383361089317,
              3.696479607856893,
              3.5165002770363336,
              0.6664926759987877,
              -0.6442975512342559,
              1.8731497591265058,
              4.527677996545071,
              2.9370636638012817,
              -0.8817215961257285,
              -1.280416866715722,
              2.0749378282167803,
              3.4192529526338937
            ],
            "metrics": {
              "initial_rmse_K": 1.8316933905989383,
              "observation_residual_rms_K": 0.017731494854362907,
              "future_predictive_rmse_K": 0.020922133914965925
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.592940655804554,
              -0.2315916426435071,
              -0.03821869109200516,
              -0.23094375143859955,
              -0.12089374846947497,
              0.014654638709057331,
              0.04225145535727689,
              -0.0008468567606319055
            ],
            "initial_K": [
              0.24859493032304328,
              0.5205713423351371,
              0.83712713442048,
              1.192406401418382,
              1.5317544063355846,
              1.7764839395901537,
              1.8859059161156928,
              1.8909645588787645,
              1.8572432381422441,
              1.8172495375296274,
              1.747561351327141,
              1.608452280319218,
              1.389169337571002,
              1.1070574583909205,
              0.7774363132611547,
              0.4042959574121913
            ],
            "metrics": {
              "initial_rmse_K": 0.06761278820353135,
              "observation_residual_rms_K": 0.027458991950803764,
              "future_predictive_rmse_K": 0.03002025350871544
            }
          },
          "learned": {
            "coefficients_K": [
              5.660751727449341,
              -0.23724129788800022,
              -0.03971612214484077,
              -0.2187932211347411,
              -0.037749986613927915,
              0.0014494261113466766,
              0.006588845505844246,
              0.00022862718367228408
            ],
            "initial_K": [
              0.2620115529280962,
              0.5488013057224381,
              0.8694712920920867,
              1.206662412828426,
              1.5188096969038642,
              1.7590095190480866,
              1.8998892387449529,
              1.9454136765698309,
              1.9206813490217265,
              1.8503432940192723,
              1.7440807471415047,
              1.5968599300390536,
              1.3973064840531861,
              1.1352643897302284,
              0.8070710677469081,
              0.4208716230523133
            ],
            "metrics": {
              "initial_rmse_K": 0.04689614437867856,
              "observation_residual_rms_K": 0.02316821516053679,
              "future_predictive_rmse_K": 0.020014709625463534
            }
          }
        }
      },
      {
        "split": "train",
        "index": 115,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.7930257147674515,
          -1.6437785873530504,
          -0.5263199975967487,
          -0.020862529853196962,
          -0.2481914214049078,
          -0.030634738244501872,
          -0.02106190791696298,
          -0.01137797678021011
        ],
        "initial_K": [
          -0.02659389137614998,
          0.07443643190591187,
          0.3356454786404881,
          0.6946409681147644,
          1.0689423885402605,
          1.413112202778902,
          1.7167556826397843,
          1.9777932839527077,
          2.1856282524894954,
          2.3122583011947273,
          2.3109098967142896,
          2.1388139126895314,
          1.7970506949421403,
          1.3451040967620345,
          0.8665662761176399,
          0.41697611662973927
        ],
        "observed_K": [
          0.17362131234668907,
          0.341417478100439,
          0.5370717914829534,
          0.8143041207703603,
          1.0490231476863145,
          1.3336379355541594,
          1.580846673739565,
          1.7960747108655961,
          1.9243342686025928,
          1.991782205180854,
          1.9249021114535694,
          1.7779422601031705,
          1.4988946018908265,
          1.2114553896765712,
          0.815154465194044,
          0.41294186328354116
        ],
        "future_observed_K": [
          0.13978312280006727,
          0.3642090267320037,
          0.5796126538852,
          0.804216892923376,
          1.068433917235666,
          1.2891219656546336,
          1.5048397534090772,
          1.7171600858632685,
          1.7982909077716056,
          1.8357693788026879,
          1.8057193156302673,
          1.6741044541971632,
          1.4311606964504746,
          1.1204076887640693,
          0.7853684010225069,
          0.40947542633984896
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.799085422296345,
              -1.5799213491542787,
              -0.5266573998452765,
              0.11596411959171328,
              -0.11697292103512918,
              -0.10934252244479266,
              0.4358864362664359,
              4.020794234231191
            ],
            "initial_K": [
              1.552879909712093,
              0.4949548929039439,
              -1.0209151524148568,
              0.0887479042800392,
              2.3071232015985745,
              2.231391146729539,
              0.622682241500323,
              0.9363107772005483,
              3.061901174061453,
              3.5402624002597554,
              1.7478785919050461,
              0.8718344808281369,
              2.0775712394941688,
              2.524960504017079,
              0.6989386768871142,
              -0.7885243657645624
            ],
            "metrics": {
              "initial_rmse_K": 1.0159190374791758,
              "observation_residual_rms_K": 0.010572190692945124,
              "future_predictive_rmse_K": 0.01836713414164147
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.729289974462725,
              -1.5458743093730811,
              -0.4972720605077889,
              0.09387531880234637,
              -0.048933301050453806,
              -0.008287284061368505,
              0.002729335992182428,
              0.0013112555504525773
            ],
            "initial_K": [
              0.08686271749529612,
              0.21421671875790255,
              0.40912085437879564,
              0.676304599447332,
              0.9988554853247866,
              1.3477998253336656,
              1.6911312498345805,
              1.9941670554769295,
              2.2158882573554193,
              2.313417317990997,
              2.2575857183397012,
              2.0481000488705785,
              1.7152657314646944,
              1.3068365286231343,
              0.8688929326533115,
              0.43075416950008094
            ],
            "metrics": {
              "initial_rmse_K": 0.06547246364968075,
              "observation_residual_rms_K": 0.02028932182335093,
              "future_predictive_rmse_K": 0.026804903237314635
            }
          },
          "learned": {
            "coefficients_K": [
              5.798754200321951,
              -1.583585760440945,
              -0.5167554756597975,
              0.08893630270519277,
              -0.015279793066358202,
              -0.000819658959130171,
              0.0004256225740383386,
              -0.00035400161811417524
            ],
            "initial_K": [
              0.09208446507134183,
              0.21906598141222583,
              0.40685952180072477,
              0.6662055418788005,
              0.9900297585746726,
              1.3537243614009562,
              1.7180988407967897,
              2.0352509588063956,
              2.2570354148589153,
              2.344958173509055,
              2.2796468600977384,
              2.066846744643847,
              1.7360632522574675,
              1.3302792750574235,
              0.8906661450115139,
              0.44415554254490874
            ],
            "metrics": {
              "initial_rmse_K": 0.06685958384581564,
              "observation_residual_rms_K": 0.011154861418105124,
              "future_predictive_rmse_K": 0.018192656683919443
            }
          }
        }
      },
      {
        "split": "train",
        "index": 116,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.667917109354459,
          2.0706744313381016,
          -0.3182957508140123,
          0.08754094780515836,
          0.1356806170668422,
          -0.035994600234962836,
          -0.02055992971649606,
          -0.0006539180207694935
        ],
        "initial_K": [
          0.6586518062673247,
          1.2679946461548777,
          1.7790668345720047,
          2.160162814458279,
          2.413485446774749,
          2.562315564679816,
          2.614221268141211,
          2.5429245180621742,
          2.316303669257658,
          1.9444253388477652,
          1.495671369996073,
          1.062620288764409,
          0.7108051821053856,
          0.45462176687236855,
          0.2710202821956423,
          0.12761147013972868
        ],
        "observed_K": [
          0.5395771760477639,
          1.036625097566512,
          1.4674523636151886,
          1.846590584287476,
          2.1023416247540867,
          2.2463912072556544,
          2.2716618410279508,
          2.2150192586446726,
          2.0450438533293296,
          1.7638661805737588,
          1.5276259880217216,
          1.1535237529083902,
          0.8587898809769269,
          0.6294733690314712,
          0.4158508287673059,
          0.18247903210993935
        ],
        "future_observed_K": [
          0.48737401963532123,
          0.9280972325215459,
          1.3904916138964256,
          1.6897464835599039,
          1.9508473673713842,
          2.052492830575174,
          2.145418087289442,
          2.0644291990340427,
          1.9379396139220038,
          1.6523970052199959,
          1.4270061392458055,
          1.153340784323319,
          0.8730965825599367,
          0.6653657888987655,
          0.4099898549713609,
          0.1943990027218145
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.694682051539866,
              2.069543671677377,
              -0.3387185656012408,
              0.003583654849851892,
              0.3114402065230198,
              -0.8800669834954232,
              1.6875216843099947,
              2.8113295383112225
            ],
            "initial_K": [
              1.9499462781429813,
              1.548697152049098,
              0.5061931170986672,
              1.528941017097198,
              3.53912434575412,
              3.5451234586263034,
              1.8180923250312673,
              1.353376777675312,
              2.71047453993976,
              3.2130863621779833,
              1.6173818973208853,
              0.04182235503454845,
              0.23085074434930086,
              0.9773735533852347,
              0.7172152406821612,
              0.05553658913744508
            ],
            "metrics": {
              "initial_rmse_K": 0.8506000433326747,
              "observation_residual_rms_K": 0.015112349543228801,
              "future_predictive_rmse_K": 0.028355862923828815
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.614107564726065,
              2.0249453530609203,
              -0.3198194482755872,
              0.0029010416557455694,
              0.13028483216581072,
              -0.06670200140060534,
              0.010566545061659764,
              0.0009168266880900797
            ],
            "initial_K": [
              0.6296609419880228,
              1.2169193580276148,
              1.7251783319581657,
              2.127712278826784,
              2.4101474530837166,
              2.569652548136477,
              2.60715113759601,
              2.516570383368272,
              2.286554413321563,
              1.9237290356982282,
              1.479238417898233,
              1.0437326664435658,
              0.7003879619069486,
              0.4723149954804019,
              0.3155058850646868,
              0.1668529496580456
            ],
            "metrics": {
              "initial_rmse_K": 0.029681891272534473,
              "observation_residual_rms_K": 0.0261348413694562,
              "future_predictive_rmse_K": 0.027152669406009654
            }
          },
          "learned": {
            "coefficients_K": [
              6.69429967645042,
              2.074343694914485,
              -0.3323501645158615,
              0.0027484105742319226,
              0.04068242347121061,
              -0.0065972027307208145,
              0.0016477854396517704,
              -0.00024751706942413164
            ],
            "initial_K": [
              0.6291266475132824,
              1.2195785682607416,
              1.7380586640668763,
              2.158907366952615,
              2.4626629800338375,
              2.6335318363318367,
              2.6595630142205824,
              2.5372766073385633,
              2.2787523789954993,
              1.9165149192944129,
              1.5015005272897333,
              1.0920922180893493,
              0.7372288903412634,
              0.46175253569212904,
              0.2626831181790231,
              0.11803415808989515
            ],
            "metrics": {
              "initial_rmse_K": 0.033984385933995456,
              "observation_residual_rms_K": 0.017729545722565267,
              "future_predictive_rmse_K": 0.028235467379328843
            }
          }
        }
      },
      {
        "split": "train",
        "index": 117,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.996552866242704,
          0.7603435362300899,
          -0.9887206045615748,
          0.036018090960396716,
          -0.08953472505820248,
          0.02011794763460275,
          0.008128723557478908,
          0.020497931220423638
        ],
        "initial_K": [
          0.2932934053634462,
          0.6061536239654931,
          0.967395399874045,
          1.381474809255002,
          1.7959277981620836,
          2.129383530224069,
          2.32960975164052,
          2.3868477791787814,
          2.3021392150117927,
          2.074624526629307,
          1.7245217931403851,
          1.3039652753565096,
          0.8759218908733312,
          0.4968289518251695,
          0.21655992730873722,
          0.061871612257917374
        ],
        "observed_K": [
          0.32836164591446537,
          0.6591632598638055,
          1.0189738110059736,
          1.3392986928603847,
          1.587960376976464,
          1.8469886891103293,
          1.9738852427732592,
          2.023786362110337,
          2.026487189771398,
          1.7952177595511645,
          1.5409348602989796,
          1.2936238828091797,
          0.9688872946986619,
          0.7180509886450257,
          0.4074611181194964,
          0.2239196419982502
        ],
        "future_observed_K": [
          0.34495528351976734,
          0.6601108692870294,
          0.9889835821755666,
          1.2204663888460838,
          1.5103029602287852,
          1.7047420136911053,
          1.835673461565967,
          1.8629724207544356,
          1.841715960006013,
          1.7038924868617404,
          1.495596515808851,
          1.2565457618163418,
          0.9872762824841299,
          0.6638941729112496,
          0.4921083873131242,
          0.20042181617490015
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.037063570411252,
              0.7464424016312383,
              -1.0000006310660643,
              0.0347992259456133,
              0.184127107888023,
              -0.34088516397647284,
              -4.8134162375846845,
              2.058342623097821
            ],
            "initial_K": [
              -0.6387811727041588,
              -0.14661444780053476,
              1.464766173598564,
              2.6805072147291233,
              2.113023053507023,
              0.7524046256559993,
              1.0821909905041882,
              3.2713656294193565,
              4.260268914824524,
              2.1936551985713955,
              -0.29211707142735444,
              0.21156087825351877,
              2.451408755137337,
              2.3024825780486338,
              -0.5881979254360051,
              -2.036497656412436
            ],
            "metrics": {
              "initial_rmse_K": 1.3135658512532278,
              "observation_residual_rms_K": 0.018720196739460765,
              "future_predictive_rmse_K": 0.024722019681706797
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.964403913790771,
              0.7303566932152368,
              -0.9442046660037466,
              0.02817068280448339,
              0.077025922940987,
              -0.025836354631434164,
              -0.030139570974318967,
              0.0006712636936981203
            ],
            "initial_K": [
              0.305860873147898,
              0.6404398717628245,
              1.004356781220487,
              1.3747866147559153,
              1.7294013722471355,
              2.0502558806401256,
              2.3011999413916855,
              2.418163219796165,
              2.342722398245209,
              2.072761033125173,
              1.675180143435453,
              1.245327700829638,
              0.8554717149936236,
              0.5376261458899687,
              0.29772113117373344,
              0.12725924260813623
            ],
            "metrics": {
              "initial_rmse_K": 0.04722805242150837,
              "observation_residual_rms_K": 0.02762063357864039,
              "future_predictive_rmse_K": 0.022592023252171925
            }
          },
          "learned": {
            "coefficients_K": [
              6.036718756019029,
              0.7481736725978898,
              -0.9811991665140493,
              0.026688552489356573,
              0.024051926561627694,
              -0.00255536064506787,
              -0.004700074236094054,
              -0.00018122206130484307
            ],
            "initial_K": [
              0.30635344920941543,
              0.6350880321782131,
              0.9962159797381352,
              1.3815419399899205,
              1.7648112679868968,
              2.103816856657175,
              2.3452755314554157,
              2.437544801079391,
              2.3506894119911133,
              2.093123061523019,
              1.7125481567986796,
              1.279729424617087,
              0.8653933630952728,
              0.5217278380341217,
              0.2725101642771427,
              0.1103075501917976
            ],
            "metrics": {
              "initial_rmse_K": 0.0315369112792483,
              "observation_residual_rms_K": 0.021535177210408096,
              "future_predictive_rmse_K": 0.02484631015136899
            }
          }
        }
      },
      {
        "split": "train",
        "index": 118,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.49496163364003,
          -0.7840227708935785,
          -0.5245833537740165,
          -0.36734112581956363,
          0.05391157707362189,
          0.009466747227121883,
          0.00904415590533906,
          -0.038911433849115135
        ],
        "initial_K": [
          0.07693128162473875,
          0.23271460655410114,
          0.488590762917688,
          0.8244288302249028,
          1.2147691112611407,
          1.6115912240432975,
          1.9236487721209086,
          2.070658231124123,
          2.057052783307531,
          1.9534388676448444,
          1.8101248529307736,
          1.6276847565382728,
          1.4028770609532935,
          1.146655835950136,
          0.8456931970526079,
          0.46175281905157783
        ],
        "observed_K": [
          0.17218175813798497,
          0.4166491898168001,
          0.6194741318228797,
          0.9296665212162911,
          1.197418576869723,
          1.438098848946461,
          1.6232454816153938,
          1.7433508254161838,
          1.8087336520571806,
          1.777145915595713,
          1.6542688384679203,
          1.4885989152805168,
          1.2885219844001514,
          1.0163485306414943,
          0.6964859230615386,
          0.3402717947372188
        ],
        "future_observed_K": [
          0.2486121278559455,
          0.4583056490042927,
          0.6941913362696699,
          0.8973149131593455,
          1.123579072934266,
          1.3201767400551565,
          1.5428291162970253,
          1.6435136155552463,
          1.6723800675773315,
          1.6858524326361681,
          1.5934372825432492,
          1.4337096536532636,
          1.2371088198840734,
          0.9751926198769381,
          0.6483955585374911,
          0.31502595409979267
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.516233028899155,
              -0.7673328821037106,
              -0.5336512501275518,
              -0.41918935902940335,
              -0.2045241453852188,
              -0.30287250846972824,
              -1.829399926945931,
              16.137050227143973
            ],
            "initial_K": [
              4.818214963278921,
              0.7355040615611244,
              -4.443754986702268,
              -0.46080667112249074,
              6.245548163331584,
              3.9543021372983174,
              -2.8267062754191943,
              -1.2820134217277683,
              6.2779670770805955,
              6.2338592083125555,
              -1.6547266780788465,
              -3.448905474122352,
              3.915253978378962,
              6.86608593935668,
              -0.4918274342434266,
              -5.634619280674936
            ],
            "metrics": {
              "initial_rmse_K": 4.0713131989848845,
              "observation_residual_rms_K": 0.00911295556877512,
              "future_predictive_rmse_K": 0.024186141010510177
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.449841878127976,
              -0.7507969873413601,
              -0.5038756824103231,
              -0.33934233154173415,
              -0.08555861894921894,
              -0.022955300974835086,
              -0.011454926442486113,
              0.0052625912806305245
            ],
            "initial_K": [
              0.04860727879362159,
              0.19491880482550222,
              0.48030751489330425,
              0.8694833575770133,
              1.2782874466131469,
              1.6254762555386166,
              1.8668866999851654,
              1.9937680761503502,
              2.015036499741554,
              1.9482002843716613,
              1.816376672951012,
              1.6372815335703164,
              1.411261299780374,
              1.1277013645566998,
              0.7855977602810004,
              0.40199123064964715
            ],
            "metrics": {
              "initial_rmse_K": 0.041251641502165745,
              "observation_residual_rms_K": 0.020486765706429835,
              "future_predictive_rmse_K": 0.02767157876870399
            }
          },
          "learned": {
            "coefficients_K": [
              5.515917962390904,
              -0.7691126056800242,
              -0.5236178313968902,
              -0.32148867991836017,
              -0.026716325376036222,
              -0.0022704082500637807,
              -0.0017863228608846528,
              -0.0014207496228891131
            ],
            "initial_K": [
              0.0744275260366391,
              0.22530837378167906,
              0.4907170185453073,
              0.8546285939480234,
              1.258342268826591,
              1.627166442075163,
              1.8982589461881143,
              2.0401815034797988,
              2.0576243001956174,
              1.979362471102316,
              1.8371610725179033,
              1.6495322457398771,
              1.4186587151389554,
              1.137781987451308,
              0.8017754617742964,
              0.4159622369105321
            ],
            "metrics": {
              "initial_rmse_K": 0.026132271615017907,
              "observation_residual_rms_K": 0.013952061122141422,
              "future_predictive_rmse_K": 0.0223108609210375
            }
          }
        }
      },
      {
        "split": "train",
        "index": 119,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.732423802358114,
          0.7201179885422414,
          -0.30543045061424756,
          -0.3161899490660909,
          -0.020797257315552393,
          -0.07820958049761087,
          0.03733632416089294,
          -0.011459274883378646
        ],
        "initial_K": [
          0.3640248768526586,
          0.7765643058644137,
          1.2433859018413043,
          1.7176275994843953,
          2.1236110986869012,
          2.3935819128171136,
          2.498478722317841,
          2.456598445341983,
          2.3104196765989164,
          2.0914071751743535,
          1.8142589570778853,
          1.5051789428631661,
          1.2111511939793198,
          0.9568522675308048,
          0.7039991491598654,
          0.3875544184901489
        ],
        "observed_K": [
          0.40282072820415815,
          0.7801766451522393,
          1.218223982730294,
          1.5649106053854742,
          1.8023802271990503,
          2.0544332943314054,
          2.1459309930633057,
          2.1242554442127073,
          2.0886624553222637,
          1.8946740356201794,
          1.746736383532405,
          1.496103933111873,
          1.2283342702175866,
          0.9342648435220736,
          0.6372763778369585,
          0.3208656531771633
        ],
        "future_observed_K": [
          0.37467374049887725,
          0.7725336391005023,
          1.1416949616520673,
          1.4742248909766187,
          1.720152489697741,
          1.8869666282250035,
          1.991708995800447,
          2.0846446033249704,
          1.988444776496745,
          1.8495744955483966,
          1.6492042691164783,
          1.4184749001123371,
          1.1713513900032049,
          0.8994544677717894,
          0.6203838912185518,
          0.3126513426788471
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.729642612056669,
              0.7096632535094703,
              -0.21591578713762,
              -0.34774178141736584,
              -0.33798046774961066,
              -0.17686697859433462,
              -0.8458962278163755,
              -14.276651897824486
            ],
            "initial_K": [
              -4.909113585074777,
              -0.3996843024144334,
              6.138757295163108,
              3.864460184764883,
              -2.16831381641181,
              -0.42174189732432743,
              6.226189096267468,
              5.8522620904710365,
              -0.8574683280926765,
              -1.9383625040836883,
              4.15987024097909,
              5.923089185196278,
              -0.23104627302934566,
              -3.5487928216863027,
              1.4062864409768565,
              4.936268431699841
            ],
            "metrics": {
              "initial_rmse_K": 3.574171968890769,
              "observation_residual_rms_K": 0.016445947329638846,
              "future_predictive_rmse_K": 0.02090250805840126
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.648647354069468,
              0.6943701295597088,
              -0.20386856502467957,
              -0.2815040609663182,
              -0.14138742395428486,
              -0.013405094924779091,
              -0.005296643410164213,
              -0.004655880891273999
            ],
            "initial_K": [
              0.3570567349856843,
              0.7739499019057513,
              1.2531151543591283,
              1.7321026023041397,
              2.124119499255403,
              2.3655305795219093,
              2.4394610703623716,
              2.3733326777583823,
              2.2187363441663086,
              2.0224461857568654,
              1.804672811896561,
              1.560973732778796,
              1.283285937339385,
              0.9760620124092723,
              0.6532574950991605,
              0.3264945933687679
            ],
            "metrics": {
              "initial_rmse_K": 0.04987787504361666,
              "observation_residual_rms_K": 0.026266292597885637,
              "future_predictive_rmse_K": 0.027200945211217586
            }
          },
          "learned": {
            "coefficients_K": [
              6.72925824015134,
              0.7113092202769201,
              -0.21185625668136354,
              -0.2666934258998836,
              -0.04414929166498351,
              -0.0013258392100138957,
              -0.0008259778233440061,
              0.001256955113508572
            ],
            "initial_K": [
              0.4000351118618652,
              0.8270234098241643,
              1.2825007035805487,
              1.7316141088851613,
              2.114204277274369,
              2.3721569432630245,
              2.4756012653107726,
              2.432178612528069,
              2.2774877570677385,
              2.0565499872454387,
              1.8066696227019843,
              1.5471820466732793,
              1.2787952308529318,
              0.992361726064549,
              0.6810279768805736,
              0.34697408123932433
            ],
            "metrics": {
              "initial_rmse_K": 0.03479236782226265,
              "observation_residual_rms_K": 0.019311665714452995,
              "future_predictive_rmse_K": 0.020630441876491774
            }
          }
        }
      },
      {
        "split": "train",
        "index": 120,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.124617216543185,
          0.999810950221605,
          -0.8822058312758693,
          0.10668056329136524,
          0.07961390322415787,
          0.033446399276101914,
          0.05833002570407218,
          0.07621604471349666
        ],
        "initial_K": [
          0.45257963184136807,
          0.8062214948327646,
          1.1099014043879332,
          1.4692052914045115,
          1.8698426313501377,
          2.1939972233709,
          2.3749708859488488,
          2.429509361390671,
          2.353063415274581,
          2.0982969361278268,
          1.681241786766301,
          1.217340700493626,
          0.8137744548706405,
          0.49204366964273044,
          0.24337052742609944,
          0.08291476520374425
        ],
        "observed_K": [
          0.35800650383803795,
          0.7394339717161477,
          1.05578081206275,
          1.4407416770563295,
          1.7106479042158722,
          1.923935615654651,
          2.049044568450236,
          2.063050621074684,
          1.956178401502166,
          1.817923922460822,
          1.5285014366297411,
          1.2559193010985803,
          0.9589288027619608,
          0.658039470529319,
          0.3755899211221509,
          0.2060635216323189
        ],
        "future_observed_K": [
          0.3421739100279371,
          0.6934776237276148,
          1.041880182851525,
          1.374276931951896,
          1.6221084408441306,
          1.7320539804677764,
          1.9236922009305302,
          1.8978386457654814,
          1.8752139761152344,
          1.6956054039033113,
          1.5190604605489162,
          1.2425689075825395,
          0.9542400184058666,
          0.6959439583485133,
          0.4726219457227963,
          0.2412251069155276
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.134680515541998,
              1.0333553750553222,
              -0.9314585494043951,
              0.008939084658960398,
              -0.3759341385701959,
              0.15279812704026438,
              -0.03706256730677986,
              3.8607860608142155
            ],
            "initial_K": [
              1.5989342487114537,
              0.8703970861508932,
              -0.21202385158530945,
              1.0665895951547844,
              3.1792118701798278,
              3.0124526158621245,
              1.3900675247468892,
              1.496688175023063,
              3.09773552492181,
              3.031540785848098,
              1.020546931086578,
              0.20042111371481441,
              1.4171684644279017,
              1.7151567026002184,
              -0.18357908039118087,
              -1.3922817454568504
            ],
            "metrics": {
              "initial_rmse_K": 0.9541699446438167,
              "observation_residual_rms_K": 0.015000376557782429,
              "future_predictive_rmse_K": 0.0249035868857442
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.060845980832059,
              1.0110867402391297,
              -0.879486953522341,
              0.007236371259623973,
              -0.1572645892315012,
              0.011580869496284868,
              -0.00023207007719608472,
              0.0012590739183450327
            ],
            "initial_K": [
              0.31099775954549436,
              0.6683662420533438,
              1.085846158627891,
              1.5300508211716446,
              1.9336493074612955,
              2.228631093210892,
              2.3767371648867357,
              2.376535889992522,
              2.2472801971727114,
              2.0088263605105308,
              1.6765765857095485,
              1.2737194651764527,
              0.8464508100972294,
              0.46329017753587504,
              0.18964967254730017,
              0.04912474150833096
            ],
            "metrics": {
              "initial_rmse_K": 0.07059038606789221,
              "observation_residual_rms_K": 0.023935412752800405,
              "future_predictive_rmse_K": 0.02971666983787726
            }
          },
          "learned": {
            "coefficients_K": [
              6.134330125636579,
              1.0357521013869948,
              -0.9139457755578144,
              0.006855647608378495,
              -0.04910705651444861,
              0.001145413064986661,
              -3.618985126653159e-05,
              -0.0003399140650086546
            ],
            "initial_K": [
              0.3382943252428282,
              0.705220405813108,
              1.109356142928799,
              1.5300505337069996,
              1.9226928324247792,
              2.233734884034947,
              2.417227595416836,
              2.446243151074322,
              2.316813591066249,
              2.0464283922522695,
              1.6710899324407236,
              1.242510263827699,
              0.8223687626808756,
              0.4694917291671022,
              0.22127905677691206,
              0.07798533329030705
            ],
            "metrics": {
              "initial_rmse_K": 0.04952172120221173,
              "observation_residual_rms_K": 0.01675329095450908,
              "future_predictive_rmse_K": 0.02480347653007473
            }
          }
        }
      },
      {
        "split": "train",
        "index": 121,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.211526275479644,
          -2.2620407173890733,
          -0.49886167040360085,
          0.27989236718136395,
          -0.03944353212931305,
          0.017892877073980618,
          0.06725062803060623,
          -0.014716503797499156
        ],
        "initial_K": [
          0.034638462464084224,
          0.06855448960702215,
          0.13601770675178138,
          0.29518048882315107,
          0.5769382295026749,
          0.9517247386297946,
          1.3561788294406818,
          1.743356300771955,
          2.084586243786131,
          2.324665493500128,
          2.375601143716345,
          2.1878320813305874,
          1.8131863420828749,
          1.3644071787003327,
          0.9148340885083417,
          0.4649063018408207
        ],
        "observed_K": [
          0.06471764412224205,
          0.22848207049575675,
          0.3809522157678722,
          0.5211355188310932,
          0.7421809859544231,
          1.0508760848076673,
          1.2954583609784793,
          1.602931312338865,
          1.7791512953930289,
          1.8697958546687192,
          1.9101022356578738,
          1.7554804290066066,
          1.5668934272465966,
          1.1997590773851554,
          0.8546004620659113,
          0.4153331228491505
        ],
        "future_observed_K": [
          0.11213723952573391,
          0.24107614084073586,
          0.37785985522987986,
          0.5924633435047543,
          0.7987258056242403,
          1.0121963618674479,
          1.239571077490458,
          1.4717157302762407,
          1.6426547278302943,
          1.7494480309603524,
          1.7427802766408222,
          1.6450669752067508,
          1.4444213812990772,
          1.157812810983938,
          0.7784761618245682,
          0.4353392622158486
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.214555031428808,
              -2.197866881232432,
              -0.47085150444232654,
              0.3866800790781626,
              0.0969218794459704,
              0.6035737108074328,
              -2.1776847613367005,
              -15.41840008527959
            ],
            "initial_K": [
              -5.711827059757959,
              -1.0420528155239306,
              5.775526749016042,
              2.712227154775598,
              -4.469794958472151,
              -2.5738007535808265,
              5.476231239035787,
              6.04748128249242,
              -0.9232554555505059,
              -2.3454612971027964,
              4.3029907981786,
              6.867041017820799,
              0.7421906835946416,
              -3.1835825347520497,
              1.3226548324560583,
              4.815296171837577
            ],
            "metrics": {
              "initial_rmse_K": 3.894636825051458,
              "observation_residual_rms_K": 0.01884296571536621,
              "future_predictive_rmse_K": 0.022155969473055214
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.151794755080351,
              -2.1505032189975024,
              -0.44457990693003646,
              0.3130254067015137,
              0.040545345566613114,
              0.04574603440268171,
              -0.0136357383580305,
              -0.0050282261446753925
            ],
            "initial_K": [
              0.06922204340158156,
              0.13492761112599633,
              0.2107369971867512,
              0.3364207172233429,
              0.5622500378589237,
              0.9086543747160094,
              1.3357766958859103,
              1.75746284386304,
              2.087262903830567,
              2.2706082210275387,
              2.2829316190598896,
              2.1184390183956294,
              1.79484097268351,
              1.3623989814780373,
              0.890558859845707,
              0.43281558941631915
            ],
            "metrics": {
              "initial_rmse_K": 0.04600493326126208,
              "observation_residual_rms_K": 0.026958598879201143,
              "future_predictive_rmse_K": 0.027128056205001423
            }
          },
          "learned": {
            "coefficients_K": [
              5.2142571956344845,
              -2.202964532587348,
              -0.4619988121589249,
              0.2965563545348628,
              0.01266059057456715,
              0.0045245398450410096,
              -0.0021264065968724945,
              0.0013574777173257543
            ],
            "initial_K": [
              0.0453964929558863,
              0.10156977539428047,
              0.1898276094378496,
              0.34144020406809916,
              0.584590300379902,
              0.9264240001177324,
              1.339834514672436,
              1.7626459110786812,
              2.1128150464060416,
              2.3151509455522534,
              2.326463046291719,
              2.146474274864435,
              1.8121552583054898,
              1.381737933637591,
              0.9144567523791707,
              0.45055295857041217
            ],
            "metrics": {
              "initial_rmse_K": 0.02861283604712368,
              "observation_residual_rms_K": 0.02160799562535599,
              "future_predictive_rmse_K": 0.021539297058797646
            }
          }
        }
      },
      {
        "split": "train",
        "index": 122,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.825136204001735,
          0.6042434901807139,
          -0.27782795081591055,
          0.020221115584566532,
          0.015011435999635484,
          -0.1248142052177078,
          0.004089870578515039,
          -0.010067908120411678
        ],
        "initial_K": [
          0.42323031105474174,
          0.8777883490476328,
          1.3406549870300672,
          1.7471786731984889,
          2.0503079633175023,
          2.2524558283622835,
          2.3803121691287012,
          2.4415288226124496,
          2.4107954294256797,
          2.25426441248597,
          1.9695796376711978,
          1.6074257621564483,
          1.247042175091082,
          0.936157386704231,
          0.654320750929178,
          0.34767026549707
        ],
        "observed_K": [
          0.40906899940300173,
          0.8065626750547541,
          1.194252572316461,
          1.5360780749513046,
          1.812919802885883,
          2.040324271874691,
          2.1538827997724628,
          2.184904054300414,
          2.113123441569284,
          2.0008935690234253,
          1.795504073886789,
          1.5612355273548437,
          1.2391162591507496,
          0.9401826526157414,
          0.6568467164034154,
          0.33003714456386707
        ],
        "future_observed_K": [
          0.4433008051651095,
          0.8008739526270201,
          1.1037288154899787,
          1.450127302655645,
          1.6813874427463773,
          1.8919549073096775,
          2.0260987930111964,
          2.0718852953197593,
          2.011162823713148,
          1.9238256946528973,
          1.6547681880333496,
          1.474973804215961,
          1.2195179287669982,
          0.9170198540124327,
          0.6651197656101103,
          0.3164477096674732
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.837060553148658,
              0.6025470703864644,
              -0.31675116953374205,
              -0.1184792311834606,
              -0.10357476302274583,
              -0.3962554877876911,
              3.003459302191526,
              -11.718456026079142
            ],
            "initial_K": [
              -2.740419127803828,
              0.5097843486366412,
              4.4629997595630675,
              2.370725464840408,
              -1.229430157607999,
              1.2078976702900834,
              5.911768869966364,
              4.274641396464822,
              -1.1032719538422757,
              -0.5230110695060417,
              5.1299446650109335,
              5.343122483093107,
              -1.1913203707310975,
              -3.624017950649802,
              2.0062946080975745,
              5.412852978589811
            ],
            "metrics": {
              "initial_rmse_K": 3.0227389301305148,
              "observation_residual_rms_K": 0.006513628176764058,
              "future_predictive_rmse_K": 0.02806220966388368
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.754772456246711,
              0.58956228219655,
              -0.2990777434980885,
              -0.09591135290780971,
              -0.043328447433567466,
              -0.030032979985721252,
              0.018806388298615823,
              -0.00382160578527312
            ],
            "initial_K": [
              0.4064253503146503,
              0.8292375017215325,
              1.2657335037442692,
              1.6867424175822123,
              2.045410046623796,
              2.297863567602934,
              2.42382329494738,
              2.431701696648533,
              2.3426985720097804,
              2.1704405066543098,
              1.920655944263139,
              1.610243315545277,
              1.2753580172750567,
              0.9498949419354944,
              0.6392072764346277,
              0.32570461865255323
            ],
            "metrics": {
              "initial_rmse_K": 0.04454457994198025,
              "observation_residual_rms_K": 0.021698719835788114,
              "future_predictive_rmse_K": 0.02811983102313489
            }
          },
          "learned": {
            "coefficients_K": [
              6.836670045934061,
              0.6039445958307871,
              -0.3107957874061837,
              -0.0908652159470518,
              -0.013529635165812098,
              -0.002970430473045531,
              0.0029327365406634563,
              0.001031724617916197
            ],
            "initial_K": [
              0.42530571424613245,
              0.8555118432866758,
              1.2863698209589003,
              1.6976534363741829,
              2.0542674686471063,
              2.3179421188112026,
              2.462422532976836,
              2.4810788804594774,
              2.383983219708108,
              2.1911159061404577,
              1.9277315414695086,
              1.6209601727185614,
              1.2948676271891604,
              0.9655505043735176,
              0.6399611941728798,
              0.3187551832969693
            ],
            "metrics": {
              "initial_rmse_K": 0.04282610852589968,
              "observation_residual_rms_K": 0.010950926244846688,
              "future_predictive_rmse_K": 0.027641432755162686
            }
          }
        }
      },
      {
        "split": "train",
        "index": 123,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.394273126218279,
          0.46881875437624776,
          -0.7819887863683909,
          -0.21824619049797614,
          -0.0008315216912107992,
          0.010065010692992897,
          -0.023022179418505418,
          0.043046893342754654
        ],
        "initial_K": [
          0.27943023035724357,
          0.5870117669341909,
          0.9620932419799962,
          1.408444095292565,
          1.8571299833389365,
          2.214246446697849,
          2.4306035201030265,
          2.4963484211399942,
          2.3994291661481295,
          2.1439695918702237,
          1.7955584476079574,
          1.4472024313991203,
          1.1330275840039254,
          0.823349464757684,
          0.5084874630857962,
          0.22853051277289319
        ],
        "observed_K": [
          0.3407644748265104,
          0.6767885603575621,
          1.0361876005920125,
          1.3447025149890186,
          1.6718130643955469,
          1.9270091433858196,
          2.04049570759109,
          2.0991071664430834,
          2.056246130552947,
          1.917012302482774,
          1.6651882916883276,
          1.402204828872013,
          1.1164832432101384,
          0.8375051725469145,
          0.544221564065951,
          0.26490137410845094
        ],
        "future_observed_K": [
          0.34747630517885725,
          0.6672435849322255,
          0.9807164107390797,
          1.2898088874025166,
          1.5655250042147952,
          1.7522816290265895,
          1.9110476679661332,
          1.9829314652385668,
          1.974188986350626,
          1.815217339387742,
          1.6516164358338463,
          1.3986022785230525,
          1.1172079318741914,
          0.867305854021871,
          0.5581485686347581,
          0.2686884654538045
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.363725803792629,
              0.5410724427357066,
              -0.8095044906911387,
              -0.2265764126434892,
              0.019804788506772412,
              -0.285632575578239,
              0.6549983755476787,
              14.834386707829651
            ],
            "initial_K": [
              5.469849120140434,
              1.5691589347242059,
              -4.048110558557226,
              -0.5290660612133462,
              6.516223785512664,
              5.090081330747757,
              -1.6218426733970874,
              -1.1499828206487401,
              5.684549457562669,
              6.359598197723047,
              -0.6419694061192094,
              -3.1640634596228647,
              2.6175480091429595,
              5.495492359847926,
              -0.2396571942321183,
              -4.5170159159786705
            ],
            "metrics": {
              "initial_rmse_K": 3.7025184717751696,
              "observation_residual_rms_K": 0.008459173480161598,
              "future_predictive_rmse_K": 0.02435708513199844
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.2871345725860035,
              0.5294124224491313,
              -0.7643374349141429,
              -0.18341822492066306,
              0.008284940391899923,
              -0.0216486526748305,
              0.004101322024415009,
              0.004837768553933693
            ],
            "initial_K": [
              0.2800771649314339,
              0.6018694407481309,
              0.986380036348382,
              1.4166309900113474,
              1.837885195184352,
              2.181662298873884,
              2.3949894167631895,
              2.4519150696154286,
              2.3497829618122905,
              2.108605944520263,
              1.7744403166588254,
              1.4093617543008445,
              1.0650412894256651,
              0.7621528372124088,
              0.49372930151357086,
              0.2436400138428954
            ],
            "metrics": {
              "initial_rmse_K": 0.03531935336339235,
              "observation_residual_rms_K": 0.021284753845332034,
              "future_predictive_rmse_K": 0.03303653064666373
            }
          },
          "learned": {
            "coefficients_K": [
              6.363362331680779,
              0.5423273861967378,
              -0.7942846303094497,
              -0.17376813182961456,
              0.0025870352507961335,
              -0.0021411733912608225,
              0.000639575062209845,
              -0.001306059597279347
            ],
            "initial_K": [
              0.28449374469502936,
              0.6108471542813788,
              0.9974142158003043,
              1.4274847939687043,
              1.852891453586929,
              2.208748103084654,
              2.4339824263820553,
              2.491587522103501,
              2.3803347508709534,
              2.1321725962246454,
              1.7982077864150727,
              1.4321197551357396,
              1.0772055595871481,
              0.7583786327656076,
              0.48024203027648027,
              0.23261389484773048
            ],
            "metrics": {
              "initial_rmse_K": 0.026429413270610908,
              "observation_residual_rms_K": 0.011501348247332803,
              "future_predictive_rmse_K": 0.02453071816669301
            }
          }
        }
      },
      {
        "split": "train",
        "index": 124,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          4.945141799824596,
          -0.9630056555477062,
          -0.45229457578660487,
          -0.09839650138258071,
          -0.029018254960896352,
          0.056997979771968146,
          -0.06985825119649629,
          -0.000552521814943273
        ],
        "initial_K": [
          0.07426635000438575,
          0.21110172445932804,
          0.4249686186949667,
          0.6917538913386074,
          0.9897664953534984,
          1.3055336306673704,
          1.601393701960943,
          1.8102766810659798,
          1.8864420204113446,
          1.849504447674274,
          1.7538691043431678,
          1.6163114268640404,
          1.399425980654104,
          1.0770140165730702,
          0.6922345773390692,
          0.32375887481272797
        ],
        "observed_K": [
          0.18325387311380872,
          0.3642828710029023,
          0.5202879414037893,
          0.7376175972760186,
          0.9655808033101603,
          1.2450411222656423,
          1.4259448194252449,
          1.5427542413289033,
          1.65017916670049,
          1.6289127425652612,
          1.5954501017124374,
          1.4180912835605106,
          1.184401913428101,
          0.948379178687585,
          0.6563955192121651,
          0.3201441221660097
        ],
        "future_observed_K": [
          0.162909222356198,
          0.3552521249587964,
          0.5350567446969118,
          0.7584480111464911,
          1.0145046349172309,
          1.1576398958637528,
          1.3467435623911932,
          1.4507220874261257,
          1.5123458531896161,
          1.5218449983916713,
          1.4573614060943678,
          1.3355422942258324,
          1.1566134503640095,
          0.884232495841173,
          0.6154752115333979,
          0.28677497837969984
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              4.9562060219658495,
              -0.9751951175402032,
              -0.5128344765976426,
              -0.018410420642065176,
              0.13978276030111678,
              0.8666644894227277,
              5.766028279495648,
              5.311713652032547
            ],
            "initial_K": [
              4.1154061824714345,
              1.8842578130926353,
              -2.706740087436496,
              -2.069030880832849,
              2.720964379399356,
              4.296699658372601,
              1.1484745010098678,
              -0.8035462418395074,
              1.4566537166106839,
              3.805169573279401,
              2.685424255052013,
              0.49648562577463107,
              0.48753998453446223,
              1.516132882009639,
              1.2035309296321273,
              0.20511707128123446
            ],
            "metrics": {
              "initial_rmse_K": 1.983874539147125,
              "observation_residual_rms_K": 0.0121351681870847,
              "future_predictive_rmse_K": 0.018810331195468096
            }
          },
          "tikhonov": {
            "coefficients_K": [
              4.896555129856416,
              -0.9541798265074604,
              -0.48422040011602113,
              -0.014903610816381077,
              0.058475344814410336,
              0.0656862001091424,
              0.03610442355116019,
              0.0017322483078953612
            ],
            "initial_K": [
              0.1481801524469381,
              0.2763539226809546,
              0.4159093217500977,
              0.6285822926111664,
              0.935837694123504,
              1.2849602608644737,
              1.5896857422873967,
              1.7933270771424288,
              1.8869885993321913,
              1.8811963990900764,
              1.7805752299809583,
              1.5893232753459687,
              1.32600010373547,
              1.0194306928929815,
              0.691332347370317,
              0.3500033054611825
            ],
            "metrics": {
              "initial_rmse_K": 0.04286082460965762,
              "observation_residual_rms_K": 0.0228460229957042,
              "future_predictive_rmse_K": 0.01930173088721706
            }
          },
          "learned": {
            "coefficients_K": [
              4.955922942096429,
              -0.9774569491163946,
              -0.5031924434496008,
              -0.014119494451537595,
              0.01825936834563598,
              0.006496734275304299,
              0.00563025502540916,
              -0.00046765766120787725
            ],
            "initial_K": [
              0.10580705888647716,
              0.237663958858804,
              0.4197322023894592,
              0.6656249778268826,
              0.966732459554333,
              1.28890802675169,
              1.5832879917208589,
              1.8041122170541803,
              1.9212605301664214,
              1.9229123360291436,
              1.813245256892746,
              1.6098560326601057,
              1.3392450290900457,
              1.0282058527967237,
              0.6955440372290124,
              0.35088570124157337
            ],
            "metrics": {
              "initial_rmse_K": 0.03579660509405598,
              "observation_residual_rms_K": 0.01815032984156559,
              "future_predictive_rmse_K": 0.0182987639334196
            }
          }
        }
      },
      {
        "split": "train",
        "index": 125,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.046957200506268,
          -0.30108803541839213,
          -0.23858519461858327,
          0.13845256277869245,
          0.04051474420458837,
          -0.029226652818855545,
          -0.02388661877108588,
          -0.052673420004798445
        ],
        "initial_K": [
          0.30896541800765076,
          0.6514379878023249,
          0.9855923715720468,
          1.2540811779882013,
          1.476505584050837,
          1.7129440454537042,
          1.957196825677257,
          2.1336924229113294,
          2.1921663145129906,
          2.1420776223927396,
          1.995386801999158,
          1.7440032590552517,
          1.4099557461442846,
          1.056251433032139,
          0.7186529736234423,
          0.3735188618354258
        ],
        "observed_K": [
          0.3508023593146197,
          0.5999776280357831,
          0.926777017652804,
          1.1259171850537255,
          1.4539230516127868,
          1.6519252930084722,
          1.7699505200250985,
          1.8910774981806513,
          1.9256792250401913,
          1.8956742559108333,
          1.726203106011865,
          1.5602955562380334,
          1.2964057317163264,
          1.0386749477149773,
          0.7172098737992044,
          0.36233751503865197
        ],
        "future_observed_K": [
          0.29279298590626085,
          0.5984313253919589,
          0.8695177211576125,
          1.1296298064634043,
          1.3771049778333393,
          1.5140569465599034,
          1.703297678129195,
          1.7861149327203714,
          1.8045117636215604,
          1.7603694295058825,
          1.6401404483188635,
          1.4678109854746746,
          1.250935883109058,
          0.971981035975748,
          0.667378664188443,
          0.314433677470625
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.068199227455752,
              -0.29890421238250403,
              -0.18993603768262945,
              0.012239022342250572,
              0.33894666924590683,
              -0.2145180660140731,
              3.575761189942685,
              23.83365002446107
            ],
            "initial_K": [
              9.660516751261472,
              2.829560253543227,
              -7.6911500358057125,
              -2.7925231664862595,
              9.01363980817308,
              7.209147153926917,
              -4.144459185226606,
              -4.305989170376097,
              6.826944488166281,
              9.164911457973474,
              -1.1730208159530573,
              -5.519556224441743,
              3.174776067990626,
              8.184267712764914,
              0.072515429904491,
              -6.419341440144533
            ],
            "metrics": {
              "initial_rmse_K": 6.03974367809366,
              "observation_residual_rms_K": 0.018572201458660693,
              "future_predictive_rmse_K": 0.016450458362823644
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.995164834653827,
              -0.29246287679627236,
              -0.17933837984783663,
              0.009907738085306131,
              0.14179161518312028,
              -0.016258744627476715,
              0.022389899990359338,
              0.007772595179343817
            ],
            "initial_K": [
              0.35537824253438705,
              0.6704290378206084,
              0.9450352248178433,
              1.2089108771260257,
              1.47961599341036,
              1.7429995619076895,
              1.967446210029264,
              2.1197319118344184,
              2.1685160495184053,
              2.094508112861484,
              1.9108634214630267,
              1.6638760347225614,
              1.3986325228126957,
              1.1222850702964025,
              0.8067443728660751,
              0.4279494257844407
            ],
            "metrics": {
              "initial_rmse_K": 0.0493781376953434,
              "observation_residual_rms_K": 0.02838871161935243,
              "future_predictive_rmse_K": 0.01424567722890317
            }
          },
          "learned": {
            "coefficients_K": [
              6.067852634711763,
              -0.29959747978475343,
              -0.18636496425657256,
              0.009386467121713028,
              0.04427550343086202,
              -0.0016080811999969213,
              0.0034915623776820633,
              -0.0020983791218153252
            ],
            "initial_K": [
              0.325886749402284,
              0.6432560572408705,
              0.948044310371696,
              1.2411146436349096,
              1.5220795006868737,
              1.780091587438547,
              1.9911395887720233,
              2.1266482333298713,
              2.1663498486455044,
              2.105046787317682,
              1.9514513651152936,
              1.7236911187127582,
              1.4429959011368731,
              1.1252945084768968,
              0.7764486796630534,
              0.3982127748892459
            ],
            "metrics": {
              "initial_rmse_K": 0.03865567455552726,
              "observation_residual_rms_K": 0.02350639036401314,
              "future_predictive_rmse_K": 0.01613143213804735
            }
          }
        }
      },
      {
        "split": "train",
        "index": 126,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.745886741282406,
          2.070551298061093,
          -0.6700512334875861,
          0.12883327793103327,
          -0.04436755215777595,
          -0.06009120529076853,
          -0.037208824427796654,
          0.022813003979179135
        ],
        "initial_K": [
          0.5554189223943202,
          1.116205907694778,
          1.659588768454841,
          2.127122525870883,
          2.456962987253573,
          2.6319388476058716,
          2.6804616596748123,
          2.619976821292222,
          2.423151400498548,
          2.0653731072300663,
          1.590103802690629,
          1.0955441756622113,
          0.6625602814476168,
          0.32506066876682826,
          0.10131628043549878,
          0.004093457841384707
        ],
        "observed_K": [
          0.5251520279324572,
          1.0078663487591586,
          1.4141502807633912,
          1.8047598021697986,
          2.0483890180847024,
          2.3002018062840794,
          2.3365324920565906,
          2.2976894459131456,
          2.1057901083410084,
          1.7971367663799678,
          1.5297004520596023,
          1.1588778003377074,
          0.8633818884859221,
          0.5863906944230463,
          0.3079541441771143,
          0.11521813787897542
        ],
        "future_observed_K": [
          0.496763738137057,
          0.9383592080395434,
          1.364262035082976,
          1.7208772491449442,
          1.941353534943749,
          2.084899204138972,
          2.1616994182786904,
          2.163525162865268,
          1.9817486944852216,
          1.7811462602469639,
          1.4991393256806556,
          1.1961495690263597,
          0.8752683392130114,
          0.6191382632595496,
          0.37352564561688134,
          0.19683737957824549
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.735659226786799,
              2.080709761105063,
              -0.7747141164125216,
              0.07506522896618122,
              0.09026931218281722,
              2.2176464626900008,
              -1.964511798231215,
              8.111528165030784
            ],
            "initial_K": [
              3.387663019301991,
              1.8964539422279203,
              -0.7396180067535847,
              0.9099725491151571,
              4.244019745848281,
              3.7093226063973255,
              1.0531998332442942,
              1.7693639336371731,
              4.473586577488113,
              3.2736235289731064,
              -0.8590691839330171,
              -1.0579528183826834,
              2.9525784350518336,
              3.5731522112409637,
              -1.352908886639445,
              -4.065179602024383
            ],
            "metrics": {
              "initial_rmse_K": 2.155836247222457,
              "observation_residual_rms_K": 0.01665017657498959,
              "future_predictive_rmse_K": 0.02168940473264022
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.654591555256953,
              2.0358708151363976,
              -0.7314882219182793,
              0.06076683309442333,
              0.037762376023187716,
              0.16807977146567407,
              -0.012300939675723398,
              0.002645319732727573
            ],
            "initial_K": [
              0.6124129833997591,
              1.1475454264252396,
              1.5895355015958306,
              1.9778225765404334,
              2.3398133767983804,
              2.6349010913928295,
              2.770887492679468,
              2.6795719092430983,
              2.3785306839030267,
              1.9596282529300129,
              1.5178808092013174,
              1.0945302348056654,
              0.6910803599981823,
              0.3290202930122357,
              0.07281075575908924,
              -0.025199955000765217
            ],
            "metrics": {
              "initial_rmse_K": 0.06972246288639997,
              "observation_residual_rms_K": 0.030605862962524176,
              "future_predictive_rmse_K": 0.033724409751139724
            }
          },
          "learned": {
            "coefficients_K": [
              6.735274511235039,
              2.0855356825580214,
              -0.760148365606797,
              0.05756973751429198,
              0.011791587302344154,
              0.016624033822202705,
              -0.0019182532392009633,
              -0.000714160916605238
            ],
            "initial_K": [
              0.5664045139268699,
              1.110766149629523,
              1.6137263028062336,
              2.0572659566919027,
              2.4187990224855835,
              2.666303620254416,
              2.762919004529819,
              2.682722027497518,
              2.427770761879727,
              2.033376525065718,
              1.5587309847778696,
              1.071659589053584,
              0.6362381955111547,
              0.3031554713669846,
              0.09859830847179019,
              0.013261911366941825
            ],
            "metrics": {
              "initial_rmse_K": 0.039028167211385065,
              "observation_residual_rms_K": 0.023677245198213664,
              "future_predictive_rmse_K": 0.021212185766886618
            }
          }
        }
      },
      {
        "split": "train",
        "index": 127,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.84452570354678,
          -1.575252854421695,
          -0.3887845039373645,
          -0.05933240345308802,
          0.03898558583537539,
          0.09727071551986445,
          -0.02535792588605169,
          0.02999937280093339
        ],
        "initial_K": [
          0.13167901651214514,
          0.2573248753947068,
          0.41729125205159556,
          0.667308230668978,
          1.014430465836258,
          1.4071970112408663,
          1.776075206544755,
          2.0619785237445183,
          2.2245747063532493,
          2.2584909979022463,
          2.195459812036922,
          2.058898437342914,
          1.8224060097467922,
          1.4491532534619038,
          0.9688273739701896,
          0.4692392514667595
        ],
        "observed_K": [
          0.18657537962915094,
          0.37329404416863,
          0.6114436395838342,
          0.79697867236266,
          1.138116566283209,
          1.3521217172282705,
          1.5849582985343507,
          1.8152298507488975,
          1.9304111471484684,
          1.983958549656044,
          1.9293596690910322,
          1.787642195236637,
          1.5531448446327323,
          1.2514849670524926,
          0.8686756185286454,
          0.4420146815380623
        ],
        "future_observed_K": [
          0.21559845943733175,
          0.38581712905443744,
          0.6247858012100366,
          0.8781446997757557,
          1.0556675821540888,
          1.3113566854925591,
          1.539700290352228,
          1.707923986823009,
          1.800498393665555,
          1.8488224695397226,
          1.7689322450473919,
          1.6899532729588724,
          1.4341267233951212,
          1.1416230675226196,
          0.8349384647221086,
          0.43349031241408814
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.891685770067652,
              -1.5619479959170528,
              -0.31682973154955896,
              -0.0318680365313469,
              0.06762538483822134,
              -0.09520569526206812,
              0.21004311558570302,
              10.27170643356923
            ],
            "initial_K": [
              3.6799310905599096,
              0.9424742426973025,
              -2.9555063690935968,
              -0.5787711669098261,
              4.229814343703857,
              3.31094509017364,
              -1.0691246134923231,
              -0.40522123730351156,
              4.565231941761041,
              5.163498108336576,
              0.45916066037656833,
              -1.1027276253352294,
              2.974774050724086,
              4.786438068782029,
              0.4434574928229155,
              -2.876085573388905
            ],
            "metrics": {
              "initial_rmse_K": 2.5616666626383773,
              "observation_residual_rms_K": 0.015645378668254484,
              "future_predictive_rmse_K": 0.020413407944485467
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.820775821882409,
              -1.528288278880115,
              -0.2991519220731819,
              -0.025797825219713827,
              0.028289738220247437,
              -0.0072158262243786336,
              0.0013152009045947382,
              0.003349793918567049
            ],
            "initial_K": [
              0.12462360553784846,
              0.2752165851560979,
              0.47510270602169485,
              0.7360218676510716,
              1.0497701706857727,
              1.389870563765384,
              1.719951438748128,
              1.999808445021647,
              2.190211915703153,
              2.262782242585626,
              2.210066376973735,
              2.0434372046379723,
              1.7792676047586147,
              1.4290126082066252,
              1.002666772847905,
              0.5174137609248637
            ],
            "metrics": {
              "initial_rmse_K": 0.039036673632845624,
              "observation_residual_rms_K": 0.0236867753487211,
              "future_predictive_rmse_K": 0.022829978062812922
            }
          },
          "learned": {
            "coefficients_K": [
              5.8913492591092576,
              -1.56557072047134,
              -0.31087287234197725,
              -0.024440536896677665,
              0.00883368455892915,
              -0.0007136857586322074,
              0.00020509720898948534,
              -0.0009043488640429179
            ],
            "initial_K": [
              0.11750108671044007,
              0.2671032543984906,
              0.47160652077437343,
              0.7387097174600974,
              1.058856664748821,
              1.405779589132909,
              1.7408150134640266,
              2.021747718566954,
              2.2128728597069944,
              2.291172813604023,
              2.2472056779242986,
              2.083230413871129,
              1.8104867494585866,
              1.4456803726867529,
              1.007833192664444,
              0.5178159757510103
            ],
            "metrics": {
              "initial_rmse_K": 0.03682088569173808,
              "observation_residual_rms_K": 0.016412754641605073,
              "future_predictive_rmse_K": 0.02028324128875338
            }
          }
        }
      }
    ],
    "validation": [
      {
        "split": "validation",
        "index": 0,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.263986406507136,
          1.8524065093679098,
          -0.6116896356318821,
          -0.06457764959665872,
          0.05917743902795743,
          0.06874986975980453,
          0.008459661221093713,
          -0.031221606066589566
        ],
        "initial_K": [
          0.4653503913771632,
          0.9083126134102708,
          1.30400623399777,
          1.64544374897815,
          1.942679866456352,
          2.175234913214886,
          2.269065347215931,
          2.159861895022754,
          1.871104278183286,
          1.4963984472873326,
          1.1127915704593216,
          0.748073605222016,
          0.42588883091252594,
          0.1899039425134551,
          0.06263069353938405,
          0.015259439493368915
        ],
        "observed_K": [
          0.39488558436956916,
          0.8023480999642315,
          1.1596428417552584,
          1.4555598965808187,
          1.6703221772844088,
          1.7796275683270812,
          1.8863392865314443,
          1.7624044103849799,
          1.6365816709330485,
          1.4342297595590492,
          1.1367419343826999,
          0.871946376942478,
          0.6165583868725288,
          0.3972238722151242,
          0.27605460668253234,
          0.09363137091337241
        ],
        "future_observed_K": [
          0.4069250869031998,
          0.750005347796773,
          1.0541394016172272,
          1.335157373647804,
          1.5336004899459945,
          1.691403590508334,
          1.7189252280898661,
          1.6936009351183723,
          1.5415399203821765,
          1.3801259010370182,
          1.104838282740898,
          0.9232082194693951,
          0.6470743881199649,
          0.4445337791910437,
          0.28597308883600586,
          0.14290902003359401
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.26697873986062,
              1.7934929405014397,
              -0.5815414287767074,
              0.0013190736514767669,
              0.2236111497108977,
              -0.5582859226810896,
              -0.3464015356307415,
              -6.108453370201795
            ],
            "initial_K": [
              -1.8612568078494307,
              0.3623526195545942,
              3.4615846379521287,
              2.677544495967071,
              0.11632373949694563,
              0.8021679501489763,
              3.647901521263682,
              3.577759167807932,
              0.7305974743821726,
              0.038392594109177836,
              2.165508240109823,
              2.4264887982675396,
              -0.42979459142154175,
              -1.7412526926223049,
              0.608189199411432,
              2.2090081669172985
            ],
            "metrics": {
              "initial_rmse_K": 1.5306782763170481,
              "observation_residual_rms_K": 0.017832384257254762,
              "future_predictive_rmse_K": 0.018446372138139884
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.203587512950021,
              1.7548434687886636,
              -0.5490937840109995,
              0.0010678170109179644,
              0.09354328856808966,
              -0.04231358418731765,
              -0.0021690194974691573,
              -0.0019920799025641717
            ],
            "initial_K": [
              0.4577090815521927,
              0.9007843703886278,
              1.3065626914668806,
              1.6495135603179745,
              1.912095580882733,
              2.0843289468491593,
              2.1518194312554657,
              2.0909527898848843,
              1.884377444673886,
              1.5465619568049869,
              1.1355753533736404,
              0.7362912962589907,
              0.4222890716697586,
              0.22172113938537996,
              0.11246666860054039,
              0.0496928100229522
            ],
            "metrics": {
              "initial_rmse_K": 0.04735344339850819,
              "observation_residual_rms_K": 0.024637417474657582,
              "future_predictive_rmse_K": 0.025579113884130967
            }
          },
          "learned": {
            "coefficients_K": [
              5.266677909821007,
              1.7976527018574386,
              -0.5706076051179991,
              0.0010116364783453661,
              0.029209598808658043,
              -0.00418505123213025,
              -0.00033824478345517706,
              0.0005378047846409857
            ],
            "initial_K": [
              0.4586577231540073,
              0.901571558336025,
              1.3121036002698978,
              1.6709828506517574,
              1.9548856506757217,
              2.137464566775742,
              2.1938534725749417,
              2.108348867688043,
              1.8837633005198857,
              1.5484423897575281,
              1.154876381841676,
              0.7668828591578261,
              0.4403082270136047,
              0.20748002017688238,
              0.07231608496845898,
              0.014916934090821843
            ],
            "metrics": {
              "initial_rmse_K": 0.03191644245246674,
              "observation_residual_rms_K": 0.018988387632031187,
              "future_predictive_rmse_K": 0.01888627676468992
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 1,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.234445094717701,
          0.2530670931050637,
          -0.2576254935663608,
          -0.1981963296499369,
          -0.027851901476258868,
          0.004391946355741649,
          0.03656991762671614,
          -0.020027732568917808
        ],
        "initial_K": [
          0.33091856178179035,
          0.6815187277828467,
          1.0556136137710963,
          1.438885012849081,
          1.7984846491570978,
          2.0809597491214378,
          2.232602731188516,
          2.2416332487664627,
          2.1497769693074034,
          2.005541058494459,
          1.8177948110053694,
          1.5742629976351175,
          1.2889406179778813,
          0.9960497848434523,
          0.700065200955933,
          0.37078609297522813
        ],
        "observed_K": [
          0.33964456952806804,
          0.654775194061632,
          1.0240902771541274,
          1.3370762279196429,
          1.6141275956032894,
          1.7970527876690554,
          1.9144105044157353,
          1.998332934874582,
          1.9467777245474902,
          1.8351517410821763,
          1.6700472162478592,
          1.4715541380928485,
          1.2071341343725204,
          0.9613727796642263,
          0.6204835386727807,
          0.31472757132872914
        ],
        "future_observed_K": [
          0.33906525505013546,
          0.649783128595374,
          0.9660691690925968,
          1.239102842454903,
          1.5127763158944454,
          1.712514071601422,
          1.830432750625123,
          1.8366648783536865,
          1.8745328829306729,
          1.781309581229492,
          1.618390037272467,
          1.380662601745898,
          1.1276223399860725,
          0.9306849738436189,
          0.597866860753772,
          0.3490199507209139
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.22414137088436,
              0.2582381145797506,
              -0.29150197228336033,
              -0.26941501348341834,
              -0.2472663161050511,
              -0.370656909496606,
              -3.8378333432364284,
              3.8648976081440836
            ],
            "initial_K": [
              0.18177906143272882,
              0.016937876759622272,
              0.6343582758280588,
              2.296087097650556,
              2.9162696613691805,
              1.487312925247069,
              0.5744813856971911,
              2.286131844106809,
              4.106839948553515,
              2.6847477034504967,
              -0.1356937213864695,
              0.10394450299961022,
              2.8668502311844035,
              3.1266320632443456,
              -0.2026424832049674,
              -2.170080384459366
            ],
            "metrics": {
              "initial_rmse_K": 1.37610870035876,
              "observation_residual_rms_K": 0.010536570892037822,
              "future_predictive_rmse_K": 0.024470895015419283
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.149230121484517,
              0.2526731265727054,
              -0.2752373486862933,
              -0.21809694558920842,
              -0.10343895816683431,
              -0.028092813569928946,
              -0.0240308846621011,
              0.001260414770162651
            ],
            "initial_K": [
              0.27433502503296936,
              0.6152361318614847,
              1.028305738927534,
              1.453318692588947,
              1.8124798602587162,
              2.0589508836624573,
              2.1854045623030314,
              2.2033752018460535,
              2.1282065675542783,
              1.9801078366309408,
              1.7832333142630932,
              1.5532460135519472,
              1.2899936386952777,
              0.9898294623027177,
              0.6626580606731893,
              0.32890417238489594
            ],
            "metrics": {
              "initial_rmse_K": 0.03433498948780265,
              "observation_residual_rms_K": 0.022027997462030723,
              "future_predictive_rmse_K": 0.028519616524085394
            }
          },
          "learned": {
            "coefficients_K": [
              6.2237858713109535,
              0.25883706253511557,
              -0.2860213117432912,
              -0.20662231797944086,
              -0.032299596427375156,
              -0.002778537112913137,
              -0.0037474634913392726,
              -0.00034027605677519043
            ],
            "initial_K": [
              0.3138914256287683,
              0.6604658451778631,
              1.046178296682629,
              1.4431973566187102,
              1.8021533652798536,
              2.0737601254628633,
              2.2261631489544214,
              2.252594253218068,
              2.1696106791952605,
              2.007519101510478,
              1.7965441713634747,
              1.555678312769951,
              1.290521394197319,
              0.999770019030987,
              0.6835449916390727,
              0.34717854139515253
            ],
            "metrics": {
              "initial_rmse_K": 0.013938517558848802,
              "observation_residual_rms_K": 0.014507668023291141,
              "future_predictive_rmse_K": 0.02438006426255624
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 2,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.089911800845842,
          -1.1140478143661863,
          -0.13096295410722383,
          -0.02222443176691706,
          0.008077127096656238,
          -0.024201729843159794,
          0.059884283051302334,
          0.006207402130843648
        ],
        "initial_K": [
          0.2336574248758742,
          0.4565837295995542,
          0.6933967669436852,
          0.9768677216130094,
          1.295688078823706,
          1.5971968353326205,
          1.8429756449126806,
          2.0359415672706116,
          2.1824698395427897,
          2.251573224920518,
          2.196157850500782,
          2.0077219834941076,
          1.7262093447493085,
          1.3907193230827675,
          0.9990897149478657,
          0.5306220214218219
        ],
        "observed_K": [
          0.25835000988111423,
          0.5105156334010582,
          0.7472766114924663,
          1.0188096871945767,
          1.2426077261085469,
          1.485112896897141,
          1.7107204585194469,
          1.8837973713397274,
          1.9306493135148481,
          1.9768381057762945,
          1.9100881769755476,
          1.7277282535154306,
          1.4933016581579335,
          1.251875638803614,
          0.8361414854592764,
          0.44215045933306346
        ],
        "future_observed_K": [
          0.24736327057504673,
          0.47425442077789765,
          0.6969944041570275,
          0.97356574252541,
          1.2653066906409203,
          1.4535686325271644,
          1.6103845588208152,
          1.7586901978894132,
          1.8279585256208086,
          1.8387205246596028,
          1.7664753963485462,
          1.6341787517775288,
          1.4321188986329896,
          1.0988221767200967,
          0.8020960547006666,
          0.40859953244876485
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.100610750475888,
              -1.1017318613407205,
              -0.11206683526212445,
              -0.031029763933395883,
              0.40900098009856495,
              0.10025018138053213,
              0.07493026202139362,
              -0.030338118298910227
            ],
            "initial_K": [
              0.37766865642036007,
              0.6302941420975238,
              0.7535660834383645,
              0.8746221893374697,
              1.13065135839198,
              1.526883208392428,
              1.9267066702590918,
              2.185126078272156,
              2.2660870457716396,
              2.2204340176695565,
              2.095649486124811,
              1.9113366332637263,
              1.6897190008494682,
              1.4397203620179648,
              1.1096001678115277,
              0.6241906620615724
            ],
            "metrics": {
              "initial_rmse_K": 0.10562046382681292,
              "observation_residual_rms_K": 0.01594341624662902,
              "future_predictive_rmse_K": 0.023355651183597136
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.027186265685414,
              -1.0779897247265406,
              -0.10581396198317057,
              -0.02511922646302093,
              0.1710974464173912,
              0.00759815771328725,
              0.0004691815207428085,
              -9.893822884806089e-06
            ],
            "initial_K": [
              0.2707046515193661,
              0.5152419551335872,
              0.7349141464998905,
              0.9604761755918669,
              1.2253746789894355,
              1.532032616197206,
              1.839345738906457,
              2.0823482616975872,
              2.209256803713284,
              2.2080189997045245,
              2.1037090815956248,
              1.9310860705375172,
              1.7049936436117878,
              1.4115851703456905,
              1.0264363017091442,
              0.544790793671684
            ],
            "metrics": {
              "initial_rmse_K": 0.048108728840065305,
              "observation_residual_rms_K": 0.023941319894079622,
              "future_predictive_rmse_K": 0.0230405510245159
            }
          },
          "learned": {
            "coefficients_K": [
              6.100262306507463,
              -1.1042871775719607,
              -0.1099598159611555,
              -0.023797640923480728,
              0.05342647071254153,
              0.0007515004911695371,
              7.316587152397351e-05,
              2.6710501315685994e-06
            ],
            "initial_K": [
              0.23717155320318659,
              0.47663333067645197,
              0.7249194362796842,
              0.9909552992998839,
              1.2776985713962743,
              1.5733065793117675,
              1.849450460895036,
              2.0695924946125204,
              2.2026216986906033,
              2.233115673477063,
              2.161943320851116,
              1.9980665605352785,
              1.748754770437396,
              1.4161608987450252,
              1.0028248671103874,
              0.5213594793986406
            ],
            "metrics": {
              "initial_rmse_K": 0.020828323404831525,
              "observation_residual_rms_K": 0.017661552053271502,
              "future_predictive_rmse_K": 0.022554158483226755
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 3,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          4.698521922597131,
          0.433845370979409,
          -0.32477872972736027,
          0.14726382546548045,
          0.0011779677945968421,
          0.06826842869445678,
          0.07463965579393765,
          -0.006144919225491256
        ],
        "initial_K": [
          0.36907670278362786,
          0.6651617979146245,
          0.8916034685330692,
          1.1093803493007748,
          1.3490031460085385,
          1.5658336767790528,
          1.692549115296997,
          1.7146255875396867,
          1.6689386732026408,
          1.5763101557797248,
          1.410798630522745,
          1.1512540683992962,
          0.8379928964873918,
          0.5491224610154612,
          0.3274703708521063,
          0.15578274103426265
        ],
        "observed_K": [
          0.3001851183117622,
          0.5650553923530655,
          0.8193901923756539,
          1.07756574545851,
          1.247180362718373,
          1.375557067154518,
          1.4706381739387933,
          1.5158120025000938,
          1.446927308958262,
          1.3913280313719538,
          1.211019231336487,
          1.0727769472227489,
          0.8272434699338754,
          0.634961012989762,
          0.42485092297807214,
          0.17082872062856805
        ],
        "future_observed_K": [
          0.25828725731527785,
          0.5588827281516358,
          0.7623377563163176,
          0.9973615942325591,
          1.180436546806686,
          1.331694361386623,
          1.427938260396458,
          1.4493938097817622,
          1.3956576123540956,
          1.3062811949693223,
          1.185576948627563,
          1.0502293994178382,
          0.8498555268809902,
          0.6525059462955766,
          0.4204736357036667,
          0.20488162792909628
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              4.6801940598773495,
              0.46270361393493,
              -0.260683513449025,
              0.12308728840857058,
              -0.09703552207706484,
              0.12221251226579906,
              -1.7014284896342775,
              3.758353616336994
            ],
            "initial_K": [
              1.0669373351028306,
              0.5799107484861852,
              0.06534390314649907,
              1.2098406593653404,
              2.4308003354198857,
              1.674568341151129,
              0.4460863423293209,
              1.2878773101068262,
              2.952849065261251,
              2.328551479591532,
              0.11494414230921635,
              -0.08148192368301621,
              1.8902606228996552,
              2.209018805136749,
              -0.25865352420993926,
              -1.746869100293956
            ],
            "metrics": {
              "initial_rmse_K": 1.041161747329462,
              "observation_residual_rms_K": 0.015568608072460757,
              "future_predictive_rmse_K": 0.02110427576056774
            }
          },
          "tikhonov": {
            "coefficients_K": [
              4.623865136164403,
              0.4527324287496806,
              -0.24613843441920677,
              0.09964166916933692,
              -0.04059288570693191,
              0.009262725812014533,
              -0.010653623578332485,
              0.0012256687989724258
            ],
            "initial_K": [
              0.314735272970609,
              0.6232891337041863,
              0.9135663260078734,
              1.1693869727509631,
              1.3779303176307443,
              1.533376706045772,
              1.6324090935544244,
              1.6684385377521673,
              1.6332846809772432,
              1.5244456201318706,
              1.3485412391808629,
              1.1187259869785142,
              0.8539953323273506,
              0.5829826908258886,
              0.34077093179919327,
              0.14996898978955042
            ],
            "metrics": {
              "initial_rmse_K": 0.04103220440773256,
              "observation_residual_rms_K": 0.02068595004143114,
              "future_predictive_rmse_K": 0.030115085427514045
            }
          },
          "learned": {
            "coefficients_K": [
              4.679926744774333,
              0.4637767916258271,
              -0.2557822847046176,
              0.09439927090903606,
              -0.01267543534266624,
              0.0009161356291834728,
              -0.001661364780017281,
              -0.0003308956350716996
            ],
            "initial_K": [
              0.3241980399942413,
              0.6364870698418886,
              0.924772260633546,
              1.1782879348438027,
              1.3891533679542403,
              1.5512549824469104,
              1.6571854254575569,
              1.6970756348136065,
              1.6615253376621917,
              1.5468634414432887,
              1.359544958307371,
              1.1178671673756406,
              0.8501201836546746,
              0.5881972814884668,
              0.35721103954894495,
              0.16530632585202443
            ],
            "metrics": {
              "initial_rmse_K": 0.034803679677022824,
              "observation_residual_rms_K": 0.01621942117500031,
              "future_predictive_rmse_K": 0.021115655992072192
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 4,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.342601484858244,
          1.6308041892385456,
          -0.14375167964818492,
          0.0698871642507116,
          -0.03216809230449138,
          0.046519672345789104,
          0.006720609026782888,
          -0.016065152336522896
        ],
        "initial_K": [
          0.5942120713235091,
          1.1447718528045936,
          1.6128323666112547,
          1.9780419527592827,
          2.239387136661133,
          2.39239839188341,
          2.41776214282847,
          2.3081569471534795,
          2.095686799414081,
          1.8311760320425063,
          1.5400242175851697,
          1.2199738890655145,
          0.8819953269324181,
          0.5683983584388401,
          0.3199142491147394,
          0.1401913938323599
        ],
        "observed_K": [
          0.5172304595385324,
          0.9294061109610621,
          1.3600190763900686,
          1.6911988954220003,
          1.9269316434815293,
          2.0534949175152186,
          2.109799360797916,
          2.0326598022567115,
          1.9090312884261504,
          1.701484514176241,
          1.4748077367675276,
          1.1790416786152793,
          0.9296505021637408,
          0.6821173524818617,
          0.4255030337724155,
          0.21337116975548062
        ],
        "future_observed_K": [
          0.4678849767422794,
          0.8793134194504711,
          1.2528233114950789,
          1.5784428442103082,
          1.7415856483442285,
          1.9351909676122883,
          1.970517691996715,
          1.9367366275454827,
          1.8636421459228598,
          1.6742095038812361,
          1.4645996193181523,
          1.1729623971471923,
          0.9242041576938378,
          0.673102542132973,
          0.42674542518637426,
          0.1976507760070132
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.319234539012929,
              1.6457873465024158,
              -0.13573895501002106,
              0.044749317712102304,
              0.013254868690639712,
              -0.07262022260523888,
              0.4036823002866414,
              6.270915967335813
            ],
            "initial_K": [
              2.8442633280325786,
              1.589505924280199,
              -0.5436186556077838,
              1.1086013677504307,
              4.2108466955154755,
              3.6426379372216404,
              0.7091257423889887,
              0.7326020897394434,
              3.4605759425030582,
              3.6247882558320113,
              0.5245851037754448,
              -0.7432814317224115,
              1.4848546977438715,
              2.549683974623398,
              0.04763500657678188,
              -1.823127447403642
            ],
            "metrics": {
              "initial_rmse_K": 1.575226856036204,
              "observation_residual_rms_K": 0.011352529502729152,
              "future_predictive_rmse_K": 0.024328592351140793
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.243178786683377,
              1.6103209055382792,
              -0.12816527379817963,
              0.03622548492759203,
              0.005544911371654293,
              -0.005504028989575321,
              0.002527687351358322,
              0.0020450619677539997
            ],
            "initial_K": [
              0.5795953117000456,
              1.1195948836941492,
              1.5876463760008015,
              1.959613378928975,
              2.2178626381938624,
              2.3530654170205243,
              2.3671298931169384,
              2.271087124078126,
              2.080014178742414,
              1.8127199353386796,
              1.4960461528926765,
              1.16464428706022,
              0.8519636095027502,
              0.5796098707380775,
              0.35339367218073287,
              0.16578343146928148
            ],
            "metrics": {
              "initial_rmse_K": 0.03177536302597629,
              "observation_residual_rms_K": 0.02170362497045704,
              "future_predictive_rmse_K": 0.033085684786311215
            }
          },
          "learned": {
            "coefficients_K": [
              6.318873608074988,
              1.6496045249532316,
              -0.1331868654696097,
              0.03431957125968446,
              0.0017314404814589607,
              -0.0005443793936843296,
              0.0003941767521224152,
              -0.0005521084318604436
            ],
            "initial_K": [
              0.5867744339421834,
              1.1354091157145167,
              1.611703773681134,
              1.9890559296841621,
              2.2504878690809518,
              2.388302617189069,
              2.4028407527611537,
              2.3022169224252025,
              2.1027285668966247,
              1.8282643833625858,
              1.5082294432766985,
              1.174548602781617,
              0.8574418262468897,
              0.579499005935896,
              0.34996708218348616,
              0.16283694843122495
            ],
            "metrics": {
              "initial_rmse_K": 0.019264629660314163,
              "observation_residual_rms_K": 0.011774704314912383,
              "future_predictive_rmse_K": 0.024580751903322845
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 5,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.4572605638760265,
          -2.380164017605933,
          -0.06182901464545654,
          -0.08087852659774869,
          0.041093459924072095,
          -0.057323457229154516,
          -0.019182875503041055,
          0.0411299540563449
        ],
        "initial_K": [
          0.08357165849392223,
          0.200476228310979,
          0.39146537022182193,
          0.6694728014664173,
          0.999815419428294,
          1.3459901137089123,
          1.7089961745908704,
          2.083794966137477,
          2.4034842983086975,
          2.5805497486862237,
          2.5949637785926805,
          2.489307481856393,
          2.2778515170376066,
          1.9172571383629993,
          1.3819142995666298,
          0.7178840637060506
        ],
        "observed_K": [
          0.20442320736932784,
          0.3526214074501408,
          0.5493889658946453,
          0.8099391941427478,
          1.060342610048781,
          1.351407279253158,
          1.6473126602916845,
          1.8989313749648808,
          2.1075833800216057,
          2.257344123420267,
          2.2490417967099505,
          2.1262304979762043,
          1.8953310811294002,
          1.5333261823956055,
          1.0932735370599151,
          0.5773901027322198
        ],
        "future_observed_K": [
          0.1941866814429204,
          0.35575093131328533,
          0.6003500791906463,
          0.8474343368993249,
          1.0759212142015642,
          1.356387809219959,
          1.6200586818828666,
          1.811187259559141,
          1.9761131750367007,
          2.1052163866619455,
          2.0561574109035914,
          1.9521494393391343,
          1.7379573569423266,
          1.4213609218953793,
          1.005143494528594,
          0.5106775185272089
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.472093272082641,
              -2.3905346026370893,
              -0.04670082310016512,
              0.12069072071216598,
              0.19494145741905244,
              -0.28282268496491686,
              3.1213781265092533,
              6.018148947964287
            ],
            "initial_K": [
              3.1828420969012257,
              1.206216826772202,
              -2.212972609211308,
              -0.9720381249329367,
              2.998605760566898,
              3.3686101402185535,
              0.3324276078833117,
              -0.17600980506815223,
              3.0386596821289267,
              4.757567839176062,
              2.6536609362807746,
              0.793168617516504,
              1.950393931449982,
              3.124095601670031,
              1.6247984175265464,
              -0.21766766494319034
            ],
            "metrics": {
              "initial_rmse_K": 1.6901106685444922,
              "observation_residual_rms_K": 0.009458377728359935,
              "future_predictive_rmse_K": 0.015294412051315244
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.394197773835765,
              -2.339018983357761,
              -0.04409510725046568,
              0.09770159876373653,
              0.08154989153631492,
              -0.021435685558531068,
              0.019544745963797874,
              0.0019626299561129852
            ],
            "initial_K": [
              0.15065477635543922,
              0.2963003705691064,
              0.4543721530721855,
              0.6588797947984955,
              0.9343848692623972,
              1.279110372935896,
              1.6670180516622304,
              2.054224573752516,
              2.3819200559721563,
              2.587419515131695,
              2.6286393372879124,
              2.501857035695228,
              2.2306163839898234,
              1.8358174607948288,
              1.32203168822585,
              0.696956079335088
            ],
            "metrics": {
              "initial_rmse_K": 0.05234127490117953,
              "observation_residual_rms_K": 0.02306723641565532,
              "future_predictive_rmse_K": 0.022532206895133626
            }
          },
          "learned": {
            "coefficients_K": [
              6.471723610428097,
              -2.396079120396634,
              -0.04582277978420078,
              0.09256127247597457,
              0.02546456994540515,
              -0.00212010974681684,
              0.0030478787184370446,
              -0.0005298541386410526
            ],
            "initial_K": [
              0.13125653652260022,
              0.2740833587871463,
              0.4453215560915643,
              0.6656380481239553,
              0.9503814877648029,
              1.2983690729400954,
              1.6859688582369565,
              2.0696717090328858,
              2.395158534105744,
              2.609261537971751,
              2.671856669325673,
              2.564103303093396,
              2.289125424776378,
              1.865410366726574,
              1.319436443403946,
              0.6839147923633797
            ],
            "metrics": {
              "initial_rmse_K": 0.04764546902440797,
              "observation_residual_rms_K": 0.01245309413904327,
              "future_predictive_rmse_K": 0.014978980833417798
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 6,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.649310709333627,
          -0.5098293442861567,
          -0.11762972440020755,
          -0.07026530071780428,
          -0.041351914905931014,
          0.0038664303640093232,
          -0.06673220172841714,
          0.006128589462447406
        ],
        "initial_K": [
          0.2253506051301828,
          0.49780603673033685,
          0.8121526628491812,
          1.1205896639798079,
          1.3871396495522013,
          1.613950689408739,
          1.8091938876081548,
          1.9496632218453984,
          1.997951414831875,
          1.9508739655049625,
          1.8435163832026107,
          1.696177171964749,
          1.4817646217192617,
          1.1682238724153609,
          0.7785312243592835,
          0.3776039594956392
        ],
        "observed_K": [
          0.27624976966384224,
          0.5291166895607851,
          0.7999084199405744,
          1.0709760109552098,
          1.306086132126703,
          1.4741316196521175,
          1.6438664885248047,
          1.7454116265395587,
          1.801772387023752,
          1.7416836863374368,
          1.64008920299002,
          1.5298439175645886,
          1.3349020387889692,
          0.9726237505380066,
          0.729500370892003,
          0.31466205720799706
        ],
        "future_observed_K": [
          0.2484871257255057,
          0.5381563392936137,
          0.7853931832270288,
          1.0251129318502243,
          1.2467526439447185,
          1.4331140484089049,
          1.5450391864915725,
          1.6589790736352634,
          1.680783794036103,
          1.6564595915642544,
          1.5801213822847058,
          1.4433993575309696,
          1.2326458154972226,
          0.9507120778877824,
          0.6423207471866986,
          0.3326151337924929
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.662146047034557,
              -0.49670390118846913,
              -0.09816897229448643,
              -0.043916620683693966,
              -0.27728754540791245,
              0.6589516453371198,
              -4.430998025843483,
              2.8027645037106326
            ],
            "initial_K": [
              -0.11069524197875347,
              0.007102964522477023,
              0.8476940810174058,
              1.9549932632704254,
              1.9054569540227593,
              0.761681148076645,
              0.7058328384603101,
              2.5393752306527935,
              3.6484370200129628,
              1.9424625201917571,
              -0.17083762859424362,
              0.8007483941687544,
              3.4291447609246544,
              3.1090950988094153,
              -0.4473716176358857,
              -2.2864368391842724
            ],
            "metrics": {
              "initial_rmse_K": 1.3075310913602762,
              "observation_residual_rms_K": 0.0212707258162398,
              "future_predictive_rmse_K": 0.011131809204237399
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.593998746163163,
              -0.4860000155220768,
              -0.09269154320275926,
              -0.035551399708105016,
              -0.11599774389588728,
              0.04994323658823674,
              -0.027745030326733155,
              0.0009140334715001268
            ],
            "initial_K": [
              0.24213812899537163,
              0.5106691278317399,
              0.8080591514177454,
              1.1119138766958887,
              1.3923860006290232,
              1.6257981745621595,
              1.7961181215253055,
              1.895679933751962,
              1.930517248050326,
              1.916181508376652,
              1.8556881742612719,
              1.7227335786318019,
              1.481545634964011,
              1.13286113773206,
              0.732102832929546,
              0.3477104573886226
            ],
            "metrics": {
              "initial_rmse_K": 0.03030726085587326,
              "observation_residual_rms_K": 0.028339323726474245,
              "future_predictive_rmse_K": 0.017790991261535865
            }
          },
          "learned": {
            "coefficients_K": [
              5.6618226465228485,
              -0.4978559378911952,
              -0.09632325300655471,
              -0.03368095135517453,
              -0.03622117218427747,
              0.00493966672487223,
              -0.0043266608648623375,
              -0.0002467629805722328
            ],
            "initial_K": [
              0.26006799679321585,
              0.5340126395783577,
              0.8236297702754238,
              1.1160564400441946,
              1.390523931913107,
              1.6267673515401961,
              1.809494695090034,
              1.9292898616601888,
              1.9818007959576156,
              1.9650932422348528,
              1.875953357203299,
              1.7092839595005056,
              1.4635695027419569,
              1.1482496034321068,
              0.7844307948941509,
              0.3961424658086493
            ],
            "metrics": {
              "initial_rmse_K": 0.019453252268047973,
              "observation_residual_rms_K": 0.024075241595047786,
              "future_predictive_rmse_K": 0.012163880684867885
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 7,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.255116571568015,
          0.9081999786079278,
          -0.03335600057957128,
          0.019372725063329224,
          0.030249105562457523,
          0.11946232703954099,
          -0.024261445765127992,
          -0.06442523255228626
        ],
        "initial_K": [
          0.5201682038830617,
          1.0155142494171319,
          1.4252954662485169,
          1.7182363020311833,
          1.9448770839099168,
          2.1527560711930818,
          2.2866682968888203,
          2.254564930471711,
          2.0719704675523736,
          1.8537173102392948,
          1.6620195235751833,
          1.4474082221859639,
          1.1582888697547777,
          0.8295356233917713,
          0.5252784484425626,
          0.25680202634956584
        ],
        "observed_K": [
          0.4371916803383539,
          0.829233376142283,
          1.2055002988288208,
          1.5335581090198227,
          1.7210610296481323,
          1.895679458394819,
          1.982880890746098,
          2.0206130564296307,
          1.9389123652681886,
          1.7852418717286203,
          1.5912064627534612,
          1.3262338626409929,
          1.1347621886681736,
          0.8164240330300652,
          0.5326876289710817,
          0.2954153953692952
        ],
        "future_observed_K": [
          0.37224834221488307,
          0.8036449194764336,
          1.151608885056601,
          1.412125707432145,
          1.6636463234864955,
          1.798929074563981,
          1.895687664894424,
          1.9217396204655992,
          1.8191132441561424,
          1.677860951856207,
          1.5298922899792693,
          1.2932690288930537,
          1.0469914391957527,
          0.816488372771915,
          0.5493276671213869,
          0.29179097028286716
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.287655868523376,
              0.8847772017824116,
              -0.1162061927510457,
              0.11219060591697903,
              0.29805971478809706,
              -0.09225488884921393,
              -4.137829153875903,
              -4.114283926572011
            ],
            "initial_K": [
              -2.2061406278172475,
              0.05278684567468678,
              3.754223579516169,
              3.487237870482895,
              0.37376513478895856,
              -0.09336586365906241,
              2.827216826585369,
              4.385813468390215,
              2.433982116332858,
              0.3873034582994328,
              1.004950896388912,
              2.314349531800214,
              1.7883030747719393,
              0.42322324124908217,
              0.13636572847692133,
              0.3897412534375533
            ],
            "metrics": {
              "initial_rmse_K": 1.4460382986440479,
              "observation_residual_rms_K": 0.015688951420506834,
              "future_predictive_rmse_K": 0.0207696767605255
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.211980184306001,
              0.8657104016516913,
              -0.1097223601720101,
              0.09082058255748117,
              0.1246873688856431,
              -0.006992178823471292,
              -0.025909331191650318,
              -0.0013417442725434361
            ],
            "initial_K": [
              0.522930168945272,
              1.0015265978531123,
              1.3971760033905867,
              1.694712289772426,
              1.9129211907965071,
              2.0824606580699148,
              2.2057667678638646,
              2.245532197007803,
              2.16081964099146,
              1.9529456588366492,
              1.6706815480519965,
              1.37210993213992,
              1.0869791863213119,
              0.814078141607866,
              0.543397584107912,
              0.27163607980207116
            ],
            "metrics": {
              "initial_rmse_K": 0.05213821710506731,
              "observation_residual_rms_K": 0.0252159755283639,
              "future_predictive_rmse_K": 0.027604484670960404
            }
          },
          "learned": {
            "coefficients_K": [
              6.287296741240463,
              0.8868293213807269,
              -0.11402134751609397,
              0.08604228379986292,
              0.03893457325915738,
              -0.0006915657740289997,
              -0.004040395270127277,
              0.0003622327039240102
            ],
            "initial_K": [
              0.5146724610653868,
              0.9902774458252563,
              1.3978458677127816,
              1.7243306828861609,
              1.9705670593058209,
              2.141586410770987,
              2.2358783213263687,
              2.243025298972376,
              2.152978728509587,
              1.9691253745048334,
              1.7129165942431424,
              1.4159612702611137,
              1.1073536812790274,
              0.8063136687381669,
              0.521988230580719,
              0.2553202019823472
            ],
            "metrics": {
              "initial_rmse_K": 0.04441473461433934,
              "observation_residual_rms_K": 0.018694784572333804,
              "future_predictive_rmse_K": 0.020833535146808455
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 8,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          7.2549229118910326,
          -0.9088538703483726,
          0.001019452719431871,
          0.43009006712375925,
          -0.14468736685907463,
          -0.06654647361716451,
          -0.03950650658549493,
          0.018575194357036532
        ],
        "initial_K": [
          0.3774765460688802,
          0.7641990461882529,
          1.1382692310838163,
          1.4513254058444722,
          1.6764399283592408,
          1.8518681804918957,
          2.0552012436319447,
          2.316976090580606,
          2.570735100174871,
          2.7031480550587976,
          2.6429661014597867,
          2.3892650861798215,
          1.9786163598743176,
          1.4647967439145921,
          0.924534832190037,
          0.43210919458539476
        ],
        "observed_K": [
          0.3403485875737928,
          0.7393712108881849,
          1.0222557835020802,
          1.3346997120664577,
          1.6167776022808844,
          1.813835066145891,
          2.0287090153727725,
          2.1995954657250896,
          2.2961858953678242,
          2.3031340565875564,
          2.212925274816252,
          2.0278464799928853,
          1.7432170261961455,
          1.335209370428208,
          0.9256677219895059,
          0.4692376762311955
        ],
        "future_observed_K": [
          0.3376611164558427,
          0.6478474960446009,
          0.9943565717787541,
          1.230030969843706,
          1.5304601934528337,
          1.783624188383392,
          1.935590462895622,
          2.081543742336509,
          2.165739542593914,
          2.175123849399355,
          2.0357854933937887,
          1.8840675631186115,
          1.6045522299444368,
          1.2748186758192914,
          0.8903418075991458,
          0.4906402547994476
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              7.276630374029174,
              -0.8831963325536378,
              0.045430429476939926,
              0.4719561775555557,
              -0.17235381662408863,
              -0.05931834383159261,
              -1.3753397610227511,
              -1.517350804434459
            ],
            "initial_K": [
              -0.5709034080632732,
              0.45559633716598213,
              1.988196398266061,
              2.0829710147889013,
              1.1407881129533197,
              1.1226674069021896,
              2.299497423139781,
              3.0195350528990823,
              2.567994091170461,
              2.118130138049971,
              2.4802199995813003,
              2.798320581699172,
              2.211610605055043,
              1.2635456902718705,
              0.7651253287284143,
              0.50272585828038
            ],
            "metrics": {
              "initial_rmse_K": 0.5092391054887855,
              "observation_residual_rms_K": 0.013047290358555562,
              "future_predictive_rmse_K": 0.025776996033379674
            }
          },
          "tikhonov": {
            "coefficients_K": [
              7.189051792461396,
              -0.8641635998893455,
              0.04289559642072562,
              0.3820581468194978,
              -0.07210080009482193,
              -0.004495853528809328,
              -0.008611794263183916,
              -0.0004948362309514706
            ],
            "initial_K": [
              0.41792403056182315,
              0.8081246893015241,
              1.145487110369035,
              1.4191021530996237,
              1.6439775974711694,
              1.8551059599456456,
              2.0814257234782625,
              2.3188730120413448,
              2.5238744352086124,
              2.6309138638602607,
              2.581557056863426,
              2.3503573088509553,
              1.958136781790091,
              1.4661047389798585,
              0.9490509714689503,
              0.4586022861940747
            ],
            "metrics": {
              "initial_rmse_K": 0.036085090300649506,
              "observation_residual_rms_K": 0.0246586139974705,
              "future_predictive_rmse_K": 0.022979295073049504
            }
          },
          "learned": {
            "coefficients_K": [
              7.2762147602377025,
              -0.8852447855421895,
              0.04457627140657659,
              0.36195710896136574,
              -0.022514019731303653,
              -0.0004446651757725599,
              -0.0013429544958493856,
              0.00013359167585439756
            ],
            "initial_K": [
              0.4338933662530035,
              0.8265239357007585,
              1.15382667518466,
              1.4186368021400355,
              1.6474980378110513,
              1.874263218729336,
              2.1173954856163473,
              2.363071358905119,
              2.5645762816690763,
              2.6597298661049025,
              2.597761228662768,
              2.3620145437857225,
              1.97743380565529,
              1.4993190897087956,
              0.9886263156626587,
              0.4861684673601964
            ],
            "metrics": {
              "initial_rmse_K": 0.042310129829245195,
              "observation_residual_rms_K": 0.014855324312145722,
              "future_predictive_rmse_K": 0.024722813543621776
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 9,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.453095375724114,
          -0.8995588273417825,
          0.05900255893021782,
          0.010456001368083695,
          0.11339564734867977,
          -0.02535310324817475,
          -0.03074298639760202,
          0.005477053862872443
        ],
        "initial_K": [
          0.26027700006067667,
          0.5147501414914919,
          0.7523961863520984,
          0.966306403245254,
          1.1681376815274427,
          1.3820616593285286,
          1.6129015537736118,
          1.822349834834199,
          1.9500183210709667,
          1.964495785159241,
          1.8857156798734966,
          1.7503685115031233,
          1.56407738383446,
          1.299488555605182,
          0.9365291467126552,
          0.49019173832492613
        ],
        "observed_K": [
          0.23382682566701635,
          0.4768218058751577,
          0.7156739286090898,
          0.9403918010324352,
          1.123205216391869,
          1.3382754155804624,
          1.5153111159313295,
          1.6224645449319774,
          1.7204186742140157,
          1.7299947055711482,
          1.675931615757148,
          1.5382641375937727,
          1.3513551822475656,
          1.0885354591154697,
          0.7694752360400154,
          0.39087648272528186
        ],
        "future_observed_K": [
          0.2480435916524315,
          0.45612447308012044,
          0.7178489683600695,
          0.8929077736785767,
          1.0862485027337763,
          1.3123694413805513,
          1.4611868964029726,
          1.5467122643390459,
          1.614506136415159,
          1.6702642325007548,
          1.590616615321589,
          1.4676913870575152,
          1.2960211244794693,
          0.9738629616264052,
          0.662043286396193,
          0.37023011494766134
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.425336492452548,
              -0.9145022065098857,
              0.0632225579285001,
              0.0009247382203203859,
              0.20435577877104982,
              -0.2158982406162748,
              -0.6470842143501765,
              -2.85915774595957
            ],
            "initial_K": [
              -0.960075139779784,
              0.19191585573260117,
              1.8523821869374555,
              1.545962684479957,
              0.25241961713461514,
              0.5999450980648404,
              2.2513854779185856,
              2.6358896843548454,
              1.5079963479876972,
              1.1644763472385706,
              2.187213887258467,
              2.5121136763602543,
              1.3195350294291681,
              0.49974431716281975,
              1.0925130517919375,
              1.351697368183103
            ],
            "metrics": {
              "initial_rmse_K": 0.7344935650697116,
              "observation_residual_rms_K": 0.007487378932072072,
              "future_predictive_rmse_K": 0.024159124682120676
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.360039335648662,
              -0.8947948375185736,
              0.059694996521295444,
              0.0007485944406505376,
              0.08548818611617459,
              -0.01636335076539078,
              -0.004051766903614982,
              -0.0009324243534003727
            ],
            "initial_K": [
              0.2546221625396058,
              0.49888750041339347,
              0.7265580393573532,
              0.9406804829895881,
              1.1532451758706235,
              1.3734739722481106,
              1.5922557754537316,
              1.7790724281044326,
              1.8975262040684644,
              1.9265191078191992,
              1.8682019054022958,
              1.736917600932966,
              1.5407641341642855,
              1.2729432796941496,
              0.9209822543084103,
              0.48670033914789274
            ],
            "metrics": {
              "initial_rmse_K": 0.025482812913632007,
              "observation_residual_rms_K": 0.017252441324235885,
              "future_predictive_rmse_K": 0.02983119767477962
            }
          },
          "learned": {
            "coefficients_K": [
              5.425026617612995,
              -0.9166232691874739,
              0.06203388199685273,
              0.0007092090085712348,
              0.02669433219162209,
              -0.0016184273348085608,
              -0.0006318472565706343,
              0.0002517279944087704
            ],
            "initial_K": [
              0.2463936078499009,
              0.48793219527109777,
              0.7229832430092047,
              0.9534349513410387,
              1.1813810070978095,
              1.404112958773338,
              1.6106554918492657,
              1.78252603594291,
              1.8989439813436553,
              1.9433539901005938,
              1.906682991272131,
              1.7855289861193884,
              1.5784561178762933,
              1.2854343072990448,
              0.9119207369785097,
              0.4740359102147888
            ],
            "metrics": {
              "initial_rmse_K": 0.02524588686761347,
              "observation_residual_rms_K": 0.008721371290741093,
              "future_predictive_rmse_K": 0.023730311946228096
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 10,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.979149661655172,
          2.461143328969765,
          0.06869748516215929,
          -0.29653621186140994,
          -0.09090612061233623,
          0.04186680774095412,
          0.0017227337126292592,
          -0.041829485054451956
        ],
        "initial_K": [
          0.5999232125417626,
          1.2085159218286774,
          1.7770838662451283,
          2.229571045825892,
          2.5192329152307202,
          2.622215136779427,
          2.5123441147048253,
          2.20011884647614,
          1.7819534956138303,
          1.38995982634553,
          1.0839726010448036,
          0.8333008043000054,
          0.6030797519012449,
          0.40576483706387045,
          0.25600277501025503,
          0.1299354941083501
        ],
        "observed_K": [
          0.5133628967093228,
          1.036206874962523,
          1.4797483048728075,
          1.8197727905630898,
          2.0672691228767475,
          2.1318589291180525,
          2.089699815611234,
          1.9339622289989011,
          1.7070515671035624,
          1.4943138811478975,
          1.2420519335346207,
          0.9286487494160206,
          0.683630414261915,
          0.4966011913464689,
          0.26989453389884943,
          0.1830791888973202
        ],
        "future_observed_K": [
          0.5130434782048898,
          0.981958802873257,
          1.347587774404802,
          1.6624176908590844,
          1.8768878249551315,
          1.9665025648778225,
          1.9497952450352423,
          1.8603638071564814,
          1.6767889576791275,
          1.4424834446693973,
          1.2094397479355328,
          0.9498922465562917,
          0.7351759099377065,
          0.5608656241562939,
          0.35376703296866774,
          0.15985735379716473
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.985449487095898,
              2.447062130809422,
              0.03937358806859512,
              -0.15189614234869164,
              -0.5265254050161372,
              -1.192765838092452,
              3.6355686880493594,
              -5.065957655804958
            ],
            "initial_K": [
              -0.38870514703028713,
              1.104281496191561,
              2.64509526565758,
              2.22005763179018,
              1.6070585198532024,
              2.856011634786832,
              3.850565439422006,
              2.002758568643219,
              -0.2538342245309929,
              0.9150393635317655,
              3.54122697602547,
              2.4972651830710157,
              -1.474694376577605,
              -2.2673394174980106,
              1.3686555149231028,
              3.267931663637529
            ],
            "metrics": {
              "initial_rmse_K": 1.5847476304539772,
              "observation_residual_rms_K": 0.015992735342073672,
              "future_predictive_rmse_K": 0.01779131183481171
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.913411036716951,
              2.3943283527898203,
              0.037176702110721875,
              -0.12296302371832069,
              -0.2202614581765395,
              -0.09040206040572443,
              0.02276438917745841,
              -0.0016521027208949248
            ],
            "initial_K": [
              0.5665634882059429,
              1.1619868058451523,
              1.7556353366064468,
              2.249426815339938,
              2.5323553561720162,
              2.556409806480423,
              2.3708652202859195,
              2.0837044226703445,
              1.7833085229942245,
              1.4915402340265804,
              1.1875372191460607,
              0.867390379782981,
              0.569380026254927,
              0.34016242953769604,
              0.18913424488543973,
              0.08669545863727068
            ],
            "metrics": {
              "initial_rmse_K": 0.06900717780150496,
              "observation_residual_rms_K": 0.02764559859278279,
              "future_predictive_rmse_K": 0.027711510800682838
            }
          },
          "learned": {
            "coefficients_K": [
              5.985107620706221,
              2.452737756432249,
              0.038633307415403786,
              -0.11649363047153805,
              -0.06877830494128545,
              -0.00894127173470421,
              0.0035499615825506366,
              0.00044602063746138293
            ],
            "initial_K": [
              0.6409302298461546,
              1.255958968611441,
              1.8061666106570762,
              2.2381622740990257,
              2.4991347257939824,
              2.5610908019127665,
              2.437155798714186,
              2.176585006760927,
              1.8419814724740213,
              1.4862154879277876,
              1.1435669247401492,
              0.8343259159467656,
              0.5716707453403685,
              0.36293684157783235,
              0.20683440225334548,
              0.09214158835055031
            ],
            "metrics": {
              "initial_rmse_K": 0.04891765730057693,
              "observation_residual_rms_K": 0.02198226729253883,
              "future_predictive_rmse_K": 0.01605290862559497
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 11,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.389564513498375,
          -1.0278624508258072,
          0.05401489773302104,
          -0.11860151431862483,
          0.06379366607111277,
          -0.052305420544299465,
          0.025182455994148117,
          0.003796861189763763
        ],
        "initial_K": [
          0.2687022196707075,
          0.541777521078916,
          0.828250618580838,
          1.1302674336876208,
          1.431000882070863,
          1.7042849685306083,
          1.9345150223349759,
          2.116719898933642,
          2.2375362656351636,
          2.2706826982337756,
          2.2003096901899895,
          2.0398565766073338,
          1.8137466662793367,
          1.5202759530328462,
          1.1259737258674434,
          0.6077544394440488
        ],
        "observed_K": [
          0.24640742906518248,
          0.5845367699944134,
          0.8338404307532243,
          1.0936575596439426,
          1.3547824513630824,
          1.5907550020154273,
          1.796547892790848,
          1.934832156962048,
          1.974764510272298,
          2.0048426933131878,
          1.9188296871551795,
          1.835500739780751,
          1.5640962334105875,
          1.2887372470334892,
          0.9081172125091593,
          0.45316832414238195
        ],
        "future_observed_K": [
          0.2601324730608974,
          0.5655982279005471,
          0.8070115750406988,
          1.1048650959827842,
          1.3316637097518356,
          1.546558974319433,
          1.710326531586201,
          1.8553904125760459,
          1.9187554206781512,
          1.8993577243251982,
          1.8238625693818,
          1.6928811198581808,
          1.436546402258128,
          1.147704493023555,
          0.8112796224234232,
          0.3898474769022358
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.364784615349197,
              -1.0228907329303414,
              0.10435167005646485,
              -0.23534953327181832,
              0.07582699013746073,
              0.8345297787548878,
              -0.7052921273973605,
              -12.869446765698713
            ],
            "initial_K": [
              -4.112182403669868,
              -0.18109119891408,
              5.171858893889057,
              2.6572579299660117,
              -2.7544796084708576,
              -0.7334527293178517,
              5.688219723922245,
              5.444892862624,
              -0.733498645047618,
              -1.7021370635231976,
              4.111960579394128,
              6.12394889363859,
              0.7470822489349983,
              -2.457325809835555,
              1.6177561586241942,
              4.528308882329032
            ],
            "metrics": {
              "initial_rmse_K": 3.2312673473201508,
              "observation_residual_rms_K": 0.01576657298026286,
              "future_predictive_rmse_K": 0.019761160472612536
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.288180640714706,
              -1.000847609394768,
              0.09852927159411792,
              -0.19052024491422223,
              0.03172071709683846,
              0.06325064741125454,
              -0.004416240167500613,
              -0.00419696520630409
            ],
            "initial_K": [
              0.2712851202128639,
              0.5397634341801012,
              0.8119763573888981,
              1.1014655306797132,
              1.4105960680193907,
              1.7116482273728328,
              1.9537072254936523,
              2.098988705667455,
              2.1531525979764514,
              2.1526466546708334,
              2.1196824804530863,
              2.0339684313769912,
              1.849820974985537,
              1.5360749430043763,
              1.0983482363099182,
              0.571380150257442
            ],
            "metrics": {
              "initial_rmse_K": 0.045746712710493014,
              "observation_residual_rms_K": 0.025222571094242845,
              "future_predictive_rmse_K": 0.025196307248814675
            }
          },
          "learned": {
            "coefficients_K": [
              6.364421082762008,
              -1.025263187957158,
              0.10238970706908293,
              -0.18049649672918308,
              0.009905033642762743,
              0.0062558444283442585,
              -0.0006886845419717306,
              0.0011330609610672331
            ],
            "initial_K": [
              0.25565749487713274,
              0.5263883420714937,
              0.8205776364789426,
              1.1333695231054028,
              1.4445703958813358,
              1.7250384687190061,
              1.9486432213025084,
              2.101731597862003,
              2.184502866703989,
              2.2044043596249576,
              2.1652514477348443,
              2.058058924478842,
              1.8608542286784668,
              1.5505144415594727,
              1.1199390476071236,
              0.5885288783337054
            ],
            "metrics": {
              "initial_rmse_K": 0.029389493772276197,
              "observation_residual_rms_K": 0.018155719025208444,
              "future_predictive_rmse_K": 0.019546827733357707
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 12,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.397349545915156,
          -0.5749808762978855,
          0.21023001831225818,
          0.19272860732948421,
          -0.009420097252787666,
          -0.07863977622775307,
          0.05814661582296944,
          0.04398265648402488
        ],
        "initial_K": [
          0.3589035586722725,
          0.6549043022232298,
          0.8984265185041054,
          1.1248528551067474,
          1.3174682972864702,
          1.4432135289183696,
          1.5367428998217307,
          1.6707333037839698,
          1.8396961064316224,
          1.940529617184479,
          1.8887463008351828,
          1.703092438728127,
          1.4523224991379553,
          1.1651100087906154,
          0.8264918983777123,
          0.4305673522988882
        ],
        "observed_K": [
          0.27904753012168704,
          0.5502312139412778,
          0.8046086353715132,
          1.0022520599106222,
          1.2041298906284055,
          1.37894961170942,
          1.4999712135575758,
          1.620908109280663,
          1.6653062003657462,
          1.7102674656569021,
          1.6336378903228412,
          1.466135032764716,
          1.2743212369420192,
          1.0413686498230401,
          0.7213908383247827,
          0.3596746929825991
        ],
        "future_observed_K": [
          0.25217563622097583,
          0.4868066193470872,
          0.7550021369670208,
          1.0059722044365775,
          1.1696981037132728,
          1.3365565287271295,
          1.47535232479384,
          1.5365781405977421,
          1.5654443376818503,
          1.575651969814422,
          1.5653161543284675,
          1.3961095035474407,
          1.205366720018178,
          0.9737485352392469,
          0.6571422487832163,
          0.32985390623255656
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.402206815065868,
              -0.611546542260497,
              0.18090092777448608,
              0.205483802280404,
              0.179212179132116,
              -0.6209006660106413,
              1.2895185317725164,
              8.239552310962527
            ],
            "initial_K": [
              3.442767267765519,
              1.2950847023383605,
              -2.049187326161629,
              -0.14245328292820214,
              3.955639625277124,
              3.2219459325902777,
              -0.7294072098480526,
              -0.5926580564298023,
              3.567495126632767,
              4.552362331056081,
              0.8706276925565568,
              -0.913320735905754,
              1.8815398620402197,
              3.57210885475189,
              0.7386504500357852,
              -1.7475439792562042
            ],
            "metrics": {
              "initial_rmse_K": 2.076891476711971,
              "observation_residual_rms_K": 0.01060584609834277,
              "future_predictive_rmse_K": 0.020416947510320544
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.337188037708722,
              -0.5983678169628469,
              0.17080739229832773,
              0.1663433268471921,
              0.07496985999645217,
              -0.04705927829423447,
              0.008074418124820142,
              0.0026870707804473896
            ],
            "initial_K": [
              0.3411713664438136,
              0.6457708399128859,
              0.8933564695269242,
              1.0853443897947659,
              1.2412105057252907,
              1.389384065707159,
              1.551087139775813,
              1.7198483928056818,
              1.8547311546421699,
              1.9029386890721987,
              1.8373975817945687,
              1.672690649054012,
              1.4427183828943235,
              1.16557921809279,
              0.8341067602352188,
              0.4396395036336529
            ],
            "metrics": {
              "initial_rmse_K": 0.03423104005000825,
              "observation_residual_rms_K": 0.019532215002613602,
              "future_predictive_rmse_K": 0.024779227975908417
            }
          },
          "learned": {
            "coefficients_K": [
              5.401898261306598,
              -0.6129649407478525,
              0.17749972753988952,
              0.15759158699230885,
              0.023409905368503875,
              -0.004654427044908084,
              0.001259154107809112,
              -0.0007254325092750848
            ],
            "initial_K": [
              0.3381203815416039,
              0.642632975555028,
              0.8940886495701217,
              1.0944279389891107,
              1.2628501042994964,
              1.421947142814823,
              1.5822629476689618,
              1.734385636983186,
              1.852048881154099,
              1.9031781849093148,
              1.8629012014528818,
              1.722494020957422,
              1.4900092909991403,
              1.1831597527691085,
              0.8209092479376346,
              0.42054158701180144
            ],
            "metrics": {
              "initial_rmse_K": 0.03118092323813415,
              "observation_residual_rms_K": 0.013019857930510133,
              "future_predictive_rmse_K": 0.019614301039590398
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 13,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.936183587894212,
          1.1362587513029834,
          0.1582291607185872,
          0.1684457697557028,
          0.16228571754157353,
          0.06151094304955515,
          0.09862866083614298,
          -0.02358449327287049
        ],
        "initial_K": [
          0.6702033692071233,
          1.1908939214220842,
          1.5221089819891938,
          1.7367489674320713,
          1.9182189371243032,
          2.067655243905338,
          2.125165900699355,
          2.0653383675422217,
          1.9307411492202846,
          1.7633408868640115,
          1.5500428260963768,
          1.2722483145760464,
          0.9741150647064425,
          0.7243378221288247,
          0.5200100237698427,
          0.2891172974397854
        ],
        "observed_K": [
          0.45728899488625996,
          0.8622197680744571,
          1.2393514728798039,
          1.4855800888055102,
          1.755103625268943,
          1.8433882888626933,
          1.8993780320443474,
          1.8830198088402448,
          1.7756397849644618,
          1.6223801357959133,
          1.449037605508307,
          1.261466322610851,
          0.9945632969217945,
          0.7613704090514438,
          0.48410666775382705,
          0.28553026477286597
        ],
        "future_observed_K": [
          0.4142201684629364,
          0.7911556368696331,
          1.104958657488001,
          1.4164535154734217,
          1.5943479167830794,
          1.7446921935257778,
          1.7488933113523446,
          1.77004106367961,
          1.7105199812975973,
          1.6030204634091079,
          1.3953772315913706,
          1.1540588767688558,
          1.0031812629254777,
          0.7300376087053578,
          0.5207689340495948,
          0.24629289569382698
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.955709661142033,
              1.1140706297952825,
              0.13403540637041664,
              0.0631625185479844,
              0.021254345879477703,
              0.4507194520450748,
              1.7460264892503479,
              -7.693296264389211
            ],
            "initial_K": [
              -1.3550980440905396,
              1.0188804858187899,
              3.589327613466515,
              2.0619893466803934,
              -0.36058170474175544,
              1.3624119558786854,
              4.593013285176939,
              3.439972902643606,
              -0.4030403845298707,
              -0.2899778198710856,
              3.4607888771675377,
              3.859733145324217,
              -0.316044277950314,
              -2.148651506350962,
              1.1838758330965582,
              3.317901897837897
            ],
            "metrics": {
              "initial_rmse_K": 1.964088765326981,
              "observation_residual_rms_K": 0.016183957523733354,
              "future_predictive_rmse_K": 0.022920977402062205
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.884029147285794,
              1.0900625947927756,
              0.126556776238969,
              0.0511313463675437,
              0.008891333962999945,
              0.034160910573174566,
              0.010932877336660205,
              -0.002508926555373783
            ],
            "initial_K": [
              0.5562475655066059,
              1.0513674238901258,
              1.4516084087160093,
              1.7538917892210453,
              1.9656148192411114,
              2.085607050644274,
              2.107313909655674,
              2.036696374904666,
              1.89846758345505,
              1.7203510479619701,
              1.5150457639299555,
              1.282177168954474,
              1.0247776079555524,
              0.7568856034463279,
              0.4942826485674663,
              0.24322535524033106
            ],
            "metrics": {
              "initial_rmse_K": 0.05702662512533903,
              "observation_residual_rms_K": 0.023994531067973005,
              "future_predictive_rmse_K": 0.02275986227146533
            }
          },
          "learned": {
            "coefficients_K": [
              5.955369493379493,
              1.116654564110842,
              0.1315153460191529,
              0.04844119792383878,
              0.0027763862261906778,
              0.003378706002593972,
              0.0017049126260024448,
              0.0006773386469368195
            ],
            "initial_K": [
              0.551231210520177,
              1.055046888464856,
              1.475875489195594,
              1.794344417945811,
              2.004613041503049,
              2.1103875600080704,
              2.1224169894197016,
              2.0557888592841818,
              1.9261303736753566,
              1.7469696386608222,
              1.5299713876742123,
              1.2864756822596999,
              1.027884484476457,
              0.7645180389600121,
              0.5039597847836286,
              0.24958871367611757
            ],
            "metrics": {
              "initial_rmse_K": 0.05845542184919193,
              "observation_residual_rms_K": 0.017240101940471226,
              "future_predictive_rmse_K": 0.022682154030996007
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 14,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.659642427750108,
          0.14214072908360137,
          0.09421450123564268,
          -0.09242090440225754,
          -0.11826104394153614,
          0.009705937151045906,
          0.02047799934687716,
          -0.013174226996749977
        ],
        "initial_K": [
          0.4058615224918695,
          0.8218792368467962,
          1.237368927973678,
          1.620887286184928,
          1.9335089976435011,
          2.1413699411820026,
          2.2313156487290855,
          2.2267034707885354,
          2.176290083693871,
          2.1093890411643206,
          2.0049295094931425,
          1.8189232450541326,
          1.5385846036701611,
          1.193209045846603,
          0.8156657168524883,
          0.4163888165380731
        ],
        "observed_K": [
          0.407700101271849,
          0.7900858674568804,
          1.125152036554263,
          1.4342173003521457,
          1.6903825121582856,
          1.887472719296129,
          1.9930255409103304,
          2.027060926949713,
          2.05575005805031,
          1.9648912024075116,
          1.8040972608788362,
          1.6215707661234597,
          1.3980094758084183,
          1.0743558067974488,
          0.7468932687920908,
          0.3562069278130919
        ],
        "future_observed_K": [
          0.40835367075011203,
          0.7761820474959844,
          1.0555293132288495,
          1.3526288572023268,
          1.5977892087433565,
          1.7919671933905972,
          1.9172095503079105,
          2.00497894267841,
          1.9507748291708296,
          1.8794045527482799,
          1.7351136680208605,
          1.5377377884879297,
          1.2956077665907977,
          1.025980066209756,
          0.700316989785533,
          0.3797028080053252
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.65587241129751,
              0.1381932139201676,
              0.12756314711526828,
              -0.010565087447684142,
              -0.04560763639518465,
              0.39616321991746745,
              -0.7449639616778566,
              18.92166910387879
            ],
            "initial_K": [
              6.782985965163886,
              2.04361195428252,
              -4.815878898516775,
              -0.6187563603610138,
              7.571895093098914,
              5.298661709524884,
              -2.944555317136771,
              -1.8697563200648362,
              6.711815762485647,
              7.086834472447137,
              -1.715306764280837,
              -3.9593746133688486,
              4.238545136416546,
              7.639629096330066,
              -0.6150090502294662,
              -6.4144385456466475
            ],
            "metrics": {
              "initial_rmse_K": 4.738648695912567,
              "observation_residual_rms_K": 0.008871359619674059,
              "future_predictive_rmse_K": 0.02037555712599929
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.575765021624676,
              0.13521517336495256,
              0.12044564270720098,
              -0.008552653664063953,
              -0.019079049938874083,
              0.030025986823013974,
              -0.004664648367822475,
              0.006170707126730696
            ],
            "initial_K": [
              0.455532531008519,
              0.8815457097479132,
              1.2624486043870773,
              1.5923161159440802,
              1.8621575394865317,
              2.0589041919737836,
              2.1753621733556,
              2.2151081830474526,
              2.18795325866642,
              2.1041482718799998,
              1.969570376224504,
              1.77994027602817,
              1.5223735442933053,
              1.1919543924167948,
              0.8076827625987718,
              0.40332423600201206
            ],
            "metrics": {
              "initial_rmse_K": 0.0403590838663451,
              "observation_residual_rms_K": 0.02215910047823177,
              "future_predictive_rmse_K": 0.030510239741152564
            }
          },
          "learned": {
            "coefficients_K": [
              6.655492252868923,
              0.13851373416195104,
              0.1251647746401686,
              -0.00810267709238241,
              -0.005957577533306563,
              0.002969738809959865,
              -0.0007274222195372837,
              -0.0016659150132995698
            ],
            "initial_K": [
              0.4558288811012802,
              0.8909292199073124,
              1.284598808195858,
              1.6195045727330004,
              1.885184583910913,
              2.077385743735301,
              2.195250653617619,
              2.2408095820687874,
              2.2194994819623712,
              2.1373130786977454,
              1.9960779140898783,
              1.7932616130982575,
              1.5274582479637262,
              1.203251564653631,
              0.831033834032225,
              0.4245627774973115
            ],
            "metrics": {
              "initial_rmse_K": 0.036518332731753776,
              "observation_residual_rms_K": 0.012751940406845106,
              "future_predictive_rmse_K": 0.020319435433984668
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 15,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.487454197025674,
          -2.1521382628931125,
          0.33555627737758814,
          -0.16906257074062397,
          0.08084265730017107,
          -0.018855685181999083,
          0.006383921356964799,
          0.035229866445992276
        ],
        "initial_K": [
          0.13118978666686326,
          0.25278574480916005,
          0.39648753460902164,
          0.5994792896218228,
          0.8520848274559089,
          1.1179315623346668,
          1.3859029835787415,
          1.6602879494688758,
          1.9127629323931161,
          2.091451924689297,
          2.1764894414651472,
          2.1806790967193255,
          2.0871358092191024,
          1.831484988485552,
          1.3687621903896785,
          0.730157557467952
        ],
        "observed_K": [
          0.15739317724558458,
          0.28925938751981073,
          0.4910927213809578,
          0.6751948954639337,
          0.9120051358159805,
          1.1352963896013972,
          1.3685285974696175,
          1.5419833358695196,
          1.7802374746675516,
          1.8617773678127452,
          1.9186387734229393,
          1.8451761972704495,
          1.7140099121617804,
          1.3844972098256532,
          1.0215705037151834,
          0.5310297079467589
        ],
        "future_observed_K": [
          0.17052158355962338,
          0.33617323357954293,
          0.5046458371659656,
          0.6978048377212326,
          0.9359181575727997,
          1.140105469368145,
          1.310563594929412,
          1.5203465049540228,
          1.6230231311550911,
          1.7366989791006378,
          1.7934668481369178,
          1.7330597933211338,
          1.5156816273146583,
          1.2586177367481897,
          0.9081456807276745,
          0.4700863239332223
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.506804564407464,
              -2.18300650748609,
              0.3112051590120604,
              -0.18708235488501068,
              -0.02182077220016842,
              -0.3163594786312675,
              0.5691030417995406,
              6.527504458595158
            ],
            "initial_K": [
              2.403553371552203,
              0.6299047925154825,
              -1.8885700881617913,
              -0.27490882906982184,
              2.980087074406658,
              2.4742276766665876,
              -0.4175318541202311,
              -0.06425583957195324,
              3.2954958181972698,
              4.045414609550475,
              1.2669669048632506,
              0.1982929647615801,
              2.648658014626242,
              3.821394703222605,
              1.1169613133985765,
              -1.233476398722241
            ],
            "metrics": {
              "initial_rmse_K": 1.6310957867734017,
              "observation_residual_rms_K": 0.015187252123398765,
              "future_predictive_rmse_K": 0.018571067907828278
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.440526890823403,
              -2.135963083810109,
              0.2938411777904298,
              -0.15144698005691654,
              -0.009128287177709662,
              -0.023977504874624488,
              0.0035634818751151677,
              0.00212874023223261
            ],
            "initial_K": [
              0.08833974462260924,
              0.21023794783577932,
              0.38430197208712247,
              0.6067546373612642,
              0.857797370581889,
              1.1179834871337901,
              1.3788640021310365,
              1.6367309354902584,
              1.8780842420698005,
              2.0747667635606217,
              2.1925324207905907,
              2.2000402360350515,
              2.069559750824973,
              1.777237260886368,
              1.3136826645586053,
              0.7009135904726196
            ],
            "metrics": {
              "initial_rmse_K": 0.02930327453669538,
              "observation_residual_rms_K": 0.023233117233753958,
              "future_predictive_rmse_K": 0.02237737179956004
            }
          },
          "learned": {
            "coefficients_K": [
              5.506490036417685,
              -2.1880696922384066,
              0.3053540499389274,
              -0.14347897438823465,
              -0.002850376658257374,
              -0.0023715099594194297,
              0.0005557023146178139,
              -0.0005746991778185368
            ],
            "initial_K": [
              0.09639753114137706,
              0.21989833331077613,
              0.3873299104284873,
              0.6008514143690494,
              0.8504938894985553,
              1.1203309449257266,
              1.394252178772383,
              1.6584669556278229,
              1.899310948336538,
              2.0976268193595367,
              2.224284336711531,
              2.2416398996045896,
              2.111830355975063,
              1.8088404108644052,
              1.3304943894809522,
              0.7067803665187883
            ],
            "metrics": {
              "initial_rmse_K": 0.027171116055684473,
              "observation_residual_rms_K": 0.015873695413536313,
              "future_predictive_rmse_K": 0.01882404062063998
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 16,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.679004377099554,
          1.9646243674033892,
          0.23191656911509245,
          0.010192402720285494,
          -0.03936519179747421,
          0.05363489287017765,
          -0.03595552942237063,
          -0.00683272379675488
        ],
        "initial_K": [
          0.6370777214375087,
          1.2270927730197914,
          1.7129451480596964,
          2.04868794387963,
          2.2261621488958996,
          2.2656742118513433,
          2.1847977198798842,
          1.9946401798693005,
          1.7269959422824366,
          1.4411961008455074,
          1.1860707461384372,
          0.9625533775093482,
          0.7391265831172595,
          0.5031873843053958,
          0.28367640804847477,
          0.1172455008869977
        ],
        "observed_K": [
          0.5242138853870951,
          0.9634114041977202,
          1.3678391730876955,
          1.65241019909303,
          1.8470424789848157,
          1.9433914662656333,
          1.90335959824733,
          1.811567721178475,
          1.6476275139251324,
          1.4199800001053475,
          1.2034850048282553,
          1.010780849630628,
          0.7872666765618166,
          0.5279256432862645,
          0.32786297983309803,
          0.20099015881233565
        ],
        "future_observed_K": [
          0.4414575742915,
          0.8340690121915106,
          1.2430977047382903,
          1.5146108390285558,
          1.7078870989747226,
          1.803379971361252,
          1.82605811847456,
          1.6911378904905798,
          1.592339362752426,
          1.4038301471530226,
          1.1966970497249823,
          0.9659571809993761,
          0.7909841930607888,
          0.5654879116475294,
          0.37474768434448474,
          0.19383269067135325
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.670993856050408,
              1.9534662895739119,
              0.21705321086631943,
              0.0599053250133478,
              -0.15066595888932757,
              0.9771896783878222,
              0.6402859054229957,
              -7.5656258192148265
            ],
            "initial_K": [
              -1.4613946462397536,
              1.0977197943854693,
              3.9820146026408167,
              2.4864430588448307,
              -0.2441474887020303,
              1.2509565729413856,
              4.6294863131260575,
              3.6840868688941164,
              -0.3966611999881908,
              -0.8483591422357186,
              2.711099547936067,
              3.5860614781736087,
              -0.08553762268594012,
              -2.1190349291908444,
              0.5727107571177268,
              2.594599364560783
            ],
            "metrics": {
              "initial_rmse_K": 1.9114928361976515,
              "observation_residual_rms_K": 0.014916896717770167,
              "future_predictive_rmse_K": 0.01771742616597286
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.60274006652647,
              1.9113694190506079,
              0.20494252513880118,
              0.04849458180155977,
              -0.0630281150470085,
              0.07406312078382903,
              0.004009198776467322,
              -0.002467290856029006
            ],
            "initial_K": [
              0.6441234529715265,
              1.2154131971060553,
              1.6692001124949638,
              1.9926292223500117,
              2.1846804113444285,
              2.2391819876242605,
              2.1537371900209568,
              1.9538652984147806,
              1.6970658157198422,
              1.4413239115210998,
              1.2073654041328505,
              0.9768018934236785,
              0.7291770637401528,
              0.4766323643168605,
              0.25871228691813647,
              0.10426053009365888
            ],
            "metrics": {
              "initial_rmse_K": 0.028983264027739476,
              "observation_residual_rms_K": 0.02392111840699834,
              "future_predictive_rmse_K": 0.02352032509747304
            }
          },
          "learned": {
            "coefficients_K": [
              5.670669950185086,
              1.957997087213597,
              0.2129722951916427,
              0.04594316015848728,
              -0.0196810052583194,
              0.007325258799151236,
              0.0006252090281148952,
              0.0006660981950399492
            ],
            "initial_K": [
              0.6463700357645881,
              1.2318180982805795,
              1.7071517642511407,
              2.0411290526754655,
              2.221478052890977,
              2.2542619556705477,
              2.1621564774819513,
              1.979132416608239,
              1.7413723063774396,
              1.4786396303274807,
              1.2106430278283216,
              0.9491457437057415,
              0.7028910144590078,
              0.4810028270123087,
              0.2914506349062074,
              0.1349733307414987
            ],
            "metrics": {
              "initial_rmse_K": 0.018836165100257526,
              "observation_residual_rms_K": 0.01711734556073168,
              "future_predictive_rmse_K": 0.017343876079102014
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 17,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.8721041694874545,
          0.2244875779353969,
          0.11934854359436442,
          0.13135331855489102,
          0.1644563213391143,
          0.051678323557063505,
          -0.020490174412989625,
          -0.023888190225966915
        ],
        "initial_K": [
          0.5587994712354081,
          1.0480616241116532,
          1.4162368112583312,
          1.668100102191579,
          1.8694104995620164,
          2.077680557499905,
          2.271771153599252,
          2.376511104125519,
          2.3510622960747383,
          2.2229860675451127,
          2.037276302741694,
          1.807279988702838,
          1.526380575758356,
          1.1972292372973232,
          0.8293117208002705,
          0.4270469344740218
        ],
        "observed_K": [
          0.45558780972815177,
          0.8426388436945568,
          1.1972447848868117,
          1.4902209421871817,
          1.7595950975337744,
          1.9479765458384248,
          2.0729438770256463,
          2.1386948789066222,
          2.107708308554793,
          2.064847773945388,
          1.8733757267396969,
          1.6500471453231114,
          1.4039025891618646,
          1.064568279551395,
          0.7655688468777104,
          0.3524440282382024
        ],
        "future_observed_K": [
          0.35936325592861174,
          0.7812709326192943,
          1.1494375960028158,
          1.42405293265404,
          1.6403325246665394,
          1.849271701384364,
          1.929165920813748,
          2.023687667184853,
          2.0204859552219867,
          1.9585589812576354,
          1.7821927824306596,
          1.5770364182581171,
          1.326734138718659,
          1.0889711761205119,
          0.7014957414737153,
          0.3521965076485574
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.897545879730842,
              0.2386094091185618,
              0.07031299915554125,
              0.1998294601239962,
              0.3120602589369649,
              0.28688476325987133,
              2.02751353602319,
              12.926918043875428
            ],
            "initial_K": [
              5.780525282225556,
              2.3619126634880145,
              -3.3151325731216046,
              -0.6680353777864909,
              5.863303207586052,
              5.102814950083747,
              -0.9284523278525172,
              -1.0716184758644014,
              4.818414934537953,
              5.988778918757071,
              0.3646565157982993,
              -2.0275068618007133,
              2.5364941800818093,
              4.994381675285812,
              0.3286384149423953,
              -3.3770894176644783
            ],
            "metrics": {
              "initial_rmse_K": 3.2787454772766234,
              "observation_residual_rms_K": 0.013029835300169995,
              "future_predictive_rmse_K": 0.023838509346101364
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.814529805889646,
              0.2334674164182439,
              0.06638981998701714,
              0.16176602160468107,
              0.13054421879281922,
              0.021743558433210766,
              0.01269542983696478,
              0.00421570765570855
            ],
            "initial_K": [
              0.5558216357443698,
              1.0255115291477153,
              1.3795801763149782,
              1.647611472338393,
              1.873780406710211,
              2.0763012350690317,
              2.241356472788787,
              2.339721348515619,
              2.3444757676890853,
              2.243836788521818,
              2.048316592664758,
              1.7856155102834592,
              1.4831378035178544,
              1.1531791393790378,
              0.7946824554879028,
              0.406973910029354
            ],
            "metrics": {
              "initial_rmse_K": 0.026294293610370223,
              "observation_residual_rms_K": 0.02442456115544132,
              "future_predictive_rmse_K": 0.026393417174507754
            }
          },
          "learned": {
            "coefficients_K": [
              6.897151917821611,
              0.2391628309786733,
              0.06899101262863332,
              0.1532551052651027,
              0.040763418905808084,
              0.0021505601040310587,
              0.0019797714686682327,
              -0.0011381208881076274
            ],
            "initial_K": [
              0.524283606930139,
              0.9977025365057887,
              1.3891592921723466,
              1.695452729454343,
              1.9330050161486945,
              2.1195641959580596,
              2.2594418463001604,
              2.3415612073549243,
              2.3480899551724908,
              2.2650914979751704,
              2.0896348819686845,
              1.8322414339221997,
              1.5139071884835924,
              1.157917795640765,
              0.78145560880793,
              0.39364647161043076
            ],
            "metrics": {
              "initial_rmse_K": 0.03761126786150367,
              "observation_residual_rms_K": 0.016218722858197934,
              "future_predictive_rmse_K": 0.023908470185154785
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 18,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.97568465926898,
          -1.1129968387267355,
          0.4335088640546986,
          0.03813348954029277,
          -0.10594793565059078,
          -0.05210567476726007,
          -0.04550728799435298,
          0.02151710440395964
        ],
        "initial_K": [
          0.2731408544858117,
          0.573281969001987,
          0.8893345200399214,
          1.1693983760931628,
          1.3672607731324806,
          1.4965845090601464,
          1.6225478542955072,
          1.788556781371872,
          1.9670621952431504,
          2.0952716679450254,
          2.136180843305761,
          2.078101079293682,
          1.8957966038332195,
          1.559553763567003,
          1.0874194785587297,
          0.5486281128529149
        ],
        "observed_K": [
          0.3043551526725277,
          0.532621044287143,
          0.8083551410369005,
          1.042306077304854,
          1.2529734158708878,
          1.4582730144862348,
          1.5975099484590458,
          1.7455570357111672,
          1.8164469761842508,
          1.8662608362176425,
          1.883443717473068,
          1.7703161283500464,
          1.5500099987868876,
          1.2659126161142633,
          0.8948796650668667,
          0.4749355247286206
        ],
        "future_observed_K": [
          0.2853434375865575,
          0.5714559182196264,
          0.7988615371765204,
          1.0441917238422171,
          1.2139353936988746,
          1.413190325563882,
          1.567827760998344,
          1.7012267791029656,
          1.7586614862700185,
          1.8004649837491866,
          1.7561472953788453,
          1.6570346581380335,
          1.4221673140614504,
          1.11790147962652,
          0.844923922819445,
          0.37675121606898887
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.973798420928496,
              -1.1260713025561788,
              0.45088864797578004,
              0.02230924390413366,
              -0.23103924216831948,
              0.2471146016393837,
              3.230384019243137,
              -7.145460728839309
            ],
            "initial_K": [
              -1.0385227192955762,
              0.7504002675670783,
              2.459658041131071,
              0.974329008254198,
              -0.6530507448962808,
              1.387256935703291,
              4.082344566216711,
              2.558381521894485,
              -0.6856725104878725,
              0.4222281794297693,
              4.537627057134081,
              4.600062552101944,
              0.13303336203511795,
              -1.544535953343039,
              2.0209911021668,
              3.959306724314939
            ],
            "metrics": {
              "initial_rmse_K": 1.9717210548615942,
              "observation_residual_rms_K": 0.01040203584501056,
              "future_predictive_rmse_K": 0.02488329419740209
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.901900198071938,
              -1.1018046550707719,
              0.42573089660253094,
              0.018059787726698754,
              -0.09665068369196166,
              0.018729299943958094,
              0.020227294631627285,
              -0.0023302672296591645
            ],
            "initial_K": [
              0.3016696053004024,
              0.5903043020986761,
              0.8606623385601728,
              1.110501267321303,
              1.3306952082980776,
              1.5088789635537325,
              1.6476385146198902,
              1.7722782259883132,
              1.9077966996162605,
              2.0425537048639075,
              2.1201619258961912,
              2.074282232262654,
              1.872612582764302,
              1.5281919401359252,
              1.0772094542483204,
              0.5564516722627879
            ],
            "metrics": {
              "initial_rmse_K": 0.031649078772611604,
              "observation_residual_rms_K": 0.021415949201890275,
              "future_predictive_rmse_K": 0.03281991740639097
            }
          },
          "learned": {
            "coefficients_K": [
              5.973457220003949,
              -1.12868307078938,
              0.4424112863937327,
              0.017109616974350664,
              -0.03017990642022136,
              0.0018524330026122454,
              0.003154317838332905,
              0.0006291057221096695
            ],
            "initial_K": [
              0.3140321589775868,
              0.6121698051348521,
              0.8830357174780235,
              1.1208031336320756,
              1.3246831047988192,
              1.5000072482805156,
              1.658329313520149,
              1.8109892221195938,
              1.957122701443585,
              2.075515727350753,
              2.128491010130694,
              2.0760446091415545,
              1.8909918924709257,
              1.5674161583563757,
              1.1210118463925882,
              0.5842563238695644
            ],
            "metrics": {
              "initial_rmse_K": 0.0276459849276097,
              "observation_residual_rms_K": 0.013486263618818738,
              "future_predictive_rmse_K": 0.025132099437656107
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 19,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.365169888103991,
          0.5106173206133143,
          0.2874213182903701,
          -0.07019834958448369,
          0.06699841318985014,
          -7.900935353834022e-05,
          -0.05620511883913252,
          -0.012292224642959157
        ],
        "initial_K": [
          0.432661770224939,
          0.8581942040466322,
          1.2298386022231926,
          1.4951102749350065,
          1.6551038490723209,
          1.7552153507024773,
          1.8179213206088995,
          1.8172281212197652,
          1.729816060448395,
          1.5837399334019526,
          1.4338267090474843,
          1.3003561570111077,
          1.1520742353952371,
          0.9465888747013931,
          0.671754643308103,
          0.3470130341865916
        ],
        "observed_K": [
          0.36707118406152034,
          0.711347714276075,
          1.0221884851604404,
          1.272269452086423,
          1.4587106566467793,
          1.5994317231060824,
          1.649344986833582,
          1.6437439348635068,
          1.5601024680139435,
          1.531662514916694,
          1.3526971117704647,
          1.230766110167467,
          1.0270317168399001,
          0.8306287840777412,
          0.5568788267566905,
          0.28988585582157655
        ],
        "future_observed_K": [
          0.35993078928553957,
          0.6521600496056199,
          0.9827208118155042,
          1.2165278915466546,
          1.3933534629996551,
          1.4986717207000444,
          1.5510845843164678,
          1.5692204371090799,
          1.5372219805242604,
          1.4436774339589107,
          1.3066511651942532,
          1.163858007178809,
          1.0141163957703454,
          0.8064805770989236,
          0.5251820645078472,
          0.2606237144759432
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.353792806085745,
              0.529939971689682,
              0.30469747526631097,
              -0.14829974367140825,
              -0.046113544854729724,
              0.21637180099359274,
              0.8271225723630327,
              3.05319035448016
            ],
            "initial_K": [
              1.7932884277126822,
              1.2145116730542225,
              -0.02484620840268914,
              0.7968594057882095,
              2.6601156917585764,
              2.6898494309081875,
              1.1748132832741949,
              0.8727507107230618,
              2.102099014330081,
              2.4159964070526,
              1.1456762834302023,
              0.4820049110141602,
              1.352941635453929,
              1.7727045028749981,
              0.5675903302976526,
              -0.4879045186745682
            ],
            "metrics": {
              "initial_rmse_K": 0.8001561416960494,
              "observation_residual_rms_K": 0.013679348230722551,
              "future_predictive_rmse_K": 0.018649700439756434
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.28935672016908,
              0.5185198542848355,
              0.2876965963104533,
              -0.12005166567447931,
              -0.019290686706903974,
              0.016399242834453154,
              0.005179090742151574,
              0.0009957019846517676
            ],
            "initial_K": [
              0.4236223310363251,
              0.8216492028429291,
              1.1747257601232346,
              1.4668747766332213,
              1.679606997032282,
              1.7958754625023372,
              1.8137386148447585,
              1.7545285205016834,
              1.6539564503702076,
              1.5421081305442292,
              1.4283849971557612,
              1.301097293832483,
              1.138890178845626,
              0.9247593025507895,
              0.654914945396287,
              0.3398595774931518
            ],
            "metrics": {
              "initial_rmse_K": 0.03531770723558583,
              "observation_residual_rms_K": 0.020394874668261165,
              "future_predictive_rmse_K": 0.02640151556732006
            }
          },
          "learned": {
            "coefficients_K": [
              5.353487017552796,
              0.531169094908097,
              0.29896872010122594,
              -0.11373544628027644,
              -0.006023662713568475,
              0.0016219772621129515,
              0.000807646233064201,
              -0.0002688111509648624
            ],
            "initial_K": [
              0.42994655526349856,
              0.8375993839765106,
              1.1997704048701363,
              1.493475733773725,
              1.699809564495684,
              1.8096160915635549,
              1.8282290926339324,
              1.775621073651527,
              1.6797718829145067,
              1.5653108775937454,
              1.4434870740969659,
              1.309181951918181,
              1.1459911766182769,
              0.9358815931388189,
              0.6689538450159109,
              0.35006827374866606
            ],
            "metrics": {
              "initial_rmse_K": 0.026596311946099817,
              "observation_residual_rms_K": 0.01408434514451348,
              "future_predictive_rmse_K": 0.018780292953776888
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 20,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          7.072340251479924,
          1.5563718188040228,
          0.1277128492719451,
          -0.033265189614751785,
          -0.03490186441273495,
          0.11652637222303282,
          -0.004719851481249165,
          -0.02410128384101647
        ],
        "initial_K": [
          0.6703902652902903,
          1.2817985089216672,
          1.7867674257202482,
          2.170955607608873,
          2.4484038610816583,
          2.616951462653792,
          2.6385279941545168,
          2.492710175383357,
          2.235064761299507,
          1.9632595246790532,
          1.7228172977783398,
          1.4781387496857625,
          1.1829532989298948,
          0.8480319888225012,
          0.5244888269810404,
          0.24498638217685567
        ],
        "observed_K": [
          0.5259494800576219,
          1.0832637799231812,
          1.492100737118909,
          1.860034953754374,
          2.1160674740370697,
          2.2753893403240872,
          2.246598655466353,
          2.199792026119123,
          2.095936168003267,
          1.9067102180900608,
          1.700103712728585,
          1.3835254075384333,
          1.13413509254857,
          0.8836355290176987,
          0.6094137128014098,
          0.25930751621148196
        ],
        "future_observed_K": [
          0.49581742220016767,
          0.9295917051237779,
          1.3872628490058294,
          1.7225452826368983,
          1.9735857210093135,
          2.116344952181495,
          2.1709921243183317,
          2.1186048501344703,
          2.037159677255557,
          1.8436318990355958,
          1.6385718668916642,
          1.3817771168963955,
          1.1301392888344277,
          0.8309738972030094,
          0.5751390955822365,
          0.2832841122518334
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              7.059389492104066,
              1.5498474174402592,
              0.2397196398219706,
              -0.017165723944342057,
              -0.0715606746459703,
              -1.0270332069495514,
              1.7038509758091194,
              23.263329848719135
            ],
            "initial_K": [
              8.84867241828937,
              2.7696799624239112,
              -6.184795776396683,
              -0.8287319165322553,
              9.988267840876258,
              7.254021073025177,
              -3.953103408759095,
              -3.617638020092683,
              7.304820532164589,
              8.913361437279676,
              -1.7523116630999276,
              -5.800650816668851,
              3.2020166944331154,
              8.092723737395623,
              -0.30499359802286197,
              -6.787220698270449
            ],
            "metrics": {
              "initial_rmse_K": 5.844579488770932,
              "observation_residual_rms_K": 0.01787473823531588,
              "future_predictive_rmse_K": 0.017145462719943966
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.9744255339704315,
              1.5164484658376234,
              0.22634425961446109,
              -0.01389600346574212,
              -0.029935988644527525,
              -0.07784085949495619,
              0.010668792159314709,
              0.0075866031955685795
            ],
            "initial_K": [
              0.6391378277415467,
              1.250552266613152,
              1.794672658364203,
              2.217487198671881,
              2.471072348761327,
              2.5491008090996896,
              2.4974415831910077,
              2.376708398321621,
              2.2137315804201867,
              1.9985978904848754,
              1.7263246831638126,
              1.4248578381412242,
              1.1339214645388696,
              0.8662575350698338,
              0.6008719368285353,
              0.31238729906395846
            ],
            "metrics": {
              "initial_rmse_K": 0.0614047533385404,
              "observation_residual_rms_K": 0.029865676587494724,
              "future_predictive_rmse_K": 0.029693440507514587
            }
          },
          "learned": {
            "coefficients_K": [
              7.0589862862956805,
              1.5534420763592733,
              0.23521256235569965,
              -0.01316489985215112,
              -0.00934773869544588,
              -0.007698898384436179,
              0.0016637302236638877,
              -0.0020481665883469446
            ],
            "initial_K": [
              0.6717314939770066,
              1.2963086814088145,
              1.8279183962369485,
              2.229236305523237,
              2.480623769895818,
              2.5835081460472997,
              2.5565193711815,
              2.4285817983025777,
              2.2313400160277577,
              1.9915790059878347,
              1.7270603374205589,
              1.4485973366013434,
              1.1642018265390894,
              0.8788705027972461,
              0.5918485972615528,
              0.29898434913996275
            ],
            "metrics": {
              "initial_rmse_K": 0.04239630219221796,
              "observation_residual_rms_K": 0.02229139199794273,
              "future_predictive_rmse_K": 0.017248575684308827
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 21,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.142889764056055,
          -2.4353248067166295,
          0.5029481290144932,
          0.23511525873783842,
          0.10777081162570273,
          -0.05621235403037739,
          0.008147232279402016,
          0.06392606404714027
        ],
        "initial_K": [
          0.2673147590086395,
          0.458781584018103,
          0.5915040604645057,
          0.7288731442501358,
          0.8941825948806891,
          1.0927053452653148,
          1.3695240312757946,
          1.7553997761906064,
          2.1704825274545763,
          2.466762729473349,
          2.5718631787668205,
          2.52069973415507,
          2.3414812684229513,
          1.9933637322313864,
          1.4463853125866872,
          0.7530059786981663
        ],
        "observed_K": [
          0.1569608401371833,
          0.378656425246897,
          0.5866258594695778,
          0.8009672962834673,
          0.9804806818346735,
          1.2537353657709194,
          1.5106827417459858,
          1.725679126299703,
          1.9454766480673389,
          2.0921063424737203,
          2.1496892071347937,
          2.116509505531654,
          1.8764211474107122,
          1.6054003511181247,
          1.1141084353361985,
          0.6033817155988164
        ],
        "future_observed_K": [
          0.15404147340981403,
          0.40633788297361767,
          0.5963854636598426,
          0.789548152731133,
          0.9941985240351477,
          1.2461972694837244,
          1.4620482447836272,
          1.7070683139512917,
          1.8447336665363705,
          1.9900830258480453,
          2.012779116987879,
          1.9344265568541437,
          1.691971537881002,
          1.416465533634213,
          1.0241436589076864,
          0.5494413630003707
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.161515450927266,
              -2.4401297611625252,
              0.492775527518298,
              0.02659142912330194,
              -0.013843843368066953,
              -0.21433098876107484,
              -1.144779432615137,
              -16.673648242996688
            ],
            "initial_K": [
              -5.9607701850963775,
              -0.9608362056396408,
              6.315935067393254,
              3.21759228831857,
              -4.199583025256421,
              -2.240926111809238,
              5.818025153322618,
              5.907983379828314,
              -1.4061945122967257,
              -2.2657838729909723,
              5.186891569424538,
              7.559884215299943,
              0.6077055000607687,
              -3.2286001936149136,
              2.367773962321083,
              6.152479906161451
            ],
            "metrics": {
              "initial_rmse_K": 4.1949328129194585,
              "observation_residual_rms_K": 0.01553294884371955,
              "future_predictive_rmse_K": 0.02059222523474863
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.0873579417831865,
              -2.3875453745447635,
              0.46528065875240054,
              0.021526303956334703,
              -0.005791297244098958,
              -0.01624456567584516,
              -0.007168123273826367,
              -0.005437585842813896
            ],
            "initial_K": [
              0.1660233657067689,
              0.3447665912582122,
              0.5346517312878784,
              0.7292042725372421,
              0.9359317760954093,
              1.1750090679231504,
              1.4576966861810192,
              1.7709056106741674,
              2.080546232881548,
              2.341247940152726,
              2.5022281291577695,
              2.5148562329219852,
              2.3452809605308245,
              1.983368655601041,
              1.4430483587697573,
              0.7614216036536894
            ],
            "metrics": {
              "initial_rmse_K": 0.06705659459688679,
              "observation_residual_rms_K": 0.025956244455750253,
              "future_predictive_rmse_K": 0.0286801077854168
            }
          },
          "learned": {
            "coefficients_K": [
              6.161163528311146,
              -2.4457893081029605,
              0.48351063175232356,
              0.020393751086113174,
              -0.0018083763321906925,
              -0.00160667882201038,
              -0.0011178231949341391,
              0.0014679931660357664
            ],
            "initial_K": [
              0.17642737772012895,
              0.35251152927242535,
              0.5319061357638463,
              0.7230235771877956,
              0.9371409125390955,
              1.1851591453715118,
              1.471773683004144,
              1.7871822796219359,
              2.1017892082646523,
              2.3694447495471636,
              2.5373945065850965,
              2.5566104861395407,
              2.3903970416961617,
              2.0234107878541607,
              1.4696006707478098,
              0.7730766714609126
            ],
            "metrics": {
              "initial_rmse_K": 0.06417885577965231,
              "observation_residual_rms_K": 0.017533591243879394,
              "future_predictive_rmse_K": 0.020503378373284066
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 22,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.010637250368426,
          -0.2559485164830184,
          0.32346515589485025,
          0.32286295671995524,
          -0.0483901287716794,
          -0.030494173963517602,
          0.042844644694521886,
          0.0056819309358853
        ],
        "initial_K": [
          0.4105642132024814,
          0.7550672720835809,
          1.00915731615227,
          1.1842468396997363,
          1.296861010128926,
          1.3645628784506432,
          1.4232238730158326,
          1.515051040293702,
          1.6409604823944226,
          1.7378572134015366,
          1.7232101942935207,
          1.5647508847108476,
          1.2996676130919682,
          0.9894879733190628,
          0.6687942532719109,
          0.3396238052296995
        ],
        "observed_K": [
          0.28855870328206984,
          0.5791824375330522,
          0.8289180951847285,
          1.0583914821628053,
          1.2132391512444414,
          1.347722026602298,
          1.3851912467058747,
          1.510102929885928,
          1.544463709665878,
          1.5653842635570892,
          1.4505717602747978,
          1.2864106205688166,
          1.1471654605514154,
          0.9031856879758212,
          0.6017214382128211,
          0.3102461014265882
        ],
        "future_observed_K": [
          0.2644368428877034,
          0.5652749425528983,
          0.7634548016360524,
          0.9558112883083939,
          1.118589612081579,
          1.27425645299174,
          1.3649544211516507,
          1.4612974660151328,
          1.4456417363004108,
          1.4613291630596388,
          1.353017280672034,
          1.2342913577713786,
          1.0688017198501183,
          0.8472034804948777,
          0.5653765765301726,
          0.30829406020637956
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.040178635917993,
              -0.21965800306342287,
              0.26694871634935635,
              0.33030654227017975,
              -0.07834340917810177,
              -1.4820857597675738,
              -3.011419544386253,
              23.750594562681044
            ],
            "initial_K": [
              7.05662733189182,
              1.2901391357306349,
              -6.0316177217761915,
              -0.33157289167497783,
              8.752335328011661,
              4.456094047776369,
              -5.925199044556588,
              -3.377019013626186,
              8.244117669585702,
              8.371238838920213,
              -3.4154835401579584,
              -6.253090082572143,
              4.6845710987908245,
              9.406436457433802,
              -1.016410644696764,
              -8.354747556686618
            ],
            "metrics": {
              "initial_rmse_K": 5.9961595009150725,
              "observation_residual_rms_K": 0.012819556008066292,
              "future_predictive_rmse_K": 0.019290263219875425
            }
          },
          "tikhonov": {
            "coefficients_K": [
              4.979517083373378,
              -0.21492440998136086,
              0.2520540644980065,
              0.26738987944965703,
              -0.0327734110827209,
              -0.112330184267557,
              -0.018856231959076222,
              0.007745509253302819
            ],
            "initial_K": [
              0.3474703442404343,
              0.6915602152858262,
              0.9972303536224001,
              1.210891165751135,
              1.3133667048612245,
              1.3545894349828274,
              1.4187230612635209,
              1.5438701753217325,
              1.6813687955071668,
              1.7415058853191936,
              1.6737117262561272,
              1.4950678026327477,
              1.2517975350254646,
              0.9737830151004555,
              0.6687595373543009,
              0.34084476683387155
            ],
            "metrics": {
              "initial_rmse_K": 0.036725773795062845,
              "observation_residual_rms_K": 0.024777674802736734,
              "future_predictive_rmse_K": 0.01736683601561428
            }
          },
          "learned": {
            "coefficients_K": [
              5.0398907598483165,
              -0.22016746973153456,
              0.26192969268904354,
              0.2533218268915781,
              -0.010233745295587855,
              -0.011110086396681554,
              -0.002940509342225966,
              -0.0020910666939340287
            ],
            "initial_K": [
              0.38829728978338124,
              0.7334522476219112,
              1.0020247827877253,
              1.1837371884488144,
              1.2988214977192143,
              1.386702956605218,
              1.4803864114067988,
              1.5857583931694001,
              1.6793321574392228,
              1.721898692385275,
              1.6778822366615225,
              1.5317210385665176,
              1.2943463425446127,
              0.9957671015020679,
              0.6685125504500327,
              0.3340346850082082
            ],
            "metrics": {
              "initial_rmse_K": 0.030359291582620893,
              "observation_residual_rms_K": 0.021071943005652294,
              "future_predictive_rmse_K": 0.018793883477438007
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 23,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.185578075618213,
          0.8862986427715477,
          0.11763233284344318,
          -0.04877992265619755,
          0.019586451938162698,
          0.037540577334801616,
          0.09901191908082921,
          -0.01367675535992588
        ],
        "initial_K": [
          0.5545155238068413,
          1.0244362051493936,
          1.3975422123525116,
          1.716534326949864,
          1.9955548912868697,
          2.18195677359731,
          2.218540779955372,
          2.124532834366226,
          1.9808480087034062,
          1.8353876756940628,
          1.6602164358643632,
          1.418901031181819,
          1.138661141994833,
          0.875698509082657,
          0.6293249854935093,
          0.3437151490902201
        ],
        "observed_K": [
          0.4152824298455064,
          0.8660835607237121,
          1.2105365700366484,
          1.5477665605700168,
          1.7141648984706646,
          1.9211572790983176,
          1.9759981958514083,
          1.9503088495224836,
          1.8997837062361507,
          1.7062853393109372,
          1.5619759186419735,
          1.3436027698924475,
          1.126943768083667,
          0.8396905678911359,
          0.5924638200602281,
          0.28122052576515244
        ],
        "future_observed_K": [
          0.416453874835863,
          0.7672123894279297,
          1.0799693079004375,
          1.3960601999179807,
          1.6286743384682225,
          1.776938917249708,
          1.8474106816780582,
          1.8205142960973915,
          1.8084287468265479,
          1.6539686480762292,
          1.5275568880019224,
          1.2952624542061943,
          1.0986568512463535,
          0.8160680496512652,
          0.5952200197464507,
          0.2910256263432544
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.2350131147610846,
              0.9050950795446066,
              0.10752501332508116,
              -0.10681186097717629,
              0.09321643331168618,
              0.4877832857156645,
              -2.1561288481659586,
              -10.143908597182806
            ],
            "initial_K": [
              -3.5006763947189046,
              0.11384930058531767,
              5.236756526137169,
              3.5137215621977833,
              -1.3571764366467411,
              -0.3385346875231505,
              4.910211244933148,
              5.215153553689969,
              0.2104218033851697,
              -1.3685587968326063,
              2.637896139920031,
              4.461632827190378,
              0.7170272866469971,
              -1.8921046546014089,
              0.7801394529149073,
              2.953838463532016
            ],
            "metrics": {
              "initial_rmse_K": 2.597133803742736,
              "observation_residual_rms_K": 0.017605854281992607,
              "future_predictive_rmse_K": 0.023481397778347547
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.159971017446898,
              0.885590432559795,
              0.1015255552243241,
              -0.08646637888001392,
              0.03899524568357508,
              0.03697005116334685,
              -0.013500764372225397,
              -0.0033081166745860297
            ],
            "initial_K": [
              0.512757406940794,
              0.9898676400325458,
              1.40190367106635,
              1.7335360334382326,
              1.9827167508398131,
              2.1462383150691884,
              2.2095075690343235,
              2.159982731713857,
              2.012046020577407,
              1.8095337032234515,
              1.5964168517502202,
              1.3862896707410373,
              1.1630900370996842,
              0.9078951442692693,
              0.6198314809113562,
              0.31281724365425306
            ],
            "metrics": {
              "initial_rmse_K": 0.031104219607869476,
              "observation_residual_rms_K": 0.02572813031362862,
              "future_predictive_rmse_K": 0.021484058491320818
            }
          },
          "learned": {
            "coefficients_K": [
              6.234656994234508,
              0.9071943236789837,
              0.10550338687437456,
              -0.08191716570450247,
              0.012176560171210835,
              0.0036565457912557716,
              -0.0021053582629806137,
              0.0008930971962785924
            ],
            "initial_K": [
              0.5095357948165753,
              0.9912451093326538,
              1.4193837560079032,
              1.771361501884777,
              2.028823835719049,
              2.180051594328459,
              2.2229257117607233,
              2.1666366247048376,
              2.031076143909841,
              1.8429988934394919,
              1.6281432296778418,
              1.401809461453847,
              1.1646457645904502,
              0.9081911628476254,
              0.6258246808293301,
              0.31972689272118493
            ],
            "metrics": {
              "initial_rmse_K": 0.03135539866879968,
              "observation_residual_rms_K": 0.019131339701381377,
              "future_predictive_rmse_K": 0.02347623155366932
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 24,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.454230547816917,
          -0.9611263700943062,
          0.5435631559008747,
          -0.2695019451221049,
          -0.0023159472584405516,
          -0.028234430804316188,
          0.029110574217616956,
          0.02752442553649948
        ],
        "initial_K": [
          0.33326751267759325,
          0.6509671531960695,
          0.967866945365149,
          1.2923401559947816,
          1.5831715995384592,
          1.7852200787946857,
          1.8991548126695879,
          1.977695373237983,
          2.054977968227226,
          2.1151048288668512,
          2.1306122125426894,
          2.0900536607536218,
          1.9710174042542767,
          1.7202092008879561,
          1.2912282460384288,
          0.6945317467499845
        ],
        "observed_K": [
          0.30245214667775017,
          0.6174724976862013,
          0.9160520037529195,
          1.1918738455453965,
          1.4470014531322475,
          1.6686765899164813,
          1.7530134822394072,
          1.8812842792167872,
          1.9645587473003794,
          2.012979283412425,
          1.9333911913718274,
          1.8374602153657984,
          1.6594557771031284,
          1.318209250450868,
          0.9580535169895047,
          0.5234588493654679
        ],
        "future_observed_K": [
          0.31246281594128006,
          0.5849203678542314,
          0.8614529997820777,
          1.1432311575994856,
          1.4017076893369884,
          1.5653491074291637,
          1.7024302265333608,
          1.8102046686073465,
          1.8753286012914465,
          1.8849544826870723,
          1.839443052045088,
          1.7255254153274697,
          1.505054433536176,
          1.2337247258855262,
          0.8564150786945494,
          0.43321513363915776
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.479406683987837,
              -0.953832360592329,
              0.528394085576559,
              -0.2860276799658989,
              -0.3314181120266038,
              -0.9733928101030981,
              2.064447142247848,
              9.067853419780302
            ],
            "initial_K": [
              3.7079636322276555,
              1.215473862356056,
              -2.469012710884535,
              -0.07837682437172933,
              4.828383300995188,
              4.0877936680496365,
              -0.6484982911678814,
              -0.9240116584264393,
              3.6675815289916147,
              5.149272252663753,
              1.3877791109812785,
              -0.6637791447819552,
              2.2140607061749913,
              4.133630832159422,
              1.2415216027253038,
              -1.519701825011746
            ],
            "metrics": {
              "initial_rmse_K": 2.3301417085012472,
              "observation_residual_rms_K": 0.015854545711564395,
              "future_predictive_rmse_K": 0.013987941169274066
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.401423164471753,
              -0.9332774333846776,
              0.4989118462438347,
              -0.2315452377651907,
              -0.13864219261909722,
              -0.07377534869557308,
              0.012926692414560646,
              0.002957195129795251
            ],
            "initial_K": [
              0.26907095981131657,
              0.5882026529986747,
              0.9598452419632756,
              1.3274722974115651,
              1.6140389545485148,
              1.782816669642777,
              1.8659990847380663,
              1.931468869747461,
              2.0197395048432316,
              2.112858942886605,
              2.158164845763078,
              2.110292751046095,
              1.9462061290948407,
              1.652357152341353,
              1.2176937414953937,
              0.6506389279740926
            ],
            "metrics": {
              "initial_rmse_K": 0.04222182589881006,
              "observation_residual_rms_K": 0.026152464593359098,
              "future_predictive_rmse_K": 0.017135204906028465
            }
          },
          "learned": {
            "coefficients_K": [
              6.479036604618679,
              -0.9560446441782259,
              0.518459509176471,
              -0.21936306175629333,
              -0.04329207243348921,
              -0.0072967965226587335,
              0.002015835395512354,
              -0.0007983583830516932
            ],
            "initial_K": [
              0.31911455135599887,
              0.6501667760422336,
              0.9882644512364734,
              1.308416438696429,
              1.5782268715760936,
              1.7769636212421782,
              1.9076259203738473,
              1.9937174591572762,
              2.062133789155841,
              2.1227231882402635,
              2.1576954651085494,
              2.1269313296100902,
              1.9840985945696679,
              1.6939899840963606,
              1.245939193637846,
              0.6624367981784227
            ],
            "metrics": {
              "initial_rmse_K": 0.021562405682167527,
              "observation_residual_rms_K": 0.019571250882450784,
              "future_predictive_rmse_K": 0.015276578002942045
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 25,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          4.283306778737242,
          -0.8084483812082601,
          0.3398528498332058,
          -0.0622226773053883,
          -0.0035226986932182097,
          -0.08115229271424697,
          0.030055471606170652,
          0.011785641010100902
        ],
        "initial_K": [
          0.2048339314372998,
          0.4098013220055975,
          0.6180742618466065,
          0.8194776145932585,
          0.9845197368073973,
          1.096113335664784,
          1.1802333273464871,
          1.280848124065097,
          1.4020878062106648,
          1.4958627734327532,
          1.5134857502352694,
          1.450727216216517,
          1.3289218300455132,
          1.146133579228077,
          0.8688692290653361,
          0.4757149689869424
        ],
        "observed_K": [
          0.20109063985394818,
          0.39361126325015217,
          0.580572199259836,
          0.7591899352315515,
          0.8872018505478337,
          1.0425371024282453,
          1.174625499775204,
          1.2371555020593303,
          1.3120122524256763,
          1.3336850501939996,
          1.3572325445531157,
          1.227253096559339,
          1.1332696548069392,
          0.8647174446940094,
          0.6297124606222827,
          0.328529763323993
        ],
        "future_observed_K": [
          0.1780523135744412,
          0.3967976251665946,
          0.508987940158789,
          0.7312068439441085,
          0.8763029501060682,
          1.014338201314435,
          1.141095958567039,
          1.2222108316384381,
          1.2543930730136383,
          1.290631546132069,
          1.2107557842427086,
          1.1623277332759236,
          1.0149147848149258,
          0.8313776924357608,
          0.5878290820153195,
          0.30076132364760516
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              4.273819114062005,
              -0.767427624352344,
              0.2712921166880089,
              0.05770508657773987,
              -0.18837332275031926,
              0.3250828868122048,
              1.3073866798671954,
              -10.359567840857567
            ],
            "initial_K": [
              -2.8219895570284668,
              0.06520472763010288,
              3.7162448453893755,
              1.612317939932338,
              -2.1693323982552775,
              -0.2742148649983496,
              4.287713377561061,
              3.3514870690162617,
              -1.442563713866699,
              -1.2929573822395322,
              3.8445630131042225,
              4.86967004050328,
              -0.22346044261066178,
              -2.6384231127605924,
              1.5083293563370401,
              4.218181473155975
            ],
            "metrics": {
              "initial_rmse_K": 2.6150597602719663,
              "observation_residual_rms_K": 0.014864724244447824,
              "future_predictive_rmse_K": 0.018889848494149583
            }
          },
          "tikhonov": {
            "coefficients_K": [
              4.222381154917798,
              -0.7508896879104442,
              0.25615512077604696,
              0.046713443934855096,
              -0.07880224269382324,
              0.02463866907645818,
              0.008186300889804009,
              -0.0033784471525466872
            ],
            "initial_K": [
              0.21766828208112507,
              0.42627706651797015,
              0.6200391764647447,
              0.796299256129771,
              0.9520220805340553,
              1.0827944705462504,
              1.1892474105987405,
              1.2832605082236936,
              1.3790279437598771,
              1.4704220978312348,
              1.519794202910426,
              1.477795337504142,
              1.318739251292476,
              1.0564472480101756,
              0.7283311068061372,
              0.3693350462592599
            ],
            "metrics": {
              "initial_rmse_K": 0.052120216034245444,
              "observation_residual_rms_K": 0.020143178607127027,
              "future_predictive_rmse_K": 0.022047715592926207
            }
          },
          "learned": {
            "coefficients_K": [
              4.273575009569299,
              -0.7692075676703336,
              0.26619143079172797,
              0.044255732424617694,
              -0.02460659582898485,
              0.0024369028139995396,
              0.001276601512804084,
              0.000912084420387747
            ],
            "initial_K": [
              0.2270727527754519,
              0.4414546407410248,
              0.6347092956237179,
              0.8035934922322598,
              0.9491814366421336,
              1.0768179075729933,
              1.1950668559731876,
              1.3101151263019892,
              1.4175830939933236,
              1.4988615504239244,
              1.5261762552765363,
              1.4732581119728492,
              1.325269998248305,
              1.0837437578083322,
              0.7652663031526893,
              0.3951175688487676
            ],
            "metrics": {
              "initial_rmse_K": 0.040908699484601733,
              "observation_residual_rms_K": 0.016364691872670017,
              "future_predictive_rmse_K": 0.01848870833388205
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 26,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.116641881602711,
          2.4612227184475195,
          0.08482416961053371,
          0.19452785559119176,
          0.04528971925385688,
          0.053946340661256684,
          0.0025878059758602688,
          -0.056755410341671225
        ],
        "initial_K": [
          0.761159223560411,
          1.4456901613052269,
          1.9626934289571962,
          2.269739556995968,
          2.416387362689052,
          2.4690576533146498,
          2.420117629762351,
          2.2281273741587744,
          1.920382161600181,
          1.582833676259372,
          1.2571759063214487,
          0.9224888232681359,
          0.5855662244992836,
          0.31417425221946005,
          0.15297883635391163,
          0.06698354528739597
        ],
        "observed_K": [
          0.5873537870622457,
          1.1077746996009894,
          1.5293607842123398,
          1.8672186717008337,
          2.064562906251434,
          2.1490887198956234,
          2.0888107503025273,
          1.9757236240687095,
          1.7622490032814146,
          1.5369184923356598,
          1.2583762897671125,
          0.9942310225925994,
          0.7210156245460542,
          0.4837416016394575,
          0.33349110876314153,
          0.1557465184825935
        ],
        "future_observed_K": [
          0.48416580147952104,
          0.9889577600692506,
          1.3753026281571918,
          1.7384027643431497,
          1.8512246317398617,
          1.9879160656369146,
          1.9402610521934591,
          1.8825924092700916,
          1.745860825995078,
          1.5198014497419245,
          1.2723188872045081,
          0.9975184559123266,
          0.7615397408802818,
          0.5798879474534615,
          0.34656826709297117,
          0.15064224708728952
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.118246409910229,
              2.456015220325437,
              0.16030392711822505,
              0.19212245641653058,
              0.06035196658233781,
              -0.33209202867266063,
              3.5488483054949214,
              -0.9370321024018595
            ],
            "initial_K": [
              1.5285616737609848,
              1.9511925574955378,
              1.483653037077863,
              1.4337081650083998,
              2.462181291501536,
              3.465070379841219,
              2.952453979223125,
              1.3714004061542866,
              0.7963042559872286,
              1.8973694308268103,
              2.6680102374103125,
              1.3329994903391253,
              -0.7194568239841963,
              -0.7898247845092343,
              0.9848218385892755,
              1.6751342359181471
            ],
            "metrics": {
              "initial_rmse_K": 0.9187571683806259,
              "observation_residual_rms_K": 0.008166180767962775,
              "future_predictive_rmse_K": 0.025415838063763536
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.0446096694521065,
              2.403088504730127,
              0.15135962044583265,
              0.1555270449919452,
              0.025247047980220615,
              -0.025169905674309247,
              0.02222138292245996,
              -0.0003055835423673754
            ],
            "initial_K": [
              0.7483970135758766,
              1.4092757097629853,
              1.923229544539541,
              2.2656907838810283,
              2.436475215190727,
              2.451428569525285,
              2.3411542797078497,
              2.1438863809594992,
              1.8884638466789316,
              1.5858592108176017,
              1.2448586170207725,
              0.8956214697828155,
              0.5879305370643069,
              0.3590329647959416,
              0.20626686082697,
              0.09667623132713454
            ],
            "metrics": {
              "initial_rmse_K": 0.03932985922974625,
              "observation_residual_rms_K": 0.021984383712750227,
              "future_predictive_rmse_K": 0.03187430925589395
            }
          },
          "learned": {
            "coefficients_K": [
              6.117896958659188,
              2.4617116114137665,
              0.15728998041696243,
              0.14734437686833238,
              0.007883581536353558,
              -0.002489445098494921,
              0.003465283213660424,
              8.249884504189548e-05
            ],
            "initial_K": [
              0.7556156005744874,
              1.4280464696950563,
              1.9548730555010991,
              2.305118632892688,
              2.4777138616015733,
              2.4927892153060496,
              2.3812809182010586,
              2.1754769011994277,
              1.9026258830532836,
              1.584510682055324,
              1.2429673364354765,
              0.9054686745108292,
              0.603407147894664,
              0.3622718156191148,
              0.1910691858327862,
              0.07895643834413357
            ],
            "metrics": {
              "initial_rmse_K": 0.030918161708831413,
              "observation_residual_rms_K": 0.011380758151769291,
              "future_predictive_rmse_K": 0.02578606342181368
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 27,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.902749875357875,
          -1.1895749598464187,
          0.5560629847147995,
          0.1232208520926766,
          -0.05019284194126841,
          0.014068316642276419,
          -0.012123126038746913,
          0.008089785793248325
        ],
        "initial_K": [
          0.4058786159668229,
          0.7788321054776566,
          1.0978168197381255,
          1.3558895461586622,
          1.5592206630731384,
          1.7287667161734566,
          1.8940446265643995,
          2.0724134706993684,
          2.2515542868101424,
          2.3941213210254535,
          2.4548762913692617,
          2.3901431105482343,
          2.1642051195184213,
          1.7679629647107242,
          1.2357063951725054,
          0.6295552837533371
        ],
        "observed_K": [
          0.37503856665395413,
          0.634233629081884,
          0.9733634976526134,
          1.2394241619720523,
          1.480443350591155,
          1.6922359084770648,
          1.8742482827400018,
          2.0368344617594514,
          2.07117676868507,
          2.165880521018924,
          2.1149220135664426,
          1.9950690259375414,
          1.7762081553118336,
          1.4469053222753436,
          1.0058211941733397,
          0.5407903747088524
        ],
        "future_observed_K": [
          0.32058064169622746,
          0.6166473036138014,
          0.9272971689758313,
          1.206137467614524,
          1.4224086273109708,
          1.6433264926278524,
          1.8134281514717123,
          1.9325665857643664,
          2.0236333319349264,
          2.0483235074815997,
          1.980000957471783,
          1.9267401288093764,
          1.6440015353028226,
          1.2967090491925748,
          0.9059660351424053,
          0.4828691739195142
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.899329478916445,
              -1.1507791034604342,
              0.5416646669546568,
              -0.012090585734313595,
              -0.043557403194064176,
              0.5262842075157317,
              1.079281889258342,
              -2.1413702578915976
            ],
            "initial_K": [
              0.16163385762053406,
              0.940728703483158,
              1.4926130189728326,
              1.1169254315915478,
              0.8819243895810609,
              1.8304507904721814,
              2.8437272049094076,
              2.3876828521996685,
              1.3500496883072688,
              1.7201333401132795,
              3.0953440288866343,
              3.195039273691401,
              1.7211034281620545,
              0.8593465010733088,
              1.4626371536020328,
              1.5919183255993026
            ],
            "metrics": {
              "initial_rmse_K": 0.6171398671021434,
              "observation_residual_rms_K": 0.01722309804474362,
              "future_predictive_rmse_K": 0.02074799886226702
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.81629193839648,
              -1.1259800070143602,
              0.5114419831942728,
              -0.00978757562521862,
              -0.018221375550936603,
              0.03988811147920238,
              0.006758005436679537,
              -0.0006983405448429555
            ],
            "initial_K": [
              0.3894236169000713,
              0.7441577504385153,
              1.0509556942720706,
              1.31803526807559,
              1.5566296995893472,
              1.7669931622822819,
              1.9437326802174701,
              2.0894355067125527,
              2.2142135894211865,
              2.3167183458380896,
              2.3673039854910973,
              2.3148877305466575,
              2.114535322835929,
              1.7523193006858053,
              1.2494684317886997,
              0.6489584140311189
            ],
            "metrics": {
              "initial_rmse_K": 0.045637247170560544,
              "observation_residual_rms_K": 0.026370359594720255,
              "future_predictive_rmse_K": 0.029018123414077675
            }
          },
          "learned": {
            "coefficients_K": [
              6.898935415134729,
              -1.1534481780554686,
              0.5314805843466587,
              -0.009272626710191823,
              -0.005689762223800103,
              0.0039451583527972236,
              0.0010538679288894144,
              0.0001885320392228774
            ],
            "initial_K": [
              0.38578142215591693,
              0.7477008785133541,
              1.069272779328413,
              1.3445046660062139,
              1.5765170999506546,
              1.7742792613528895,
              1.948813272347234,
              2.107969304301605,
              2.249727319882566,
              2.357071709487704,
              2.398553635910778,
              2.335929090163622,
              2.136206805260893,
              1.7832765701314521,
              1.2849189184965082,
              0.6733510600127524
            ],
            "metrics": {
              "initial_rmse_K": 0.03691000560612972,
              "observation_residual_rms_K": 0.017835513563259554,
              "future_predictive_rmse_K": 0.020878146958161876
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 28,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.6406118096005935,
          -0.5431435271645573,
          0.33744228998450765,
          -0.10942771804292072,
          0.04745064993508021,
          -0.010345946486991798,
          -0.04077410825347644,
          0.066183201835858
        ],
        "initial_K": [
          0.34281248097169414,
          0.6492576116121607,
          0.9311446384261063,
          1.202537550512837,
          1.4302552722029918,
          1.5838279792242016,
          1.694698157015912,
          1.803032382446307,
          1.8787018688448267,
          1.8669442655499682,
          1.7876258719125477,
          1.7036845972152648,
          1.5969095205757389,
          1.3669451739450595,
          0.9723399950120262,
          0.4891264887444734
        ],
        "observed_K": [
          0.3066453015132771,
          0.5881166028334115,
          0.8510296638900204,
          1.0832424736482653,
          1.2763579964238605,
          1.4826685021917139,
          1.5813743747870777,
          1.7012876432342816,
          1.7136391986609514,
          1.6941862828727243,
          1.675920634456302,
          1.5260853047357914,
          1.2999336712304148,
          1.1123395679608588,
          0.7634659759163643,
          0.3822193986072579
        ],
        "future_observed_K": [
          0.2879461129144908,
          0.5603183424311281,
          0.8324176112831588,
          1.0288199321441671,
          1.2510336139291172,
          1.412712249858509,
          1.518003206560815,
          1.612306867771163,
          1.637018837652268,
          1.6269961040061647,
          1.5539709917099898,
          1.414791046386628,
          1.19796880868333,
          1.016476289430241,
          0.742536560971142,
          0.4023527148782608
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.628929956053728,
              -0.5350841634767386,
              0.30851386531230035,
              -0.08497969357214809,
              0.1810595740030616,
              0.34073756257910537,
              1.564224105451792,
              -0.9102889841111867
            ],
            "initial_K": [
              0.6838640071839017,
              1.0175793678188019,
              0.8740146988138506,
              0.6844580579315441,
              1.0963002595078022,
              1.9606771327625234,
              2.2859501831159195,
              1.6968039731347047,
              1.1994514329389248,
              1.6959295267713579,
              2.441825006133329,
              2.1351236610700646,
              1.0599112548056935,
              0.691453793342581,
              1.2511273567054428,
              1.2682867589158007
            ],
            "metrics": {
              "initial_rmse_K": 0.4790788132939318,
              "observation_residual_rms_K": 0.01707600705358473,
              "future_predictive_rmse_K": 0.022158968455328665
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.5611824306256095,
              -0.5235531896026699,
              0.2913000473251511,
              -0.06879279430480989,
              0.0757426809927911,
              0.02582516763226413,
              0.009794507916826596,
              -0.00029686211564115556
            ],
            "initial_K": [
              0.35411933068948714,
              0.6678288174140964,
              0.9296534726260165,
              1.1564743837065876,
              1.366676708438249,
              1.5575159860261483,
              1.708816570558553,
              1.8040652363077971,
              1.8435487580209264,
              1.8378401359056336,
              1.792444998255447,
              1.6993950676866532,
              1.5397342879942426,
              1.2918744433348213,
              0.9426796247970675,
              0.49999773265111425
            ],
            "metrics": {
              "initial_rmse_K": 0.03496309082210032,
              "observation_residual_rms_K": 0.023546099009999207,
              "future_predictive_rmse_K": 0.025217856668683293
            }
          },
          "learned": {
            "coefficients_K": [
              5.628608452720356,
              -0.5363252179437916,
              0.3027133564703303,
              -0.06517343276469079,
              0.023651224565204305,
              0.0025542541879912694,
              0.0015273911614176894,
              8.014430845115964e-05
            ],
            "initial_K": [
              0.33568155812584655,
              0.6529485836135329,
              0.9395936785444102,
              1.1906195989874977,
              1.4044425618912821,
              1.5792073321046536,
              1.7126474187775986,
              1.8040545553899716,
              1.8546229657566533,
              1.86460790979107,
              1.8291468942533384,
              1.7359088561884881,
              1.5668865581343063,
              1.3049917177467756,
              0.943921529110723,
              0.49708491065799404
            ],
            "metrics": {
              "initial_rmse_K": 0.02530682886860087,
              "observation_residual_rms_K": 0.017883568768920128,
              "future_predictive_rmse_K": 0.022839646672024958
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 29,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.865598047616838,
          1.1594584966852544,
          1.1816455600113083,
          -0.13644139107315814,
          -0.03355377529238353,
          0.03992511401523205,
          -0.06812152423943357,
          -0.03380774850898304
        ],
        "initial_K": [
          0.6642346808874976,
          1.296337722994137,
          1.8015650359632795,
          2.0842216947361916,
          2.1466356017946677,
          2.0721972245665676,
          1.925615906991389,
          1.7268184764940528,
          1.5168134840473182,
          1.3773366211777778,
          1.3497588776705274,
          1.37155582718621,
          1.3273962568617819,
          1.146987149055827,
          0.8360961943720563,
          0.4385420528383221
        ],
        "observed_K": [
          0.5267726532136907,
          1.0135225328078223,
          1.3595026771163303,
          1.6239935528483096,
          1.8122460041762942,
          1.8433576074581388,
          1.8003721086938695,
          1.6978354178476145,
          1.601193954381169,
          1.536962639465645,
          1.3623229665773346,
          1.293350241699473,
          1.0689095053809368,
          0.8986383286593398,
          0.6455150384150796,
          0.33182409261730256
        ],
        "future_observed_K": [
          0.47077542075155365,
          0.8827521453741254,
          1.2215184050771721,
          1.4449429766433828,
          1.652402238454147,
          1.7150049157492755,
          1.736543867452097,
          1.703018556738923,
          1.6284434885778853,
          1.4792520428774172,
          1.3612217545557181,
          1.1918563943719958,
          1.0441631120003099,
          0.8263729533892459,
          0.5740067965288765,
          0.3120955312848904
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.906873794673363,
              1.18247590782593,
              1.205652431615787,
              -0.06487573972920022,
              -0.026750609182382708,
              -0.1561573882673384,
              4.444714894094053,
              11.463275562209322
            ],
            "initial_K": [
              6.047662547531349,
              2.8266263484846266,
              -2.978660243544719,
              -0.6339968183262867,
              6.01303675011261,
              5.657435291212886,
              -0.738464058079991,
              -2.1996773527006868,
              2.989355256753464,
              5.176738161504694,
              0.8662713000968565,
              -1.9020992817529718,
              1.304146967748597,
              3.8745888713122625,
              0.9649852328324103,
              -1.9496882535753972
            ],
            "metrics": {
              "initial_rmse_K": 3.088234156478546,
              "observation_residual_rms_K": 0.01657116224516951,
              "future_predictive_rmse_K": 0.017916358846709945
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.835781049563799,
              1.1569937505681602,
              1.138381933116183,
              -0.05251823383870129,
              -0.011190586682976405,
              -0.011835474488035996,
              0.027830919538007953,
              0.003738386704632863
            ],
            "initial_K": [
              0.7083378040240867,
              1.3203546243088753,
              1.775093884978092,
              2.048861956000778,
              2.1390452874435915,
              2.0653773400327706,
              1.8849070506433074,
              1.6829342937738123,
              1.530081234562559,
              1.4449632159219856,
              1.3989291258518712,
              1.3489214513093717,
              1.2582938006404067,
              1.094335763205771,
              0.8275297982099317,
              0.4506091801162819
            ],
            "metrics": {
              "initial_rmse_K": 0.038410464509983644,
              "observation_residual_rms_K": 0.026558976154010126,
              "future_predictive_rmse_K": 0.022914233523222388
            }
          },
          "learned": {
            "coefficients_K": [
              5.906536416232058,
              1.1852184988195689,
              1.1829844144657287,
              -0.04975511776482076,
              -0.0034943452646025303,
              -0.001170594929272077,
              0.00434005474062172,
              -0.0010092578385043143
            ],
            "initial_K": [
              0.7209964347595831,
              1.3511993258369404,
              1.8198013450982207,
              2.090126951449092,
              2.164720108748474,
              2.081767743391978,
              1.904707314343102,
              1.7056373342063522,
              1.5438657076524138,
              1.446383590457947,
              1.4007630822335715,
              1.364815438395623,
              1.2857913286537737,
              1.1184102199312504,
              0.838203111054088,
              0.4516903727857497
            ],
            "metrics": {
              "initial_rmse_K": 0.034255180531530635,
              "observation_residual_rms_K": 0.019666833425823066,
              "future_predictive_rmse_K": 0.017253586957017206
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 30,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          6.179127131300785,
          0.05175556735951481,
          0.5422124694295783,
          0.033425838254586754,
          0.15619315001592052,
          0.05557074116139579,
          -0.009340100160998475,
          -0.0018217944252887984
        ],
        "initial_K": [
          0.5575957385645471,
          1.0204175871983903,
          1.3445666871481852,
          1.5525997583516806,
          1.7022233950980217,
          1.8334697721407343,
          1.940470425685729,
          1.9915935039203914,
          1.9724427264998117,
          1.9033500910535994,
          1.8140784806732049,
          1.7069465856286483,
          1.5492483240213002,
          1.3002890243221827,
          0.9434748123369251,
          0.4964421051941876
        ],
        "observed_K": [
          0.4101792371549849,
          0.7538388586669387,
          1.098386542800314,
          1.3526934896127882,
          1.523009168163553,
          1.7299231310149086,
          1.7977856273534163,
          1.8265446922304809,
          1.861480333871437,
          1.7744020041492252,
          1.6979281733283875,
          1.5216634216958946,
          1.3346632362463522,
          1.0905731667119654,
          0.7210249319886733,
          0.387366801720877
        ],
        "future_observed_K": [
          0.35178815348429215,
          0.7010015750832624,
          1.0467187509168183,
          1.2620722927512904,
          1.472621990313729,
          1.6375198630784518,
          1.707441822465312,
          1.7691997695840795,
          1.7784768152921173,
          1.7478796894641175,
          1.5994882967145343,
          1.5006162254703985,
          1.297380771046932,
          0.9928942262891418,
          0.6811802936857779,
          0.36569439701290235
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              6.1512751038505185,
              0.04480091246731826,
              0.4839917230982003,
              0.029610431893787814,
              0.19336570670479603,
              0.5194995263050157,
              -0.7258606898699232,
              7.147870229518491
            ],
            "initial_K": [
              2.9016834619812073,
              1.4566643075213723,
              -0.901297714958649,
              0.7019660295531422,
              3.7159535992870643,
              2.9231021391256116,
              0.059664038437578615,
              0.640509576536848,
              3.7579917532899456,
              3.619811179160614,
              0.20806997423832296,
              -0.4521680833499553,
              2.7817127809139146,
              3.836679223163075,
              0.23034406996482149,
              -2.324597319414161
            ],
            "metrics": {
              "initial_rmse_K": 1.8002141856016844,
              "observation_residual_rms_K": 0.016615826767092844,
              "future_predictive_rmse_K": 0.021257487592911357
            }
          },
          "tikhonov": {
            "coefficients_K": [
              6.0772408433841445,
              0.04383546032640932,
              0.45698695486755503,
              0.023970248243087862,
              0.08089070748415278,
              0.03937388719388445,
              -0.004545031781996972,
              0.0023310530125058714
            ],
            "initial_K": [
              0.5100348610770059,
              0.9484179717544265,
              1.2812546790485921,
              1.5193811917130498,
              1.6939082787976625,
              1.8262909389006248,
              1.9172041379176488,
              1.9572670447938312,
              1.9445398242951506,
              1.8904744956554485,
              1.8075105521233954,
              1.6904069520174034,
              1.5129739361863366,
              1.2477153410356838,
              0.8899375550134244,
              0.4623232589891201
            ],
            "metrics": {
              "initial_rmse_K": 0.03854329953763981,
              "observation_residual_rms_K": 0.02439412227916095,
              "future_predictive_rmse_K": 0.03110089584871363
            }
          },
          "learned": {
            "coefficients_K": [
              6.150923766124555,
              0.04490482205078332,
              0.47489197561544266,
              0.022709113330996147,
              0.025258734743334975,
              0.0038942986816019355,
              -0.0007087687744126993,
              -0.0006293178610776415
            ],
            "initial_K": [
              0.49188634333995757,
              0.9353031021061595,
              1.2960907490162832,
              1.5625331208277224,
              1.7434071332751016,
              1.8577294920200285,
              1.9236171958498578,
              1.9528954958201132,
              1.9511655455224948,
              1.9183413020431996,
              1.84739285806909,
              1.7241657552607823,
              1.5314110982573161,
              1.2561596149165097,
              0.8969858565920535,
              0.4683019104700259
            ],
            "metrics": {
              "initial_rmse_K": 0.03982732831472189,
              "observation_residual_rms_K": 0.017773945847279825,
              "future_predictive_rmse_K": 0.021321433060939105
            }
          }
        }
      },
      {
        "split": "validation",
        "index": 31,
        "scenario": "smooth",
        "true_kappa_m2_per_s": 0.01,
        "coefficients_K": [
          5.596084706878826,
          -2.105944780334851,
          0.3180650407721406,
          0.10770899727867181,
          -0.1199456547922617,
          -0.046438251559060645,
          -0.01044340309963642,
          0.04574716750367415
        ],
        "initial_K": [
          0.13916917525471365,
          0.28991004502494605,
          0.47734741128372915,
          0.7022321954399421,
          0.9220342311986209,
          1.1128554089439309,
          1.3221048202648675,
          1.6073228743422665,
          1.9373832699118891,
          2.205529284249816,
          2.331778269614763,
          2.30089433958059,
          2.107855176830157,
          1.73592656005862,
          1.2092582567982761,
          0.6085331702904185
        ],
        "observed_K": [
          0.16740719331590895,
          0.34717152190169703,
          0.5330993617226113,
          0.7062718901035817,
          0.9814724195027538,
          1.177378367379673,
          1.4225794535886036,
          1.589608329196372,
          1.8206942496016818,
          1.9252496198098523,
          1.9508712058080686,
          1.8850055391185634,
          1.7040217216382016,
          1.3965084564520374,
          0.9821570831785874,
          0.49764099670147743
        ],
        "future_observed_K": [
          0.1636890757082007,
          0.3423262728777894,
          0.5511073237342213,
          0.74298829527286,
          0.9194861125465064,
          1.157206363524721,
          1.380967497756116,
          1.521877156378086,
          1.6736889170357074,
          1.7878657471131463,
          1.7986325150220346,
          1.7025454656972674,
          1.5194100024653776,
          1.2680322932072083,
          0.9016742297407354,
          0.43839449751915477
        ],
        "x_m": [
          0.058823529411764705,
          0.11764705882352941,
          0.17647058823529413,
          0.23529411764705882,
          0.29411764705882354,
          0.35294117647058826,
          0.4117647058823529,
          0.47058823529411764,
          0.5294117647058824,
          0.5882352941176471,
          0.6470588235294118,
          0.7058823529411765,
          0.7647058823529411,
          0.8235294117647058,
          0.8823529411764706,
          0.9411764705882353
        ],
        "estimators": {
          "least_squares": {
            "coefficients_K": [
              5.65805288886674,
              -2.0905099411668537,
              0.25851271169193324,
              0.04318990087464245,
              -0.22769794951271455,
              0.27645529630762655,
              0.4926417126367078,
              16.368558647283493
            ],
            "initial_K": [
              5.929737100252583,
              1.433262150521593,
              -5.079627929764625,
              -1.5625535650957096,
              5.953985676535179,
              4.345197147323315,
              -2.923112672154173,
              -2.227188609459213,
              5.511941524186195,
              6.630243098456368,
              -0.4615643757096606,
              -2.5748745899967727,
              4.0986581284159325,
              7.0153985898808475,
              0.15527591333683932,
              -4.922778052528069
            ],
            "metrics": {
              "initial_rmse_K": 4.083617632702631,
              "observation_residual_rms_K": 0.01279035972877624,
              "future_predictive_rmse_K": 0.024008474929491038
            }
          },
          "tikhonov": {
            "coefficients_K": [
              5.589954851592374,
              -2.0454598029634576,
              0.24408875456467496,
              0.0349631052080917,
              -0.09525292019279005,
              0.020953088693631203,
              0.0030847134613013766,
              0.00533809046890035
            ],
            "initial_K": [
              0.13422237438420556,
              0.28205668677981355,
              0.45865178751305036,
              0.6708018997956925,
              0.9087194730801332,
              1.1561587146867722,
              1.407743508979591,
              1.667844815255006,
              1.929241759187509,
              2.156499264687669,
              2.291864397259183,
              2.277359771669432,
              2.0787307416329095,
              1.7017447398831145,
              1.1913432844794702,
              0.6084358977921696
            ],
            "metrics": {
              "initial_rmse_K": 0.03659550064146101,
              "observation_residual_rms_K": 0.022983671852048127,
              "future_predictive_rmse_K": 0.017960798952342538
            }
          },
          "learned": {
            "coefficients_K": [
              5.65772972214085,
              -2.0953585927958733,
              0.25365229717405474,
              0.03312360850509969,
              -0.029743444204009345,
              0.0020723782052123655,
              0.0004810414281460329,
              -0.001441132251435166
            ],
            "initial_K": [
              0.14257269622320967,
              0.2967784746408793,
              0.4704765084167021,
              0.6679621835136963,
              0.892069564645855,
              1.1437237457053093,
              1.4186609583831777,
              1.7039041391489231,
              1.974820390674925,
              2.1934926693085233,
              2.312659075769741,
              2.2884063526196767,
              2.0960695816721016,
              1.7383652498448148,
              1.2415728653322942,
              0.6462266309837834
            ],
            "metrics": {
              "initial_rmse_K": 0.04066629143617883,
              "observation_residual_rms_K": 0.015551503189830448,
              "future_predictive_rmse_K": 0.023939440950301996
            }
          }
        }
      }
    ],
    "test": {
      "smooth": [
        {
          "split": "test",
          "index": 0,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.064136750230109,
            1.768324303923217,
            0.2456775890493475,
            0.005338822758752014,
            0.08703779952503056,
            0.008671880120626883,
            -0.009365291777447502,
            -0.002943137637902704
          ],
          "initial_K": [
            0.6692855762874994,
            1.2664598933935682,
            1.736654368808024,
            2.0574636298236393,
            2.2394901043514093,
            2.305931789950305,
            2.2695599894446725,
            2.132380473991563,
            1.90631236400416,
            1.6267097319388422,
            1.3403251111018104,
            1.0804804834308834,
            0.8538973310738912,
            0.6469957081128842,
            0.44120325626692913,
            0.2252954098552855
          ],
          "observed_K": [
            0.5507147014287179,
            0.9840400511592335,
            1.4006330639942592,
            1.7267819363081736,
            1.9204949993776659,
            2.0250030134982313,
            2.0096705892518227,
            1.947653337074254,
            1.7953884448190913,
            1.5801617904154344,
            1.3557633585792002,
            1.1554403316332083,
            0.8656189854216914,
            0.6238605767909828,
            0.47441704629894454,
            0.21996669488076245
          ],
          "future_observed_K": [
            0.47080114079585883,
            0.8844597816698365,
            1.2590501240068845,
            1.5719571248643656,
            1.7508615005615376,
            1.888186652647225,
            1.9107584939633184,
            1.7697082102519308,
            1.7017978546694303,
            1.5284508864090756,
            1.3180193483166613,
            1.1487678023181138,
            0.9272364143436105,
            0.6537839088426031,
            0.43521893190499916,
            0.2298059569267655
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.110819678615166,
                1.8017809741668627,
                0.2228236936016802,
                0.037373020120453807,
                0.21941131555389853,
                -0.4082124388380277,
                2.8456679416074033,
                -8.24275050140351
              ],
              "initial_K": [
                -1.2844066287901088,
                1.2096606159238545,
                3.8576074528615765,
                2.3334177666114932,
                -0.04418647228689898,
                1.7253250547121914,
                4.76154317228474,
                3.241918706450608,
                -0.6379175484328496,
                -0.09971890026343022,
                3.841484778648319,
                3.6535095743385235,
                -1.2140073389206476,
                -2.7593637150080146,
                1.613914612745325,
                4.132855534642596
              ],
              "metrics": {
                "initial_rmse_K": 2.1829138006023263,
                "observation_residual_rms_K": 0.017685063928849973,
                "future_predictive_rmse_K": 0.025806303199984892
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.037272323292616,
                1.762952896720285,
                0.21039103842425105,
                0.03025422165723763,
                0.09178637126323155,
                -0.030939220738599886,
                0.01781836572239958,
                -0.002688113769648737
              ],
              "initial_K": [
                0.6645054416436189,
                1.255213981625933,
                1.721641866535585,
                2.0451655383894263,
                2.2308167042171645,
                2.2935423103349337,
                2.2503004396762494,
                2.1182268884142124,
                1.9134327249267633,
                1.6518866127838339,
                1.3570394026205963,
                1.0658859302972237,
                0.8160551797385223,
                0.6168173368158227,
                0.43707320481511364,
                0.23448174119860032
              ],
              "metrics": {
                "initial_rmse_K": 0.01758385574252485,
                "observation_residual_rms_K": 0.02635872256207588,
                "future_predictive_rmse_K": 0.02318147150347596
              }
            },
            "learned": {
              "coefficients_K": [
                6.1104706515511165,
                1.8059599584823616,
                0.2186342844688731,
                0.028662471134540977,
                0.028660988102316036,
                -0.003060062775585814,
                0.0027786607092884818,
                0.0007257140866265212
              ],
              "initial_K": [
                0.6630539466660632,
                1.2605141069646029,
                1.743213819787576,
                2.0853198339794528,
                2.2815669096881996,
                2.3413153459336185,
                2.28354354621114,
                2.1323947526975613,
                1.9132947686036106,
                1.6514466329104458,
                1.3720770455985223,
                1.0984729884126174,
                0.8462742111130879,
                0.6186176917880157,
                0.4078924781590681,
                0.20365648228068525
              ],
              "metrics": {
                "initial_rmse_K": 0.023109836180847654,
                "observation_residual_rms_K": 0.019598532576784494,
                "future_predictive_rmse_K": 0.02551775225785468
              }
            }
          }
        },
        {
          "split": "test",
          "index": 1,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.184809778754638,
            -2.9132134703184316,
            0.12478018733153877,
            0.44910633776766584,
            -0.04817235905362789,
            0.06297486629680303,
            0.022310270053648815,
            -0.0271975656568205
          ],
          "initial_K": [
            0.15936968186868739,
            0.28851202182038094,
            0.38171436211981635,
            0.4810999040850209,
            0.6611364175348915,
            0.9671936865354203,
            1.3763207707564038,
            1.8286623041396564,
            2.271857602126564,
            2.6462488760941696,
            2.8525291209434225,
            2.791285766741742,
            2.449223902575053,
            1.9147878565538514,
            1.2970411488360951,
            0.6536436012780684
          ],
          "observed_K": [
            0.14655953318417025,
            0.3191245815515799,
            0.4387456663626663,
            0.6756964813137301,
            0.8562643170759252,
            1.1730384070225763,
            1.4507418899459141,
            1.7712146798472834,
            2.1047579079505514,
            2.2202545677651018,
            2.2635601146127087,
            2.1892843457383524,
            1.9446399447479659,
            1.6007046867459638,
            1.0995317418206403,
            0.5690306505631353
          ],
          "future_observed_K": [
            0.164622215540105,
            0.3055918179006152,
            0.47795770735044396,
            0.7215408465958086,
            0.9282848077241933,
            1.2336476571108195,
            1.4452837093334123,
            1.7028852734999234,
            1.8809963656659778,
            2.0712207835919463,
            2.088934325875657,
            1.9796360817330059,
            1.7730176818074999,
            1.4654947953376163,
            1.0368688607464176,
            0.5306486476136644
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.201054259012774,
                -2.8509822712210418,
                0.030036920422250618,
                0.562097026089272,
                0.3609844149169502,
                -0.05578214346064461,
                -3.021152254120767,
                15.830995085298742
              ],
              "initial_K": [
                4.664700002380062,
                0.8668111153576967,
                -4.067896956573935,
                -0.5778520532847056,
                5.2189320857808195,
                2.6726341360144557,
                -3.3524222653879407,
                -0.8718214628640131,
                6.963302289049258,
                6.726870887426945,
                -1.0989777360841613,
                -2.444209195159779,
                5.184979075118021,
                7.813482937237027,
                -0.1645316308506306,
                -5.667964528242572
              ],
              "metrics": {
                "initial_rmse_K": 4.038504755564548,
                "observation_residual_rms_K": 0.01762553691747143,
                "future_predictive_rmse_K": 0.02212821633916307
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.1264208767583375,
                -2.7895440819999697,
                0.028360982517418646,
                0.4550290012787017,
                0.15101066890813278,
                -0.004227837972585451,
                -0.018917174059517348,
                0.005162781024220861
              ],
              "initial_K": [
                0.1863087788615361,
                0.32418464108111844,
                0.4055994510884732,
                0.47868037074100267,
                0.6277756953287869,
                0.924648972839322,
                1.3754857849177275,
                1.9004194291669916,
                2.3687180122218523,
                2.668009412561035,
                2.7511584421540047,
                2.627536404479759,
                2.325261605735029,
                1.8723687542419465,
                1.3042242797550359,
                0.6663623664432279
              ],
              "metrics": {
                "initial_rmse_K": 0.06845258338715389,
                "observation_residual_rms_K": 0.02899210310505043,
                "future_predictive_rmse_K": 0.026527919393663977
              }
            },
            "learned": {
              "coefficients_K": [
                6.200700078088468,
                -2.8575947343150685,
                0.0294721826840668,
                0.4310887836511152,
                0.04715422262948275,
                -0.00041815693130810267,
                -0.0029500128748549087,
                -0.0013938036989910474
              ],
              "initial_K": [
                0.15299780279646247,
                0.2790781749550375,
                0.37730913031268876,
                0.4848040320671192,
                0.663700918437274,
                0.9653969873296951,
                1.3933255860011942,
                1.890043634877061,
                2.3565815374827492,
                2.6895315975832914,
                2.814787564092497,
                2.705503299324282,
                2.381775050635003,
                1.895126625305048,
                1.3056612256106097,
                0.6631181657590892
              ],
              "metrics": {
                "initial_rmse_K": 0.04120371798147193,
                "observation_residual_rms_K": 0.02211128655482009,
                "future_predictive_rmse_K": 0.020401481109668718
              }
            }
          }
        },
        {
          "split": "test",
          "index": 2,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.475793918696814,
            -0.03163023368275662,
            0.3355965009422605,
            0.11297519515169935,
            0.19505591894691615,
            -0.03313017528591373,
            0.11145245560602077,
            0.05838141932070094
          ],
          "initial_K": [
            0.5278243832025117,
            0.8918796777488686,
            1.105806779562422,
            1.2877547244560041,
            1.4755562725067433,
            1.6136283539542802,
            1.6873441083119647,
            1.7533741839079795,
            1.8243029018841872,
            1.8227323945420035,
            1.6926124073808857,
            1.4860629535636722,
            1.2877276387135923,
            1.0977279370986268,
            0.8401054764614775,
            0.46391701582748557
          ],
          "observed_K": [
            0.3440450969191118,
            0.6563028222315517,
            0.961663253020174,
            1.213938494556134,
            1.3828618060256441,
            1.5215864211944699,
            1.6229994075836047,
            1.6378644162154792,
            1.668153663377168,
            1.6007460778559794,
            1.5507218798140892,
            1.3990354648053762,
            1.1652290223769233,
            0.9469181478621504,
            0.6670655068710739,
            0.3435010341844119
          ],
          "future_observed_K": [
            0.321437548388602,
            0.6296621228820362,
            0.8420392126641965,
            1.1299915235821687,
            1.3114355752040487,
            1.4598056518460178,
            1.5452825515324276,
            1.6134870619438288,
            1.6108281861019982,
            1.5463116041162883,
            1.4699655847342372,
            1.30410087908099,
            1.1053185568223731,
            0.8417623881558164,
            0.6299436483857795,
            0.29768814909351393
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.517670107088666,
                0.011193117124321805,
                0.36219962862562854,
                0.06310106187480244,
                -0.11943984742097807,
                -0.6117697858588157,
                1.6887877467463974,
                -11.466863746639735
              ],
              "initial_K": [
                -3.15059385054582,
                0.19438718360742602,
                4.557187094979813,
                2.5076087614328944,
                -1.6847128475098987,
                0.11162121512810552,
                4.85071371511145,
                3.7981938400525004,
                -1.2660790204511032,
                -0.9740651852371622,
                4.439753330255375,
                5.089495983435562,
                -0.7532413215114601,
                -3.1272607313568828,
                1.9264274542023714,
                5.025791663641687
              ],
              "metrics": {
                "initial_rmse_K": 2.9128999376937474,
                "observation_residual_rms_K": 0.010649653995616608,
                "future_predictive_rmse_K": 0.020801699575480836
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.451261660225344,
                0.01095190732978907,
                0.3419903635546299,
                0.05108159593777456,
                -0.049965290766020534,
                -0.04636723099317924,
                0.010574472607663771,
                -0.0037395568781051513
              ],
              "initial_K": [
                0.39277941965895113,
                0.7729173218491807,
                1.113973153513946,
                1.3817580546573556,
                1.5561678043284577,
                1.647075619060052,
                1.6890067440590173,
                1.7175845559459189,
                1.7438789053754522,
                1.7460445248759233,
                1.6876248659126316,
                1.5482564252112792,
                1.3363181444876855,
                1.0709719433275773,
                0.7588181129404159,
                0.3974854188939201
              ],
              "metrics": {
                "initial_rmse_K": 0.0709457387428857,
                "observation_residual_rms_K": 0.02002034450061139,
                "future_predictive_rmse_K": 0.02378167186619053
              }
            },
            "learned": {
              "coefficients_K": [
                5.517354958499907,
                0.011219078027214406,
                0.3553897494447545,
                0.04839406498902577,
                -0.015602039654304739,
                -0.004585979678285767,
                0.001649021689987272,
                0.0010095737519832096
              ],
              "initial_K": [
                0.41968825684972966,
                0.8058251005715646,
                1.1319502131319905,
                1.3827835678370872,
                1.555997153302954,
                1.662529624647935,
                1.7226179509947739,
                1.7555277034954042,
                1.768228755032686,
                1.7519693033651138,
                1.6890905091747792,
                1.5633318785157735,
                1.366244368948626,
                1.0986562721915092,
                0.7699670195737178,
                0.3966692121162674
              ],
              "metrics": {
                "initial_rmse_K": 0.06551037512845585,
                "observation_residual_rms_K": 0.013275983577527023,
                "future_predictive_rmse_K": 0.020587986194882908
              }
            }
          }
        },
        {
          "split": "test",
          "index": 3,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.6585834541058055,
            1.133465957070806,
            0.1259019836794421,
            -0.2656798847535495,
            -0.13024952652174732,
            -0.005406078317735114,
            0.03481519825014512,
            0.01213347660713752
          ],
          "initial_K": [
            0.43673684386642164,
            0.8735621263519217,
            1.3121912055988982,
            1.725504221351472,
            2.038014362866824,
            2.1708752648936187,
            2.11486860159269,
            1.9421184811672547,
            1.7409655519247713,
            1.5527277437091729,
            1.3720364756844161,
            1.1842514944711797,
            0.984198961186709,
            0.7689227434886668,
            0.5326367185585184,
            0.2736690301047573
          ],
          "observed_K": [
            0.39103591093042145,
            0.7891445970916956,
            1.140172152345368,
            1.464577004639208,
            1.651333315690986,
            1.8262482089193135,
            1.8091498763321876,
            1.7748025356980788,
            1.6739312299419806,
            1.5635715995147539,
            1.3293917351074798,
            1.1580972762311676,
            0.9379560838016231,
            0.743041794764672,
            0.5009027917710401,
            0.2309618111372512
          ],
          "future_observed_K": [
            0.35786526126672374,
            0.7553194843667762,
            1.0592802813240203,
            1.3516400839189946,
            1.5592577907766387,
            1.6873999636840804,
            1.7009404190245512,
            1.6912866248492895,
            1.615396215001487,
            1.4494333534205188,
            1.3133483114235769,
            1.1541663329422571,
            0.9437649640867316,
            0.7288586046941087,
            0.46121160855649534,
            0.22329444935806175
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.654059473951637,
                1.0947223892814426,
                0.10043358399737799,
                -0.30826794202014784,
                -0.25796451218967587,
                -0.7348008273871549,
                -0.7504737599723837,
                15.060021807716987
              ],
              "initial_K": [
                5.038597353243754,
                1.4065081637077803,
                -3.4736202922088264,
                0.3418692798367249,
                6.811480505559753,
                4.5625880019906155,
                -2.347994485031557,
                -1.481359727139743,
                5.529625869761196,
                5.813675263712923,
                -1.4966261192323629,
                -3.609751091080841,
                2.8801503345246227,
                5.8669772228957076,
                -0.384928193875291,
                -4.926013924513974
              ],
              "metrics": {
                "initial_rmse_K": 3.7716701680376126,
                "observation_residual_rms_K": 0.015080660291783196,
                "future_predictive_rmse_K": 0.01700627929491252
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.586009499804833,
                1.0711313056131422,
                0.09482979878993564,
                -0.24954918327817457,
                -0.10791433627206701,
                -0.05569199474212391,
                -0.004699148387882117,
                0.00491135234357041
              ],
              "initial_K": [
                0.3977274380667526,
                0.8321489013004719,
                1.291200968115373,
                1.705540213844447,
                1.990106283862643,
                2.10197559808942,
                2.063212183027295,
                1.931918011369053,
                1.7574417924949342,
                1.5638827527494594,
                1.362973608322689,
                1.1644927569337815,
                0.9698117570850251,
                0.766276459013338,
                0.5374518164643977,
                0.2784645560571296
              ],
              "metrics": {
                "initial_rmse_K": 0.030638358925497784,
                "observation_residual_rms_K": 0.02392596166307639,
                "future_predictive_rmse_K": 0.022938594227407166
              }
            },
            "learned": {
              "coefficients_K": [
                5.653736535314606,
                1.0972614480018001,
                0.09854528671965981,
                -0.2364197745159256,
                -0.03369706706339782,
                -0.005508251208016897,
                -0.0007328022780512293,
                -0.0013259251227975269
              ],
              "initial_K": [
                0.4438395837448642,
                0.8907473746708503,
                1.323489953882226,
                1.701557295924911,
                1.9767453846237704,
                2.1146536892182546,
                2.1093996998538027,
                1.9860480102179774,
                1.7905262568050206,
                1.5710029563546302,
                1.3598264566239964,
                1.165655080421717,
                0.9778911225641993,
                0.777542343285087,
                0.5483197919595125,
                0.28547742780326674
              ],
              "metrics": {
                "initial_rmse_K": 0.029268162866841807,
                "observation_residual_rms_K": 0.01843088191995334,
                "future_predictive_rmse_K": 0.017780972014318393
              }
            }
          }
        },
        {
          "split": "test",
          "index": 4,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.497192439893651,
            -1.1318418722730608,
            0.05168256978725702,
            -0.18610872515166946,
            0.08827460384575889,
            0.1058831793403847,
            0.048580982748094505,
            -0.0148131148411177
          ],
          "initial_K": [
            0.30321572873227864,
            0.5617413082720306,
            0.7902803061899073,
            1.0532463002224979,
            1.388903920832873,
            1.7498622146955727,
            2.036075868432583,
            2.190034646177437,
            2.2415015981346706,
            2.2500976270261432,
            2.22578715102297,
            2.126522155893968,
            1.9160221134049606,
            1.5907736973059834,
            1.1558515488792591,
            0.6148055197359373
          ],
          "observed_K": [
            0.26480376691271623,
            0.571227330239715,
            0.8522606474047275,
            1.1064242827641273,
            1.3850085401189913,
            1.6356551449785228,
            1.8351589782665885,
            1.9661750145823875,
            2.023000191702992,
            2.047130731151915,
            2.003536808117417,
            1.8510004494966485,
            1.6356999793826437,
            1.3594402254180458,
            0.9165632571431261,
            0.4734558922577891
          ],
          "future_observed_K": [
            0.2631780363383735,
            0.527967729137781,
            0.7933965749591194,
            1.0702725503123123,
            1.309149475945426,
            1.5844981172473516,
            1.7666264237373492,
            1.8532709339168578,
            1.9393448185868645,
            1.939911884963833,
            1.8952168803520413,
            1.7210112901390178,
            1.5059176790091882,
            1.207453276637641,
            0.8837190018663588,
            0.44724613084945125
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.523282563076323,
                -1.0958701023776256,
                0.13248700716250783,
                -0.29448397396857384,
                -0.056725794093168636,
                0.9577590127016201,
                -0.6078433266695028,
                0.841990282263732
              ],
              "initial_K": [
                0.5968050216562484,
                0.6818931905693834,
                0.6013343030255749,
                0.927378435108819,
                1.5118681310583244,
                1.8679545139018114,
                2.0317312051211966,
                2.278969522710311,
                2.387381158348318,
                2.0533670506945776,
                1.7321603947628021,
                2.0541668343374258,
                2.553641724922024,
                2.111771441514247,
                0.7590587533547253,
                -0.15880587554430053
              ],
              "metrics": {
                "initial_rmse_K": 0.34748846208947004,
                "observation_residual_rms_K": 0.01214223093187898,
                "future_predictive_rmse_K": 0.022725261811148673
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.444770971216573,
                -1.072254285684821,
                0.12509477140464664,
                -0.2383907801465965,
                -0.02373011065401586,
                0.07259043255199912,
                -0.003806057108124615,
                0.0002745886426233788
              ],
              "initial_K": [
                0.25546004682782153,
                0.519127649003242,
                0.8052210116653389,
                1.1237061612659618,
                1.4600271625877705,
                1.7692869532417297,
                1.9995795420708156,
                2.128597136955466,
                2.17859279970256,
                2.190978013070146,
                2.180897130299543,
                2.114797201985564,
                1.9341419065649306,
                1.6035024650458805,
                1.13773540517911,
                0.5865840592993085
              ],
              "metrics": {
                "initial_rmse_K": 0.04405036838288038,
                "observation_residual_rms_K": 0.023036250529201833,
                "future_predictive_rmse_K": 0.024408124678531012
              }
            },
            "learned": {
              "coefficients_K": [
                6.522909977681777,
                -1.098411823061394,
                0.12999605896569225,
                -0.22584844297450032,
                -0.007409906391994411,
                0.007179601658128172,
                -0.0005935303780615066,
                -7.413110569553055e-05
              ],
              "initial_K": [
                0.24625119486486172,
                0.516591683562727,
                0.8219232205742681,
                1.1526498007705568,
                1.4807646646470216,
                1.7708304855538022,
                1.994833259727852,
                2.142865958976898,
                2.2227275404631945,
                2.247869093460094,
                2.2213711170696437,
                2.127307470465779,
                1.93612701046115,
                1.6209260998242645,
                1.1745730673938788,
                0.6184663241187105
              ],
              "metrics": {
                "initial_rmse_K": 0.04403443242905255,
                "observation_residual_rms_K": 0.014463971533513054,
                "future_predictive_rmse_K": 0.023096011716496053
              }
            }
          }
        },
        {
          "split": "test",
          "index": 5,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.522111901523194,
            -0.9107309638742822,
            0.0861641534473814,
            0.14234900537895906,
            -0.05158663102566782,
            -0.021699515731567264,
            0.04003948010891521,
            0.02107881625588748
          ],
          "initial_K": [
            0.283267362181444,
            0.5344415686118913,
            0.7646303525156298,
            0.9991045959623999,
            1.227647472964337,
            1.4205383823248134,
            1.5822299776933995,
            1.7469385084480342,
            1.9145905840938824,
            2.0248965575937863,
            2.010792694242107,
            1.8569880366735307,
            1.5941585746014602,
            1.2571350769444802,
            0.8673251780698562,
            0.4420954797125666
          ],
          "observed_K": [
            0.22946450666024265,
            0.4951461462134451,
            0.7020482572951237,
            0.9585276419326555,
            1.1582043884132946,
            1.3854606392654014,
            1.5010693519695044,
            1.6898622406741155,
            1.7348004172030236,
            1.781731779558528,
            1.7186343136122548,
            1.6107153362376418,
            1.3839871778755604,
            1.1052374024557476,
            0.7844379062616171,
            0.39904787860565627
          ],
          "future_observed_K": [
            0.2507230205076721,
            0.481636149065752,
            0.7149442957580335,
            0.9221888583489533,
            1.1350310942067878,
            1.3352325219868373,
            1.4350255252652853,
            1.5927529194304242,
            1.6735122974750403,
            1.6746950118569082,
            1.6072158812116921,
            1.4703592403773535,
            1.2620753340582294,
            1.0121579991037855,
            0.7000764890933109,
            0.3756872658928409
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.551119391042541,
                -0.9660579337139248,
                0.05801967241200236,
                0.03977878391116654,
                -0.11116671829175294,
                -0.21540874432270984,
                0.7011100366455738,
                -1.2803703923561198
              ],
              "initial_K": [
                -0.05272708702511675,
                0.4462425131169237,
                0.9966146409291603,
                1.0056885014460748,
                0.9395475875996138,
                1.4304611511522967,
                1.9880321829753596,
                1.8418686212097108,
                1.4595643657287194,
                1.8075502912310413,
                2.5013215697381703,
                2.2780191111489225,
                1.2011411724544738,
                0.696122445357656,
                1.144850408558569,
                1.175145256974019
              ],
              "metrics": {
                "initial_rmse_K": 0.36971886663560594,
                "observation_residual_rms_K": 0.014710792776826907,
                "future_predictive_rmse_K": 0.017088369268152492
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.48430836211959,
                -0.9452395474583646,
                0.054782410840101076,
                0.032201736488647936,
                -0.04650439131401767,
                -0.01632625088200545,
                0.004390053688955437,
                -0.0004175525246526633
              ],
              "initial_K": [
                0.2294284849925547,
                0.46988454632690935,
                0.7219622234234249,
                0.9739703494957226,
                1.2100914117072434,
                1.4212358653900874,
                1.608220694635449,
                1.7731089511515492,
                1.9059402855535519,
                1.9802722659569085,
                1.964136886087805,
                1.8381072386805062,
                1.6046985332251702,
                1.2824502296612428,
                0.8937225483857828,
                0.4590967637309068
              ],
              "metrics": {
                "initial_rmse_K": 0.03309537463522557,
                "observation_residual_rms_K": 0.021543767991629683,
                "future_predictive_rmse_K": 0.016643985931113228
              }
            },
            "learned": {
              "coefficients_K": [
                5.550802331956339,
                -0.9682985728430622,
                0.056928818286229595,
                0.030507522323489165,
                -0.014521347644674096,
                -0.001614757947881036,
                0.0006846009273360383,
                0.00011272727831251815
              ],
              "initial_K": [
                0.24298823803840658,
                0.4868179500317189,
                0.7308749703819541,
                0.9723844092521674,
                1.20686311056154,
                1.4290265920219376,
                1.6324537995413007,
                1.8072355239432876,
                1.93748594746056,
                2.002033630627548,
                1.979595932068239,
                1.8559549164389595,
                1.628915186914685,
                1.308654747877322,
                0.9143495434857347,
                0.4697575453692854
              ],
              "metrics": {
                "initial_rmse_K": 0.03645717409218684,
                "observation_residual_rms_K": 0.015020101402323157,
                "future_predictive_rmse_K": 0.01724137692011433
              }
            }
          }
        },
        {
          "split": "test",
          "index": 6,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.822054874763854,
            2.859774744073671,
            0.01098550497731065,
            0.20400532732130353,
            0.19347015101728815,
            -0.04255049655318044,
            -0.0029728544021611013,
            0.015425310860645847
          ],
          "initial_K": [
            0.8145816491780948,
            1.5078681757408505,
            2.011162252461714,
            2.316015379202442,
            2.4498783424008685,
            2.454162718378249,
            2.364985242977714,
            2.1887361951255975,
            1.9013079337848486,
            1.4950204763071726,
            1.0281990941025625,
            0.6075143363283373,
            0.312627063818542,
            0.14817496616012849,
            0.06821903065889945,
            0.027213012889801047
          ],
          "observed_K": [
            0.5587308123367705,
            1.1126814099685005,
            1.6081323969335033,
            1.8668973466318743,
            2.0639204547244487,
            2.1588800149329677,
            2.09438704053271,
            1.9391106857814189,
            1.6786874822537488,
            1.4041135435034962,
            1.097946177836374,
            0.801519784679524,
            0.6150448917471212,
            0.35810201194710206,
            0.21481582976455554,
            0.05604593632857429
          ],
          "future_observed_K": [
            0.5534400855427049,
            1.0201004944194811,
            1.4229622132820419,
            1.697046592066237,
            1.9162810657036073,
            2.0072110680781874,
            1.9421342849899017,
            1.8211897092403848,
            1.630071896581667,
            1.3809625045609002,
            1.0863026409156922,
            0.8725036307756532,
            0.6429232992225138,
            0.43154939391333424,
            0.25184878510846365,
            0.13906964315524117
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.856219147045664,
                2.862813631308267,
                0.04211079711788782,
                0.10528559014273652,
                0.02093621085374217,
                1.0773069986577037,
                -4.75511582178158,
                -5.078264936851195
              ],
              "initial_K": [
                -2.2108833466845805,
                0.5591470661837951,
                4.688446603269374,
                4.079177896987524,
                0.418603094890737,
                0.13195546848710882,
                3.5769379714005543,
                4.829565165300567,
                1.7588205035748379,
                -0.9081504296514447,
                0.20116242143692065,
                2.184044890496782,
                1.5627812565207027,
                -0.3420570381577517,
                -0.7854583280749686,
                -0.1617234019757965
              ],
              "metrics": {
                "initial_rmse_K": 1.764657946579031,
                "observation_residual_rms_K": 0.018817078078112403,
                "future_predictive_rmse_K": 0.017314551461966955
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.785736060797554,
                2.8011204782639827,
                0.039761186035911625,
                0.08523083152565797,
                0.008758248486025874,
                0.08165120869316396,
                -0.029774518497408784,
                -0.001656116353436841
              ],
              "initial_K": [
                0.7556750039359452,
                1.4252273328856209,
                1.945026285142077,
                2.2907046368556054,
                2.4730504836395504,
                2.5101608974183622,
                2.4043637925185024,
                2.15485488728496,
                1.7926394823733638,
                1.388454942438428,
                1.0133286661791856,
                0.6943832998075756,
                0.420069037445018,
                0.18746390437678317,
                0.02797713245480904,
                -0.026868362772013932
              ],
              "metrics": {
                "initial_rmse_K": 0.06626153422907366,
                "observation_residual_rms_K": 0.02936245958168826,
                "future_predictive_rmse_K": 0.02843445703442181
              }
            },
            "learned": {
              "coefficients_K": [
                5.855884661807542,
                2.869453535622367,
                0.04131905295826163,
                0.0807466235969975,
                0.002734829280212218,
                0.008075763330128619,
                -0.004643146626108835,
                0.00044710420382940597
              ],
              "initial_K": [
                0.752578101483776,
                1.4312003621041094,
                1.975367878571336,
                2.347779647347283,
                2.537085812583848,
                2.5530228466449905,
                2.417891504596474,
                2.160661962923977,
                1.8162641375420168,
                1.4259603342106761,
                1.0332971529213153,
                0.6764180887817447,
                0.38300877042314674,
                0.17041200751849372,
                0.045445645410599256,
                -0.0010821368052415514
              ],
              "metrics": {
                "initial_rmse_K": 0.059435407887922447,
                "observation_residual_rms_K": 0.02257924998015176,
                "future_predictive_rmse_K": 0.01739749193969649
              }
            }
          }
        },
        {
          "split": "test",
          "index": 7,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.719353124787714,
            -0.11954545828251328,
            -0.014730721284114578,
            -0.03840727740350079,
            -0.09190249194734669,
            0.021902025373027635,
            -0.030855775710861892,
            -0.05555103725941407
          ],
          "initial_K": [
            0.34956135749198214,
            0.7538996496880537,
            1.1737183638902817,
            1.5311234348259508,
            1.8122026740506352,
            2.0473586914027346,
            2.2234188656702405,
            2.2939911250825205,
            2.265959811023671,
            2.197634059837623,
            2.102094289196215,
            1.921444261010157,
            1.6183074142594482,
            1.2342617886866465,
            0.830394862101637,
            0.42143147071060677
          ],
          "observed_K": [
            0.3657793418015168,
            0.7400537596845799,
            1.0602250577558385,
            1.3487407579581536,
            1.6605769685778031,
            1.852677572994155,
            1.979400143291499,
            2.061112742411319,
            2.0843591699959263,
            2.0115116889854967,
            1.9293599226879823,
            1.6952002691040988,
            1.4524583996373113,
            1.1097149701882,
            0.7468292557454911,
            0.3993441507503656
          ],
          "future_observed_K": [
            0.349827558556264,
            0.7007912403814902,
            1.04344204763713,
            1.3364688261718485,
            1.574752781278396,
            1.7847429143646516,
            1.8937646391905114,
            1.9350771843653862,
            1.96832540881527,
            1.8970966694774825,
            1.8061742866526782,
            1.5962801628210361,
            1.3701079653016413,
            1.0488814356862322,
            0.7368226901865073,
            0.3790994777312517
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.714832949967143,
                -0.14249669010309532,
                -0.023933869811991356,
                0.0685711462703781,
                -0.3853092517765346,
                0.2971789049391848,
                2.8216470270856395,
                3.8600075567335455
              ],
              "initial_K": [
                2.6520480277229233,
                1.5221411108649647,
                -0.8126105065924366,
                0.1276428458072878,
                3.2015432158809314,
                3.788121998768187,
                1.5442693682984705,
                0.5548291481080693,
                2.2663714416804903,
                3.547948082867666,
                2.4437670704243386,
                1.0873265571745778,
                1.3689624756611174,
                1.8216747015510422,
                0.8919128640165261,
                -0.16346855100572788
              ],
              "metrics": {
                "initial_rmse_K": 1.2155840289287962,
                "observation_residual_rms_K": 0.012872038273365468,
                "future_predictive_rmse_K": 0.018368981560275343
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.634015935085971,
                -0.13942591035875798,
                -0.02259845729088895,
                0.05550974076669541,
                -0.1611864818614209,
                0.022523771605149588,
                0.017667956943610893,
                0.0012588200337298643
              ],
              "initial_K": [
                0.3786382481483923,
                0.758047527219552,
                1.136646824365133,
                1.4987473271749105,
                1.8083730115279417,
                2.0281448238445714,
                2.1509661770783945,
                2.206981648950474,
                2.2307600641659957,
                2.220708091289563,
                2.135060994778576,
                1.9300497801388479,
                1.6021609296062678,
                1.1955467957674561,
                0.772077495191749,
                0.37284425349893163
              ],
              "metrics": {
                "initial_rmse_K": 0.041035461978011535,
                "observation_residual_rms_K": 0.023705716572973955,
                "future_predictive_rmse_K": 0.023797070264076663
              }
            },
            "learned": {
              "coefficients_K": [
                6.714449423934078,
                -0.1428271916687624,
                -0.023483878291103037,
                0.052589234006310596,
                -0.05033169712783909,
                0.0022277275706794053,
                0.00275520541768299,
                -0.00033984552340015365
              ],
              "initial_K": [
                0.4010969225728459,
                0.7941808831557561,
                1.1680121537431836,
                1.5072016174465483,
                1.7950831227626023,
                2.0194167984408495,
                2.176633336860165,
                2.269715251581612,
                2.299789346525163,
                2.2587985505892045,
                2.1318748628177624,
                1.9095512578441283,
                1.5995190237466463,
                1.226986412190774,
                0.8230899473690828,
                0.41105084499379463
              ],
              "metrics": {
                "initial_rmse_K": 0.03083854219879584,
                "observation_residual_rms_K": 0.015987765572132048,
                "future_predictive_rmse_K": 0.019026221576578285
              }
            }
          }
        },
        {
          "split": "test",
          "index": 8,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.741946397165456,
            -0.7547739471050924,
            -0.10218431985307472,
            -0.1775817626729975,
            0.05262716988903501,
            0.026150007209080988,
            -0.07053828811899616,
            0.002862834288456887
          ],
          "initial_K": [
            0.20902450387344565,
            0.4569837803302624,
            0.7417696146874112,
            1.033055127711684,
            1.3144900875986631,
            1.5889335395774755,
            1.8388635753487748,
            2.008740479929308,
            2.051753622396379,
            1.9860908173922844,
            1.8774396818036143,
            1.7586924334003362,
            1.5889648418847242,
            1.307658581090374,
            0.9124277363699712,
            0.4601208711818634
          ],
          "observed_K": [
            0.2531990271047843,
            0.47806311967032744,
            0.7733438684814068,
            1.0047965362735032,
            1.2245136852342406,
            1.4759395824306205,
            1.6620373379811049,
            1.7459639785683865,
            1.8453741855553385,
            1.8485968947443665,
            1.710711199228356,
            1.5892527139298962,
            1.3578535117204267,
            1.0445704762794064,
            0.7751686774443695,
            0.39966444611260454
          ],
          "future_observed_K": [
            0.23491801859575584,
            0.4790552135929122,
            0.7538107440330398,
            1.031919088846628,
            1.1911710895764844,
            1.4191190741159432,
            1.57423457027785,
            1.651785183092697,
            1.740978441207573,
            1.6903605872884555,
            1.6302621363173264,
            1.482518158128174,
            1.2475017948515463,
            1.0331443855988287,
            0.6853187491851755,
            0.3564901436614085
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.743778821891298,
                -0.7645910228121421,
                -0.18952616898321792,
                -0.0916698988724467,
                0.2047893841314144,
                -0.6703945658544991,
                1.7425201213525343,
                -8.785748426620676
              ],
              "initial_K": [
                -2.3636869378296232,
                0.09047638967011307,
                3.275965048166,
                1.746223711535602,
                -1.189768589383949,
                0.4748127230774053,
                4.2334410572713566,
                3.482433738116997,
                -0.26215207468640944,
                0.10156128921383134,
                4.1718155057921145,
                4.366911002747732,
                -0.33947853923098725,
                -2.0857357343609975,
                1.980901138052569,
                4.281089078184255
              ],
              "metrics": {
                "initial_rmse_K": 2.2506985797879047,
                "observation_residual_rms_K": 0.01793902651977965,
                "future_predictive_rmse_K": 0.02059889178937174
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.674649021942185,
                -0.7481142146571246,
                -0.17895138015362572,
                -0.07420865187894492,
                0.08566957631698388,
                -0.050810517959645224,
                0.010910921948033508,
                -0.002865195460938365
              ],
              "initial_K": [
                0.22596231942376485,
                0.466100395335183,
                0.7257527184131048,
                1.0004064544973414,
                1.2799625840573565,
                1.5504409950426323,
                1.7913216266372587,
                1.9739716141103916,
                2.066907651158247,
                2.049056434760591,
                1.924647789401908,
                1.7250519070122574,
                1.4865382703571277,
                1.21748165159547,
                0.8907086145918885,
                0.478806631003855
              ],
              "metrics": {
                "initial_rmse_K": 0.046659657047601825,
                "observation_residual_rms_K": 0.02510528294163103,
                "future_predictive_rmse_K": 0.022032383535296393
              }
            },
            "learned": {
              "coefficients_K": [
                5.743450758822153,
                -0.7663643870211746,
                -0.1859628016841209,
                -0.07030434848105312,
                0.026750972652680977,
                -0.0050254457256760565,
                0.0017014888229059874,
                0.0007735210951332053
              ],
              "initial_K": [
                0.22380871510607586,
                0.4612499340357672,
                0.7219881381208006,
                1.0063094943169584,
                1.3012799951216423,
                1.5825235769925101,
                1.8209323250080103,
                1.990005706467787,
                2.0713570211724206,
                2.0583729949299143,
                1.9566372118572175,
                1.7787460508810096,
                1.5355262954022684,
                1.2309588385346384,
                0.8661025620700301,
                0.44877016938309405
              ],
              "metrics": {
                "initial_rmse_K": 0.03994395766759109,
                "observation_residual_rms_K": 0.019694280684279024,
                "future_predictive_rmse_K": 0.0205626744574229
              }
            }
          }
        },
        {
          "split": "test",
          "index": 9,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.532372949943475,
            1.3849097516507591,
            -0.09422401342588824,
            -0.03524605733377563,
            -0.025646583943571666,
            -0.0831566784603012,
            -0.01762022259597104,
            0.07964854294653081
          ],
          "initial_K": [
            0.4839574394355701,
            0.9351547677474741,
            1.3622024364767942,
            1.7509843342159965,
            2.0172033574167254,
            2.099278519113066,
            2.0538080357090918,
            1.975758667266523,
            1.8592949267868726,
            1.6324365906416383,
            1.309718035529355,
            1.003360580909578,
            0.7743099223400631,
            0.5731268825445451,
            0.35467535559633,
            0.15371155854292184
          ],
          "observed_K": [
            0.44155812316956433,
            0.818889134013198,
            1.1581743133427864,
            1.4496631543418648,
            1.7198737438915732,
            1.804465933555315,
            1.8182740652829998,
            1.782081420405512,
            1.6695194808257254,
            1.4728037145020112,
            1.2776134196540245,
            1.0173228143298525,
            0.8069554100998367,
            0.5930215782336836,
            0.3980586132688287,
            0.15155309825893715
          ],
          "future_observed_K": [
            0.38839691863561565,
            0.759317167015431,
            1.1069085109605663,
            1.385705918827578,
            1.539490987658397,
            1.704524300660901,
            1.7221411414640602,
            1.7125931528354352,
            1.6122738219963095,
            1.4510326964706828,
            1.2446593120447416,
            1.060164683572225,
            0.8338784948269288,
            0.6085126824819194,
            0.4435041982710188,
            0.1814430834091808
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.5031286267337896,
                1.44201112232901,
                -0.14042620543412687,
                -0.0715280419719976,
                -0.07672640859903569,
                -0.07568582641197184,
                0.761473642664676,
                27.549282895434015
              ],
              "initial_K": [
                10.099615459022724,
                2.77530820200697,
                -7.900413732217186,
                -1.8872789979922315,
                10.52791984116405,
                7.35967398639818,
                -5.34677114915004,
                -4.5860438511789585,
                7.973735682758224,
                9.221700953025952,
                -3.407031149839569,
                -7.401717975146257,
                3.913788083585229,
                9.420905426910988,
                -1.2734458653047724,
                -8.99622906869343
              ],
              "metrics": {
                "initial_rmse_K": 6.8702166564012614,
                "observation_residual_rms_K": 0.012793754066373382,
                "future_predictive_rmse_K": 0.022928023837691037
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.436895195249552,
                1.4109360247786504,
                -0.13259099472642608,
                -0.05790340811511422,
                -0.03209697096791488,
                -0.00573637710994026,
                0.004768024987941099,
                0.008984331951155748
              ],
              "initial_K": [
                0.4742585509571381,
                0.928472427361191,
                1.346108538092255,
                1.7033859627627257,
                1.9630203080494697,
                2.0929500273927135,
                2.090982556551459,
                1.9824544275947926,
                1.796479016353584,
                1.554731485177163,
                1.2805257911105978,
                1.0029961421516869,
                0.7453609940360311,
                0.5165884623888468,
                0.31796614575872856,
                0.1487606717821822
              ],
              "metrics": {
                "initial_rmse_K": 0.038168151180243484,
                "observation_residual_rms_K": 0.023986169477275048,
                "future_predictive_rmse_K": 0.03373365493329928
              }
            },
            "learned": {
              "coefficients_K": [
                5.502814308699762,
                1.44535566972372,
                -0.13778598877663428,
                -0.05485696450875221,
                -0.010022521757544457,
                -0.0005673599283304084,
                0.00074354314538749,
                -0.0024255135067197905
              ],
              "initial_K": [
                0.48484854102071034,
                0.9512905682960715,
                1.3747424185351802,
                1.7261020516763346,
                1.978734411897171,
                2.1140382653809935,
                2.1249906098374702,
                2.0199228985822333,
                1.8232240300707963,
                1.5684033981660215,
                1.287621063856453,
                1.0064954773713553,
                0.7447651995568925,
                0.5155415665553071,
                0.3214047928904621,
                0.15403274656862073
              ],
              "metrics": {
                "initial_rmse_K": 0.03618368170719808,
                "observation_residual_rms_K": 0.018004318503568602,
                "future_predictive_rmse_K": 0.022900265552218434
              }
            }
          }
        },
        {
          "split": "test",
          "index": 10,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.857473922033986,
            0.046136057016025515,
            -0.07095537977773908,
            0.12194996194946563,
            0.006794916496936428,
            0.027784206927363494,
            -0.02724361969343163,
            -0.030469329332704697
          ],
          "initial_K": [
            0.444276913309555,
            0.883206469405026,
            1.2769678216603402,
            1.5903639493515624,
            1.8416072662703498,
            2.0694430306306715,
            2.26446962898741,
            2.374867444941711,
            2.375157191549243,
            2.28703670998618,
            2.1287681326633145,
            1.8867571251653548,
            1.55425957052406,
            1.16527537367356,
            0.7672151460065686,
            0.3802355866274073
          ],
          "observed_K": [
            0.39917071706276713,
            0.814358737822797,
            1.1507191003202535,
            1.4156969904155978,
            1.653233683470469,
            1.9143876617287303,
            2.065964901499801,
            2.1375892768385905,
            2.143598071037763,
            2.091505236673818,
            1.9275901221379057,
            1.7106733243688474,
            1.3945345334719268,
            1.0824017753312338,
            0.7027190069730027,
            0.3982979644232937
          ],
          "future_observed_K": [
            0.40456504768316986,
            0.7605835154894912,
            1.0746882125238384,
            1.373288848468681,
            1.6236483791674046,
            1.833458257011421,
            1.9359088284945924,
            2.036862768788482,
            2.006835262123448,
            1.9613527692982382,
            1.8471989677190963,
            1.6052081365854352,
            1.3834749862886375,
            1.0532436993904393,
            0.7121444525815436,
            0.34660602478019253
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.87068423456452,
                0.03940996581290863,
                -0.1378679300022201,
                0.39619781791127184,
                0.3287082878086594,
                0.7461554858062489,
                3.2277689186153804,
                -16.3145096092123
              ],
              "initial_K": [
                -3.6834664801502166,
                0.8206702011187614,
                5.944119574736854,
                2.313227230930569,
                -3.2854264971747353,
                0.17139721045288203,
                7.325048628489941,
                5.46749326538857,
                -2.2485249102844307,
                -1.8867009546485098,
                6.1179827248954695,
                7.1948503789884874,
                -1.3142094260159065,
                -4.967346897878924,
                2.1798172822687905,
                6.809386691701624
              ],
              "metrics": {
                "initial_rmse_K": 4.156806683792659,
                "observation_residual_rms_K": 0.01390108131410153,
                "future_predictive_rmse_K": 0.01768884437499992
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.7879914566255914,
                0.03856068766717942,
                -0.13017546065105853,
                0.3207302103112973,
                0.13750859141398872,
                0.0565525865561307,
                0.020210919980634127,
                -0.005320464075447013
              ],
              "initial_K": [
                0.5430555924454558,
                0.9837050876594761,
                1.2914004280423141,
                1.517260144016175,
                1.7362808678138046,
                1.9782979384234005,
                2.2098902580678024,
                2.3720946938764973,
                2.4238324788811743,
                2.3513760141000315,
                2.1567155726414957,
                1.856066425012521,
                1.4864874933446588,
                1.0957601973285689,
                0.716515433750932,
                0.3541805620198175
              ],
              "metrics": {
                "initial_rmse_K": 0.0655285660864906,
                "observation_residual_rms_K": 0.026370336218149625,
                "future_predictive_rmse_K": 0.026187076461226425
              }
            },
            "learned": {
              "coefficients_K": [
                6.870291806891552,
                0.039501371833600266,
                -0.135275812639221,
                0.30385578909195365,
                0.042938096890004565,
                0.005593368574005708,
                0.0031517643157454884,
                0.001436373627685703
              ],
              "initial_K": [
                0.49868672232142097,
                0.9389886774550649,
                1.2933958660500329,
                1.572427786423545,
                1.806607151294926,
                2.0206457899647488,
                2.216243105081618,
                2.3689056285018593,
                2.4378687514067012,
                2.385534502267022,
                2.1976026972717575,
                1.8919780953371024,
                1.5111907884460043,
                1.1044503782269726,
                0.7099358302013854,
                0.34405462012991483
              ],
              "metrics": {
                "initial_rmse_K": 0.0507295410102595,
                "observation_residual_rms_K": 0.01939106129641369,
                "future_predictive_rmse_K": 0.017782314315136487
              }
            }
          }
        },
        {
          "split": "test",
          "index": 11,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.064394954021725,
            -2.411669180940734,
            -0.2575990270640851,
            0.06749840108382132,
            -0.006010335171964219,
            0.02343749436883363,
            -0.008668201445281585,
            -0.00471828157506624
          ],
          "initial_K": [
            0.05355825429045091,
            0.1406599895020456,
            0.28637507542741825,
            0.5080112293201009,
            0.814850180579118,
            1.196333949462685,
            1.611846148847614,
            2.0016692178773012,
            2.311745072083807,
            2.505627852630594,
            2.556998580112885,
            2.4441909835927373,
            2.1611320324986574,
            1.730215694816407,
            1.1968745093761335,
            0.6088293651942323
          ],
          "observed_K": [
            0.14633884787455628,
            0.258539672676809,
            0.43334517265677813,
            0.6588925758020291,
            0.9545751600662032,
            1.2484118189404168,
            1.5319511427334753,
            1.8381295740019954,
            2.0139489449462777,
            2.126194676128678,
            2.125099841505565,
            2.028288018479076,
            1.7846292988924772,
            1.4543193119033622,
            1.0457007985533666,
            0.5237839236762536
          ],
          "future_observed_K": [
            0.17036844959736508,
            0.3201548531457458,
            0.5079730419510254,
            0.7164959075872694,
            1.0070355479830586,
            1.277067078017321,
            1.5063897056210083,
            1.7038078882396916,
            1.8930127955675982,
            1.9664081301063476,
            1.969449708977189,
            1.8441876345519272,
            1.6382863256204983,
            1.3147800040500932,
            0.9197987729640801,
            0.4823006602530954
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.052894587528758,
                -2.432653643579365,
                -0.30182058218537594,
                -0.09280436490895347,
                0.2521322263515765,
                0.31999760236710156,
                1.1555737265335493,
                7.251807598964827
              ],
              "initial_K": [
                3.0293577733235275,
                0.899963022703189,
                -2.430812246302726,
                -0.9250541387849852,
                2.972962595974709,
                2.9277263062118393,
                -0.060728303362707514,
                0.16819767149597897,
                3.6877110416575194,
                4.512100985903855,
                1.500073760922494,
                0.23924941368289754,
                2.756517025386312,
                3.93895777060542,
                0.9983324784146478,
                -1.4748982313655825
              ],
              "metrics": {
                "initial_rmse_K": 1.8404387678343004,
                "observation_residual_rms_K": 0.010898745528106666,
                "future_predictive_rmse_K": 0.017079686021201405
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.980044395186019,
                -2.3802303660401654,
                -0.284980222154052,
                -0.07512702526221612,
                0.10547451519038002,
                0.024253245402418577,
                0.007235712564179301,
                0.002364948915814141
              ],
              "initial_K": [
                0.052667845215150666,
                0.12067541283307248,
                0.2401568707110583,
                0.4566134122443629,
                0.7894069877580719,
                1.2088691247848282,
                1.647150739839909,
                2.029934708952122,
                2.303682628547647,
                2.44531637053854,
                2.4554576766520433,
                2.342525347478875,
                2.108530994457414,
                1.7475462227954661,
                1.2584438864081449,
                0.660723389847123
              ],
              "metrics": {
                "initial_rmse_K": 0.05119069854979872,
                "observation_residual_rms_K": 0.022426286756526245,
                "future_predictive_rmse_K": 0.02051809622821588
              }
            },
            "learned": {
              "coefficients_K": [
                6.05254886892831,
                -2.438295850688506,
                -0.2961459167894378,
                -0.0711744039360228,
                0.03293521449169665,
                0.002398782246978061,
                0.001128363314516279,
                -0.0006384687886862436
              ],
              "initial_K": [
                0.019334055244192794,
                0.08295822077709203,
                0.22748023747527513,
                0.47328419792601695,
                0.8165171382019153,
                1.2260629970001151,
                1.6499816376214986,
                2.030378899002646,
                2.318929793887708,
                2.4848275482823734,
                2.5135469834695865,
                2.4011191750959138,
                2.1492022199980276,
                1.7636260052972064,
                1.2572043189447353,
                0.6554239436429863
              ],
              "metrics": {
                "initial_rmse_K": 0.038436083009071136,
                "observation_residual_rms_K": 0.012806840717223685,
                "future_predictive_rmse_K": 0.01749235724867332
              }
            }
          }
        },
        {
          "split": "test",
          "index": 12,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.219832099640153,
            2.6671383183638744,
            -0.18560462213307943,
            -0.05593799433153152,
            -0.014870897683554967,
            -0.1263067944977912,
            0.05443173497232211,
            0.048045278628120774
          ],
          "initial_K": [
            0.6045295703027185,
            1.1603591519624197,
            1.6604200402432898,
            2.08445452884174,
            2.3482091776596183,
            2.377935949832441,
            2.2132139243525604,
            1.9656371449834946,
            1.6833966684907709,
            1.3282592178162518,
            0.8948914898501101,
            0.48033556531978916,
            0.1982367009796796,
            0.06899379915315695,
            0.02903553827756067,
            0.014182441698113724
          ],
          "observed_K": [
            0.5235696961574455,
            0.9727078916337731,
            1.411323751158781,
            1.6576787033130753,
            1.8776370070025186,
            1.9550593132928804,
            1.959174707917386,
            1.739045926340727,
            1.4995802577010313,
            1.253410559007289,
            0.9710081961134086,
            0.681237116623414,
            0.4585195969774089,
            0.2818649512836774,
            0.1512051604952864,
            0.0629505969634188
          ],
          "future_observed_K": [
            0.44877472005460056,
            0.8603833852522365,
            1.2413300086383368,
            1.5094209602699225,
            1.7112054592947268,
            1.809426428253352,
            1.7474600495625157,
            1.6442864942555193,
            1.4977537420315241,
            1.2037013864524755,
            0.9645281249691608,
            0.7826512176256233,
            0.5014928954902508,
            0.3412146547094185,
            0.21471608202588324,
            0.11004006659798704
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.226964914098197,
                2.685889061180446,
                -0.16927067756726655,
                -0.07420577921069789,
                0.06815078861258109,
                1.0213151605302315,
                3.4816420339431366,
                -8.631714238662207
              ],
              "initial_K": [
                -0.8526653268744275,
                1.577651990906224,
                3.677538627017281,
                1.725410099367216,
                -0.3808906806132426,
                2.1165175303741233,
                5.418423162482705,
                3.266434326061099,
                -1.4484997649064932,
                -1.0200314295364947,
                3.4612802232284556,
                3.592682159093191,
                -1.5650330836829185,
                -3.4977081743103695,
                0.915985552841312,
                3.7849212759899755
              ],
              "metrics": {
                "initial_rmse_K": 2.350650540814834,
                "observation_residual_rms_K": 0.016126945062290725,
                "future_predictive_rmse_K": 0.02156616380234658
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.1640552774186865,
                2.6280086029140617,
                -0.15982606271582442,
                -0.060071090996999935,
                0.02850953046648936,
                0.0774074775508281,
                0.021800565754075872,
                -0.002814962056254174
              ],
              "initial_K": [
                0.6461519537603969,
                1.211883634147717,
                1.6628624172423119,
                2.0062791222604943,
                2.2444114705240192,
                2.3447274475661644,
                2.2652473430025375,
                2.0069163338296865,
                1.6315116191430434,
                1.2248920974870512,
                0.8482616812607007,
                0.5262422705862485,
                0.2691189618730543,
                0.0898479094334913,
                -0.0036423338765532165,
                -0.02294356971653383
              ],
              "metrics": {
                "initial_rmse_K": 0.05720398183899973,
                "observation_residual_rms_K": 0.025852651320619115,
                "future_predictive_rmse_K": 0.023456883432141837
              }
            },
            "learned": {
              "coefficients_K": [
                5.226666369497995,
                2.692118613174152,
                -0.16608814293167964,
                -0.05691060015454065,
                0.008902316348897783,
                0.007656034475029991,
                0.0033996594550172307,
                0.0007599595078930596
              ],
              "initial_K": [
                0.6260084143740043,
                1.2049545016752232,
                1.6976176996087133,
                2.072886373520567,
                2.304105076027497,
                2.3711006943337636,
                2.2696388630762394,
                2.0196107571299784,
                1.663749561337347,
                1.2576744048481228,
                0.8576182363359708,
                0.510345988399785,
                0.24639974620180705,
                0.07707105778048051,
                -0.004625048081320027,
                -0.02004398026269988
              ],
              "metrics": {
                "initial_rmse_K": 0.039054401707380906,
                "observation_residual_rms_K": 0.019472193725430218,
                "future_predictive_rmse_K": 0.021901880882213974
              }
            }
          }
        },
        {
          "split": "test",
          "index": 13,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.026781424113795,
            0.3370523805996143,
            -0.11418621892443814,
            -0.04510213638445195,
            0.024253871011956536,
            -0.0023616910011002618,
            0.02941545941533061,
            -0.012254116718890413
          ],
          "initial_K": [
            0.40199636783922166,
            0.7860627753051285,
            1.140768053437169,
            1.4625466139078,
            1.7451804799377721,
            1.9667235841282846,
            2.097070559001417,
            2.1246530488048445,
            2.066180086039314,
            1.942559683631435,
            1.7574610824364496,
            1.5129367780173046,
            1.2334071407771263,
            0.9500994114422118,
            0.6639388909469914,
            0.3491361760616862
          ],
          "observed_K": [
            0.37497706077092197,
            0.7346808824959127,
            1.0325091330177967,
            1.3221031852691765,
            1.565796091275526,
            1.7447038815129277,
            1.8158886170415336,
            1.869409938070565,
            1.859697510915666,
            1.7719177804490203,
            1.613726186876061,
            1.421256154326004,
            1.1743994168683458,
            0.9193379575129619,
            0.5991454245011502,
            0.34183011973597516
          ],
          "future_observed_K": [
            0.29433366843605907,
            0.7132485945926919,
            0.9572686362020101,
            1.2470275939593813,
            1.446985104661002,
            1.6984327998571491,
            1.7832240639869115,
            1.8082214724787702,
            1.7538255070548616,
            1.6924462353688912,
            1.563880907554171,
            1.3319821292854357,
            1.1400590764290424,
            0.88694396356966,
            0.5672577730836031,
            0.32286789827550266
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.010678856873694,
                0.31567022398687383,
                -0.029005403026029896,
                0.049587024376378006,
                0.02560248704218681,
                -0.31373685108285077,
                2.3778666427186543,
                9.952332274074655
              ],
              "initial_K": [
                4.518365442842016,
                1.8049072502990113,
                -2.6239243781952855,
                -0.37243911280636033,
                5.006190183998746,
                4.481756330441149,
                -0.5036178789534653,
                -0.9232236520591679,
                3.762057816412665,
                5.0753961710060125,
                0.8253315934339382,
                -1.4406756767724773,
                1.6649652601565625,
                3.6821552224348557,
                0.5423964100069371,
                -2.188238654187562
              ],
              "metrics": {
                "initial_rmse_K": 2.560787226456003,
                "observation_residual_rms_K": 0.010906669180217677,
                "future_predictive_rmse_K": 0.03004811019720539
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.9383367559992,
                0.308867583665839,
                -0.027387019593477953,
                0.04014170709165501,
                0.010710292561638484,
                -0.0237787307930052,
                0.014889192396468612,
                0.0032456400835503053
              ],
              "initial_K": [
                0.41851897124313425,
                0.812379247583937,
                1.1670368197951855,
                1.4736648242176122,
                1.7204542071218876,
                1.8965735947721996,
                2.002362178389381,
                2.0458412562658634,
                2.0269428323760956,
                1.9334903525455436,
                1.7586948579247363,
                1.5181751369783736,
                1.2427422805190842,
                0.9545375280008191,
                0.6548243458444684,
                0.3358120076054163
              ],
              "metrics": {
                "initial_rmse_K": 0.039139836608866385,
                "observation_residual_rms_K": 0.020871232501950863,
                "future_predictive_rmse_K": 0.03655011372430162
              }
            },
            "learned": {
              "coefficients_K": [
                6.010335549477191,
                0.3164023778578631,
                -0.028460059313367,
                0.03802975114815142,
                0.003344369795392617,
                -0.002351850085854626,
                0.0023218747751425446,
                -0.0008762302977451445
              ],
              "initial_K": [
                0.42231749178855177,
                0.8228964615322348,
                1.1834068820456511,
                1.4910791605096687,
                1.7384025390135238,
                1.9208273211172984,
                2.034796597551954,
                2.07752153658893,
                2.0475071735868284,
                1.9450143577852923,
                1.7736090279528545,
                1.5428228782408027,
                1.2683922195102675,
                0.9674180498355925,
                0.6520916891743113,
                0.3283771403724579
              ],
              "metrics": {
                "initial_rmse_K": 0.03187622599429528,
                "observation_residual_rms_K": 0.012920893208210476,
                "future_predictive_rmse_K": 0.029962167102779012
              }
            }
          }
        },
        {
          "split": "test",
          "index": 14,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.311080076657534,
            -1.3591251807694569,
            -0.38326473334367095,
            0.12561504020200748,
            -0.022651107013994504,
            0.06272293803486029,
            0.055553774881321766,
            -0.037699810452175825
          ],
          "initial_K": [
            0.2076896065927406,
            0.41048823598105294,
            0.6185803775329761,
            0.868171932920262,
            1.1940722721089614,
            1.5736145388505403,
            1.9238285735512444,
            2.1785411243018915,
            2.3409148960691306,
            2.428303810789674,
            2.3986004765973767,
            2.1883338822926,
            1.812755597470356,
            1.3674534184810734,
            0.9232215771184211,
            0.4736757196955397
          ],
          "observed_K": [
            0.22025616118403915,
            0.44558361713985045,
            0.7148130042131245,
            0.966897220493914,
            1.2427762685333439,
            1.5048726983939624,
            1.784678186105546,
            1.938682367757408,
            2.053605621181767,
            2.0760337028009417,
            1.9961118489413299,
            1.8221111476056293,
            1.6313878592669242,
            1.2731078360269108,
            0.8716655847173352,
            0.4257196750083736
          ],
          "future_observed_K": [
            0.2354132634957243,
            0.4907343602013128,
            0.7100623860153076,
            0.9788664363318836,
            1.226466991170397,
            1.4918123993835113,
            1.64048003203494,
            1.8376257003629548,
            1.934367235901303,
            1.9674336813849373,
            1.8515128428525263,
            1.7147414173376105,
            1.4930181867887506,
            1.1552239832660707,
            0.8150616347947963,
            0.41683226863793293
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.307038379439732,
                -1.3471089764322535,
                -0.33755020859410106,
                -0.08405550359989668,
                0.022266524547557526,
                0.9581204489606863,
                -3.993801522199807,
                5.102923793823271
              ],
              "initial_K": [
                0.8757460292853447,
                0.20791509620860305,
                -0.2313068355742285,
                1.173494498193104,
                2.3413643634661114,
                1.2877400693410979,
                0.37830371638575677,
                2.2847913824262824,
                4.446084043402669,
                2.9522271370777373,
                -0.11051314387339572,
                0.5090501222859227,
                4.0009855770976435,
                4.129653426341166,
                -0.2798392443467942,
                -2.8255845628144964
              ],
              "metrics": {
                "initial_rmse_K": 1.652143606391112,
                "observation_residual_rms_K": 0.011571937982309658,
                "future_predictive_rmse_K": 0.017140373851810903
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.231129415156445,
                -1.31807900419044,
                -0.31871628083405923,
                -0.06804464368214753,
                0.009314758829573319,
                0.07261782651440266,
                -0.02500749124827094,
                0.0016641580639021945
              ],
              "initial_K": [
                0.17329604537502952,
                0.3649326926571328,
                0.5947508166616221,
                0.8800002374064684,
                1.2225005547321843,
                1.5935552954585952,
                1.9340470217388455,
                2.1810792349167643,
                2.3049071112725428,
                2.3195676702310264,
                2.251625562826394,
                2.1001438213880186,
                1.8372410845857055,
                1.4516543758564429,
                0.9806005367487074,
                0.4856461194080893
              ],
              "metrics": {
                "initial_rmse_K": 0.060676827220428345,
                "observation_residual_rms_K": 0.02377988790974995,
                "future_predictive_rmse_K": 0.02004931186639899
              }
            },
            "learned": {
              "coefficients_K": [
                6.306678145100609,
                -1.3502334112911472,
                -0.33120377431771314,
                -0.06446464422372963,
                0.002908603840811048,
                0.00718231107493395,
                -0.0038997590717364757,
                -0.0004492752364066625
              ],
              "initial_K": [
                0.15704291517608862,
                0.347905840183943,
                0.5943847203660129,
                0.8998085820393629,
                1.2483679407461252,
                1.6077563351717294,
                1.9353928462945342,
                2.1894597548383494,
                2.340881857049113,
                2.3782637336953387,
                2.3027699496572795,
                2.1195764476557906,
                1.8348632760281598,
                1.4594310631824292,
                1.0120766171739706,
                0.5173327232052065
              ],
              "metrics": {
                "initial_rmse_K": 0.05454324865842084,
                "observation_residual_rms_K": 0.015816409922843857,
                "future_predictive_rmse_K": 0.016914494065763026
              }
            }
          }
        },
        {
          "split": "test",
          "index": 15,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            4.884268549802298,
            0.6877274449795013,
            -0.25992970679231264,
            0.35035125405665124,
            0.11789004813219005,
            -0.0268493879993177,
            0.07154517271454933,
            0.03169186925118979
          ],
          "initial_K": [
            0.48552172691417017,
            0.8504093211119879,
            1.089519706863466,
            1.2761288391525716,
            1.4485071252796695,
            1.5882908810024505,
            1.686458893772129,
            1.758272026330791,
            1.782746205267835,
            1.6889320722971826,
            1.438177462773347,
            1.089392217927572,
            0.7523401919885704,
            0.4929336092275198,
            0.3039648935369203,
            0.1480207347089167
          ],
          "observed_K": [
            0.3172284833183981,
            0.6562889279694181,
            0.9107388878190168,
            1.1631106441246948,
            1.3251065840632306,
            1.4607139005998977,
            1.5161458833994461,
            1.5837281857745122,
            1.5308015683255651,
            1.468166601999248,
            1.2951090870668318,
            1.0652560706297165,
            0.8535171506499108,
            0.6107882501658092,
            0.37558895528790687,
            0.1869215675171548
          ],
          "future_observed_K": [
            0.3293281926070821,
            0.5579654651353064,
            0.8451313881069954,
            1.09491581111432,
            1.3099464045551892,
            1.4000406860452679,
            1.4718677979685624,
            1.4440128231940814,
            1.4484598908913553,
            1.3409174509705344,
            1.20489827098508,
            1.0548105091465525,
            0.8111665826020172,
            0.632561468566864,
            0.40482497505340975,
            0.18841609156734035
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                4.910539980485875,
                0.6261196272059115,
                -0.27981729764083463,
                0.5081208845175135,
                -0.07096043018014418,
                -0.6209255942998776,
                -1.1335936789411534,
                5.09602318908622
              ],
              "initial_K": [
                1.6103756215473957,
                0.7638710303738379,
                -0.2664802233623278,
                1.2382745272016678,
                3.085187092681359,
                2.0015723539060435,
                -0.11016315517585173,
                0.7447445991678445,
                3.3711076015722794,
                3.1896293118238583,
                0.30762123919241613,
                -0.560745572461554,
                1.599696181418385,
                2.3549939689626807,
                -0.17501504037534377,
                -1.8792460178228076
              ],
              "metrics": {
                "initial_rmse_K": 1.3114442157105322,
                "observation_residual_rms_K": 0.011003879857775421,
                "future_predictive_rmse_K": 0.024488591691941636
              }
            },
            "tikhonov": {
              "coefficients_K": [
                4.851438706390969,
                0.6126268543747327,
                -0.26420463133045835,
                0.4113342143427994,
                -0.029684888279671987,
                -0.047061167658129205,
                -0.007098082828513153,
                0.0016619076487514011
              ],
              "initial_K": [
                0.40466646299903114,
                0.7781921510112646,
                1.0868332438555073,
                1.3067487483163687,
                1.4440994363995008,
                1.5371203832047644,
                1.6266028560939276,
                1.7156850112378617,
                1.758158556685411,
                1.6910118615622884,
                1.4842100407236518,
                1.1656589705621576,
                0.8057943515066702,
                0.48061876775732837,
                0.23965000939644404,
                0.09051686226332467
              ],
              "metrics": {
                "initial_rmse_K": 0.0498300435749252,
                "observation_residual_rms_K": 0.018996048163856253,
                "future_predictive_rmse_K": 0.026064133683213673
              }
            },
            "learned": {
              "coefficients_K": [
                4.910259508889194,
                0.6275718259688213,
                -0.27455632595822055,
                0.3896928891055812,
                -0.009269330708829083,
                -0.004654613913613429,
                -0.001106900833339089,
                -0.00044866768846947005
              ],
              "initial_K": [
                0.4232197171971375,
                0.7976554992648286,
                1.0917525793322498,
                1.301993212001254,
                1.4507129998562063,
                1.5692652411877566,
                1.674833343232772,
                1.7555860568857615,
                1.7745231784023288,
                1.6904338760722777,
                1.4841478309087186,
                1.1754907211018781,
                0.8210154143479517,
                0.49216078775957167,
                0.24404021094478617,
                0.09076895492494155
              ],
              "metrics": {
                "initial_rmse_K": 0.04259502921328463,
                "observation_residual_rms_K": 0.013791986284330442,
                "future_predictive_rmse_K": 0.02374263484902912
              }
            }
          }
        },
        {
          "split": "test",
          "index": 16,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.125696078420558,
            1.6783579303051732,
            -0.14240359145815265,
            0.04012788816479341,
            -0.09569853536567843,
            -0.09255828759098637,
            0.010008089659754228,
            -0.0006444199244397005
          ],
          "initial_K": [
            0.5260599646423819,
            1.061673338072496,
            1.575629230443767,
            1.997088577571985,
            2.2600222504585807,
            2.3499042414306848,
            2.308299070603891,
            2.191233992246892,
            2.0227468683382743,
            1.7897069748576695,
            1.4807580851749338,
            1.1247411720003302,
            0.7843675062524665,
            0.5109286166665549,
            0.3093587001222755,
            0.14887945877780975
          ],
          "observed_K": [
            0.43736648834309666,
            0.9435296103808382,
            1.349727808582041,
            1.6765914719935473,
            1.9016813374025945,
            2.0066059149688202,
            2.071478317523844,
            1.9907570907449772,
            1.8693007359569584,
            1.6272760342179948,
            1.3786398063100798,
            1.14207017334139,
            0.8839911867733912,
            0.6279001818423393,
            0.3825394804618159,
            0.22693268351204915
          ],
          "future_observed_K": [
            0.44653657406871755,
            0.8457669187359959,
            1.2256826600927726,
            1.5803815225603004,
            1.7551196843553005,
            1.9074242884695687,
            1.902871217315203,
            1.8846083508267404,
            1.743032180479335,
            1.5572806809981596,
            1.4142025645076162,
            1.119681084812274,
            0.9017913846627088,
            0.6378097638396655,
            0.3976286191304751,
            0.18607568003545222
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.14342578199981,
                1.7191093889375726,
                -0.14817108347454883,
                -0.03884994987937084,
                -0.017667761026724457,
                -0.45010764846608964,
                -4.389678225320622,
                -17.79826116552116
              ],
              "initial_K": [
                -7.105450704989259,
                -0.9437156705147737,
                8.488114760051179,
                5.668498729539086,
                -3.394009804679813,
                -2.3856767907085947,
                6.55627035636121,
                7.48781230839662,
                -0.8014549183728219,
                -3.524349923126322,
                3.186606512754321,
                6.179164097767256,
                -0.20843941945891675,
                -4.346435812944626,
                0.778228414482085,
                4.920315367729153
              ],
              "metrics": {
                "initial_rmse_K": 4.584311409764915,
                "observation_residual_rms_K": 0.01385652428754069,
                "future_predictive_rmse_K": 0.022650948885929223
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.0694859927981035,
                1.6820628702708562,
                -0.13990374009499698,
                -0.03144982640511275,
                -0.007390957339165226,
                -0.034114540780934115,
                -0.027486303260750515,
                -0.005804342968611674
              ],
              "initial_K": [
                0.5348718690113499,
                1.0699207727825937,
                1.5655035386848732,
                1.9584637139559256,
                2.211480615130292,
                2.3302142911310932,
                2.3341163931371716,
                2.22943587446201,
                2.019253658144656,
                1.7274863317166453,
                1.3991929172945623,
                1.0780846175363445,
                0.7895172794446614,
                0.5416743216412937,
                0.33344258263707083,
                0.15748860432783465
              ],
              "metrics": {
                "initial_rmse_K": 0.036184659189122226,
                "observation_residual_rms_K": 0.025704171581893722,
                "future_predictive_rmse_K": 0.02784692076896974
              }
            },
            "learned": {
              "coefficients_K": [
                6.143074892597624,
                1.7230966278284254,
                -0.14538525185901224,
                -0.02979517211632586,
                -0.0023078822863040584,
                -0.0033741197695939394,
                -0.004286314025883065,
                0.0015670071347030534
              ],
              "initial_K": [
                0.5649878591210972,
                1.1021475892285386,
                1.580870424819527,
                1.968990811671187,
                2.2390684901079165,
                2.375729081555986,
                2.3782376640854843,
                2.257816261290916,
                2.035177140310996,
                1.7408427270868303,
                1.4130563451144071,
                1.0888758310006375,
                0.7939163947195358,
                0.5396760396431507,
                0.3278177905653066,
                0.15275921143624033
              ],
              "metrics": {
                "initial_rmse_K": 0.0387996046653936,
                "observation_residual_rms_K": 0.018531920400198715,
                "future_predictive_rmse_K": 0.02264305928421824
              }
            }
          }
        },
        {
          "split": "test",
          "index": 17,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.66936998021999,
            -2.9652521436342125,
            -0.4790226749520172,
            -0.25661258666649445,
            0.0812490107136822,
            0.09913406257747438,
            -0.00947824150363086,
            -0.03526847257965021
          ],
          "initial_K": [
            -0.05535493681063591,
            -0.04354579180999474,
            0.07760919615818473,
            0.3410095204026522,
            0.7721763212333901,
            1.3348625380314174,
            1.9017663949074373,
            2.3343474797138497,
            2.5924301562287875,
            2.728003983997841,
            2.7770015711807496,
            2.703472418379978,
            2.455494178895258,
            2.0282065597748615,
            1.4523096283676225,
            0.7612721100198756
          ],
          "observed_K": [
            0.07561558356913603,
            0.1696320545683111,
            0.3732828676817506,
            0.694345157855224,
            0.9588234177363907,
            1.3225025497723448,
            1.6725665968688648,
            1.9939182694343123,
            2.2564907890942156,
            2.4006685950203672,
            2.40213655923865,
            2.2642514577179003,
            2.0152391331127664,
            1.636019284299092,
            1.193827478527609,
            0.5832282311970134
          ],
          "future_observed_K": [
            0.09930370834036448,
            0.3347927407891029,
            0.5000063146043063,
            0.7358809453132904,
            1.0121297312574682,
            1.3481264649181173,
            1.6556459246139017,
            1.9292674581205482,
            2.091671756968619,
            2.215348888893049,
            2.1905525418313374,
            2.08418386349724,
            1.8635459616241647,
            1.516190611425407,
            1.0781911017233863,
            0.5331846868090749
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.645171270813741,
                -2.986826460992954,
                -0.5186063674037931,
                -0.23283298838264244,
                -0.11617291497778164,
                -1.7127153436266767,
                -2.039736675486484,
                3.619191985031918
              ],
              "initial_K": [
                -0.09321790969671745,
                -0.7528956044678624,
                -0.587139182974793,
                1.1226582533111173,
                2.229439350369181,
                1.1037640065747731,
                0.00863312390555393,
                1.6583237684182923,
                4.2682449823326465,
                4.095461368778439,
                1.7026640336011725,
                1.1020891704432858,
                2.9590222566259397,
                3.5465414168498093,
                1.2679087922283006,
                -0.6658643822567556
              ],
              "metrics": {
                "initial_rmse_K": 1.1402299000426461,
                "observation_residual_rms_K": 0.014413998484316331,
                "future_predictive_rmse_K": 0.023734894661982118
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.56519267574178,
                -2.9224608522926245,
                -0.4896702429076418,
                -0.18848305052527195,
                -0.04859863438658023,
                -0.12981005240724264,
                -0.012771965952106112,
                0.001180285610769136
              ],
              "initial_K": [
                -0.13727258132435682,
                -0.13036726069666638,
                0.0740258753221994,
                0.42840132015502497,
                0.8523914622680256,
                1.2998775138075547,
                1.759905845433515,
                2.2078070914649928,
                2.576902354712581,
                2.7888647532982853,
                2.807115284805353,
                2.6518679670277874,
                2.3630422509776836,
                1.9562400596777794,
                1.4199126811828593,
                0.7529565298982062
              ],
              "metrics": {
                "initial_rmse_K": 0.0741848152841095,
                "observation_residual_rms_K": 0.02858157449073836,
                "future_predictive_rmse_K": 0.03222803273279531
              }
            },
            "learned": {
              "coefficients_K": [
                6.644791723594097,
                -2.9937539960888206,
                -0.5088558143238445,
                -0.178566484249263,
                -0.015175290871320836,
                -0.012838943573412795,
                -0.001991706788623949,
                -0.00031864346801425633
              ],
              "initial_K": [
                -0.09415443457684985,
                -0.09458693003252294,
                0.057443323662359824,
                0.37007077825447077,
                0.8082663167669303,
                1.3129221029257687,
                1.8184835179425654,
                2.2643789876624636,
                2.6019838054971385,
                2.7985582276703034,
                2.837286004510199,
                2.713342516970037,
                2.4289666816147837,
                1.9917636425353547,
                1.418022376250302,
                0.7383534655430385
              ],
              "metrics": {
                "initial_rmse_K": 0.044378200869772524,
                "observation_residual_rms_K": 0.01974015341387165,
                "future_predictive_rmse_K": 0.023562714938760106
              }
            }
          }
        },
        {
          "split": "test",
          "index": 18,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.807302046901371,
            0.0017489550590784845,
            -0.3149889416754652,
            -0.1285277374178691,
            -0.061114877660351924,
            -0.01244514269873259,
            -0.0513899601285698,
            0.014605475623798663
          ],
          "initial_K": [
            0.24713484261318136,
            0.5474196623815,
            0.9066397535289007,
            1.2773150368230044,
            1.5993111149124961,
            1.8434639566601954,
            2.0099466877089305,
            2.093022108589769,
            2.072195474775573,
            1.94688559906659,
            1.7555125824595095,
            1.5370215606080795,
            1.28772943549715,
            0.9839944512351427,
            0.639376439887629,
            0.3037664502787767
          ],
          "observed_K": [
            0.2854281623006744,
            0.6087152012333685,
            0.9270039722488514,
            1.1905132977371262,
            1.4492910509566599,
            1.6125837153954248,
            1.793547410736716,
            1.803882389920868,
            1.8465076252027055,
            1.7568470905587228,
            1.6236599572373671,
            1.4758685786923913,
            1.1652902618926924,
            0.88566279146054,
            0.6108015871861813,
            0.31840730397318323
          ],
          "future_observed_K": [
            0.2746843055537364,
            0.5970409078918855,
            0.8854623523462852,
            1.1095112850409063,
            1.3468779877846389,
            1.5856815154742163,
            1.6585506290125822,
            1.7269894309896285,
            1.749420616192639,
            1.678054430686885,
            1.5423750649156784,
            1.381627098584965,
            1.1154425815357198,
            0.8750388966728196,
            0.5729712651243886,
            0.30764299147908425
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.8201629818924685,
                0.013178473658957957,
                -0.28886096252919036,
                0.03414151714505074,
                -0.4180948483965962,
                -0.4196275447565362,
                0.9581453235151501,
                -21.324142473713387
              ],
              "initial_K": [
                -6.88592294418293,
                -0.776588447511906,
                7.753799676434957,
                3.834391952338335,
                -4.691712289287359,
                -1.680968043398301,
                7.764582858158514,
                6.540768792246792,
                -3.1558741625247637,
                -3.606164972951645,
                6.139108774689028,
                8.212654922987559,
                -1.7401167596647378,
                -6.3956950788462175,
                2.1116512960742724,
                7.918555912379858
              ],
              "metrics": {
                "initial_rmse_K": 5.34252981822244,
                "observation_residual_rms_K": 0.01604255358067044,
                "future_predictive_rmse_K": 0.018474361715409022
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.750113853072257,
                0.012894479764475688,
                -0.27274369652710384,
                0.02763825412266954,
                -0.17490168581915067,
                -0.031804393987049984,
                0.005999499639426022,
                -0.006954198237564046
              ],
              "initial_K": [
                0.2631058042623416,
                0.5753822091172018,
                0.9378819529706417,
                1.3012956759285375,
                1.6047038342587432,
                1.8143756699359905,
                1.9346105514326857,
                1.9917471510479468,
                2.005242427800859,
                1.964843579936238,
                1.8359454931971784,
                1.5957489230695392,
                1.2662959579846336,
                0.9062361860686279,
                0.5688316325788507,
                0.27141790446019165
              ],
              "metrics": {
                "initial_rmse_K": 0.05399524159402965,
                "observation_residual_rms_K": 0.025347301584741123,
                "future_predictive_rmse_K": 0.022685956140207904
              }
            },
            "learned": {
              "coefficients_K": [
                5.81983055604705,
                0.013209039324548064,
                -0.28342995680906025,
                0.026184136216593518,
                -0.05461437321627487,
                -0.003145633271183713,
                0.0009355837781748311,
                0.0018774352779172094
              ],
              "initial_K": [
                0.3083429437153907,
                0.6274852763558937,
                0.9578736848426098,
                1.2837825422542366,
                1.5775167278094586,
                1.812641374077662,
                1.9749072368206881,
                2.0607361099230608,
                2.067563419811297,
                1.989392593617089,
                1.8227882759746192,
                1.5756505269520318,
                1.2698490661712225,
                0.9362704319461879,
                0.6049805324067833,
                0.29361782486633997
              ],
              "metrics": {
                "initial_rmse_K": 0.04201839882113589,
                "observation_residual_rms_K": 0.0205539181603398,
                "future_predictive_rmse_K": 0.018924400877732266
              }
            }
          }
        },
        {
          "split": "test",
          "index": 19,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.955620357912321,
            1.1049016266397764,
            -0.15437426852275474,
            0.15907621310153364,
            0.022577552990945143,
            -0.042911330097955495,
            -0.0173039345769594,
            0.012378956026638271
          ],
          "initial_K": [
            0.5126667764136865,
            0.9935359090594259,
            1.4108569090159437,
            1.7351905707091064,
            1.951733008455496,
            2.0740766796598398,
            2.132350650925062,
            2.13596203164056,
            2.0573260669733506,
            1.8671111665585993,
            1.5803375545764957,
            1.2527251865378928,
            0.9351703115512102,
            0.6480370510183397,
            0.39617500004345957,
            0.18323928868240497
          ],
          "observed_K": [
            0.42329275279095213,
            0.8366162565863866,
            1.1517146811219972,
            1.5033877448176878,
            1.6938751921087476,
            1.8107147170237528,
            1.9022624201232863,
            1.8963589395417508,
            1.820568103271191,
            1.6578535853997804,
            1.4540823661166888,
            1.2067016286737706,
            0.9610894000512374,
            0.6921063754459649,
            0.4619647321724071,
            0.24749653518026526
          ],
          "future_observed_K": [
            0.40244401436859883,
            0.7216357466448846,
            1.138995902570245,
            1.356169985697574,
            1.6122613294587842,
            1.7624299165508077,
            1.8221252506585872,
            1.7924049013458554,
            1.7258383354629991,
            1.6049008905763478,
            1.426606491314878,
            1.1901126165593334,
            0.9628026219267511,
            0.724235707713439,
            0.48025077605161226,
            0.2581121505755987
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.900430141514305,
                1.1010727288096651,
                -0.17288566290883517,
                0.18678188465657833,
                0.18903399138912955,
                -0.7883050543427722,
                -0.6804069230848928,
                -3.102115763831344
              ],
              "initial_K": [
                -0.9539947568424052,
                0.5244528555683539,
                2.649290381558811,
                2.5231600315421656,
                1.0453966759748794,
                1.1284475112140882,
                2.6354668653217064,
                2.9372492266729133,
                1.6957771940956206,
                1.192793774544337,
                1.964536550937381,
                1.9269751938392679,
                0.45864475834520535,
                -0.27526827705928425,
                0.7105770340032395,
                1.2898631941351613
              ],
              "metrics": {
                "initial_rmse_K": 0.8188129128432764,
                "observation_residual_rms_K": 0.013159172289965076,
                "future_predictive_rmse_K": 0.023575508862448913
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.829414949609284,
                1.077344796390851,
                -0.16323934658886105,
                0.15120374328174835,
                0.0790786203127748,
                -0.05974718495862003,
                -0.00426041957261219,
                -0.0010116574677808791
              ],
              "initial_K": [
                0.5079041620942396,
                0.9816629701089086,
                1.3838905124576868,
                1.686699685520546,
                1.8897242931698632,
                2.017834717498811,
                2.093297308624367,
                2.1088539106169706,
                2.031632073663044,
                1.8373446452220696,
                1.5429946979492544,
                1.2064978315863282,
                0.892068210824999,
                0.6313449383321132,
                0.4133193642662932,
                0.20842900834306508
              ],
              "metrics": {
                "initial_rmse_K": 0.03592788593080125,
                "observation_residual_rms_K": 0.022104847046251378,
                "future_predictive_rmse_K": 0.03461530078235586
              }
            },
            "learned": {
              "coefficients_K": [
                5.900093131110262,
                1.103626516273231,
                -0.16963516129738435,
                0.14324853491019746,
                0.02469289682922594,
                -0.005909332306156446,
                -0.0006643853120951023,
                0.00027311867656012057
              ],
              "initial_K": [
                0.5158911121772032,
                0.9893372945629025,
                1.3889735048704401,
                1.7005513065360573,
                1.9251396195154622,
                2.0704551044038535,
                2.14033397736082,
                2.129486553520257,
                2.028131823109338,
                1.833933516861014,
                1.562173127110881,
                1.2457917237485938,
                0.9248113620262474,
                0.6322779205593283,
                0.38464681487452473,
                0.17964142903954666
              ],
              "metrics": {
                "initial_rmse_K": 0.018312150143081615,
                "observation_residual_rms_K": 0.015026558699903884,
                "future_predictive_rmse_K": 0.023360690392039883
              }
            }
          }
        },
        {
          "split": "test",
          "index": 20,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            7.180732206431159,
            -1.189659729794893,
            -0.5444413310804779,
            0.16352564588851226,
            -0.16319068955682428,
            0.015665053162013543,
            -0.03842669357752824,
            -0.026288524616383802
          ],
          "initial_K": [
            0.18313104007782438,
            0.445366634597879,
            0.786475107762756,
            1.1536208379361117,
            1.517656278888774,
            1.8812758253917239,
            2.22723573575444,
            2.506152153706002,
            2.678826962698064,
            2.732182707694785,
            2.646044524281446,
            2.385038769647284,
            1.949448107895559,
            1.4121272634382276,
            0.8782085004779696,
            0.41070400282354635
          ],
          "observed_K": [
            0.2785395086663571,
            0.5312710551257165,
            0.8669413597724009,
            1.193838917094915,
            1.494380370775748,
            1.7789340995133616,
            2.0552030563607637,
            2.2555349922201793,
            2.319062470371611,
            2.3550962134536513,
            2.2540051349569126,
            2.0316588168671896,
            1.7143247501356804,
            1.3345288069440102,
            0.9519186816241685,
            0.4309833441310413
          ],
          "future_observed_K": [
            0.2938834798591346,
            0.5745753181312125,
            0.8840430768950538,
            1.155641662291519,
            1.4888598653633163,
            1.7312179961078051,
            1.9526092991226949,
            2.126091608580042,
            2.1786003883189786,
            2.171512331386363,
            2.086683590014518,
            1.8900447708303534,
            1.6407321303810505,
            1.2807718263796932,
            0.8806547024844248,
            0.4649204733461862
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                7.1949633174263,
                -1.191495904555885,
                -0.5206264887594036,
                0.06795363558295124,
                -0.2648203123872137,
                -0.32723151780895454,
                -0.7322575751876954,
                -7.644565312688968
              ],
              "initial_K": [
                -2.7978818569683157,
                -0.3114357753814274,
                3.453097079424176,
                2.445225111184638,
                -0.727734604802375,
                0.28360988225270445,
                4.1312120306808415,
                4.37207523489912,
                1.1243306086746476,
                0.6418415578664176,
                3.8224821699275378,
                4.626083593742906,
                1.1402248539968567,
                -0.9376181752956365,
                1.3355429443267322,
                2.8886809096796533
              ],
              "metrics": {
                "initial_rmse_K": 1.9147022647546976,
                "observation_residual_rms_K": 0.016661395397878125,
                "future_predictive_rmse_K": 0.01537686017904107
              }
            },
            "tikhonov": {
              "coefficients_K": [
                7.108367647537481,
                -1.1658193678831807,
                -0.4915776497138034,
                0.055009853276925744,
                -0.1107823242819341,
                -0.024801518030506373,
                -0.004585086364757577,
                -0.002493034488490137
              ],
              "initial_K": [
                0.18720584724828937,
                0.43490220485615255,
                0.7624544774412502,
                1.1432198015852189,
                1.5327486534777304,
                1.8967810042746973,
                2.2159324075711444,
                2.472968415195547,
                2.6413576404857126,
                2.6863007863180126,
                2.5783339308835918,
                2.311898911045099,
                1.9156376505506478,
                1.4434717647165467,
                0.9500032618076781,
                0.46761731209477075
              ],
              "metrics": {
                "initial_rmse_K": 0.040674698952290846,
                "observation_residual_rms_K": 0.02682812205232774,
                "future_predictive_rmse_K": 0.021013197658951457
              }
            },
            "learned": {
              "coefficients_K": [
                7.194552368150311,
                -1.1942594161971503,
                -0.5108379544633656,
                0.05211564685181794,
                -0.034592617994294174,
                -0.0024530094905876884,
                -0.00071501503162157,
                0.0006730482419200037
              ],
              "initial_K": [
                0.21504170903611172,
                0.46425775543863845,
                0.7680069329119299,
                1.1252568790669752,
                1.5151230579864983,
                1.9046841298937784,
                2.256616580266272,
                2.5329612379563238,
                2.697610655112182,
                2.7219459077459525,
                2.593214981537892,
                2.3203772498048707,
                1.9329963205589857,
                1.4729790472535145,
                0.9818459095066413,
                0.48795210253882637
              ],
              "metrics": {
                "initial_rmse_K": 0.04525507851611725,
                "observation_residual_rms_K": 0.017965624850785334,
                "future_predictive_rmse_K": 0.014837969828295914
              }
            }
          }
        },
        {
          "split": "test",
          "index": 21,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.656457177825757,
            -0.8046586944460525,
            -0.3496565046537763,
            -0.0662370360402944,
            0.12229509305188335,
            0.037066554291200905,
            -0.037136746228791595,
            0.03332413208248
          ],
          "initial_K": [
            0.2223438377553089,
            0.43083134764895104,
            0.6471501904404015,
            0.9053325292007383,
            1.2090065152252487,
            1.5300568342004048,
            1.8285707024347484,
            2.0514251889573205,
            2.138454112126707,
            2.0714058735480916,
            1.9056319729226379,
            1.7126725442442343,
            1.4960332097720548,
            1.2041928154370631,
            0.8234578044141322,
            0.4068332720868984
          ],
          "observed_K": [
            0.24749507606267648,
            0.4705729984090913,
            0.6953340457088675,
            0.9770148964849745,
            1.2073198878942482,
            1.4276918777623946,
            1.6223792900767238,
            1.7853001363119396,
            1.8257358016721235,
            1.7965326909632755,
            1.6965851480379857,
            1.5686650385841334,
            1.3462626891801384,
            1.0623451165518838,
            0.7024279266231941,
            0.38447246273720265
          ],
          "future_observed_K": [
            0.23960349286169327,
            0.518977458830753,
            0.7248681150493993,
            0.9565530859499493,
            1.1641839792131317,
            1.4090671976273208,
            1.5466814388949885,
            1.7056029678507871,
            1.74077127127242,
            1.7028420437144995,
            1.647260974505286,
            1.484478120091167,
            1.253483471339404,
            0.9647817710797654,
            0.6258397723999941,
            0.3477168367538919
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.650781809888637,
                -0.7956803953773995,
                -0.3008862144965533,
                -0.10735210548551516,
                0.14632183724391645,
                0.7971321156252859,
                -2.7691475132637704,
                1.6319919644517393
              ],
              "initial_K": [
                0.10704960075069436,
                0.2565569591211305,
                0.713253591305703,
                1.303508514028868,
                1.3587092293532836,
                0.9854743198305622,
                1.3146833161842242,
                2.5620620480312084,
                3.102115022515916,
                1.885019079041228,
                0.5633286740790919,
                1.211163743421521,
                2.790921002455783,
                2.437909955644032,
                0.05551786561392476,
                -1.2504220853939314
              ],
              "metrics": {
                "initial_rmse_K": 0.8140209004228153,
                "observation_residual_rms_K": 0.012211136650885872,
                "future_predictive_rmse_K": 0.02540003220712081
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.582771284381483,
                -0.7785336164639841,
                -0.2840979883792504,
                -0.08690371782269798,
                0.06121083793369391,
                0.060416205232157565,
                -0.017339227254581244,
                0.000532222838826898
              ],
              "initial_K": [
                0.21377987635075418,
                0.4285560985933246,
                0.6558033248892743,
                0.915181115117216,
                1.215957018352909,
                1.5351181580874804,
                1.8157287881469497,
                1.9964576087921582,
                2.0514849572364424,
                2.0025376420453087,
                1.8888113410197354,
                1.725850020784402,
                1.497921756710005,
                1.1894237331271262,
                0.8145765972036022,
                0.40940701953694636
              ],
              "metrics": {
                "initial_rmse_K": 0.03219171562301531,
                "observation_residual_rms_K": 0.021454368621245484,
                "future_predictive_rmse_K": 0.033239938593155126
              }
            },
            "learned": {
              "coefficients_K": [
                5.6504590584594645,
                -0.79752586713013,
                -0.29522911657050893,
                -0.08233149514793385,
                0.019113546745617688,
                0.005975502170370585,
                -0.0027039421152503192,
                -0.0001436849941851634
              ],
              "initial_K": [
                0.19109856821317744,
                0.40450877373399874,
                0.6547000602097192,
                0.9427286123015836,
                1.2536864115833606,
                1.5577541435649092,
                1.8165500081686075,
                1.9948786556033917,
                2.0727808112760586,
                2.0498419071970035,
                1.9385961658975768,
                1.7530170097262208,
                1.5017780682556816,
                1.190171894959321,
                0.826071390159169,
                0.4232115889730529
              ],
              "metrics": {
                "initial_rmse_K": 0.032812940138111,
                "observation_residual_rms_K": 0.014874582517894084,
                "future_predictive_rmse_K": 0.02560459600151365
              }
            }
          }
        },
        {
          "split": "test",
          "index": 22,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.616317898180286,
            2.8494047653427668,
            -0.14949376274781773,
            -0.15241351632198927,
            -0.08747961663688894,
            -0.08000786612325637,
            -0.005665201640811569,
            0.02009165091951631
          ],
          "initial_K": [
            0.6012971730607417,
            1.2058465558071387,
            1.785094592131872,
            2.261878766696778,
            2.5404883688195863,
            2.5760557775222077,
            2.409645766953102,
            2.1215539423852983,
            1.762792284251721,
            1.3526977584588793,
            0.9281985642881142,
            0.5560767258955849,
            0.28694258161169606,
            0.12194886777863767,
            0.03436551000394805,
            0.0010320653522276069
          ],
          "observed_K": [
            0.5712586283789645,
            1.0587859106029416,
            1.4937910368433913,
            1.8298715724592296,
            2.013775649726056,
            2.0916844449459897,
            2.049275864543383,
            1.8779312616351969,
            1.6195170885161305,
            1.3707080828724592,
            1.026590501644462,
            0.7350063896523052,
            0.5368339080840683,
            0.345423821083723,
            0.17090996288239785,
            0.07714984962449047
          ],
          "future_observed_K": [
            0.4657221683201324,
            0.9412619365759001,
            1.3375517630629963,
            1.6633263877058715,
            1.8384890142487034,
            1.9386333870401005,
            1.9104214923894354,
            1.7322423657370203,
            1.5678448322339122,
            1.3287115442440127,
            1.0527002616325745,
            0.7920817533132032,
            0.5492411503122319,
            0.40663226069097724,
            0.24769501912374303,
            0.09063062466475674
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.634324549304429,
                2.8387408584130456,
                -0.07154636964920304,
                -0.04562077963039229,
                0.16205919084699844,
                0.37280164956654627,
                -1.3902647816879155,
                13.924714941778296
              ],
              "initial_K": [
                5.1393130860856155,
                2.0986222419348395,
                -2.4239312418137775,
                0.7982972998808169,
                6.524404014421171,
                4.57476146922991,
                -1.4442628101790542,
                -0.5875672874931364,
                5.343997768873335,
                4.870801140871746,
                -2.130375403153767,
                -3.7436476373685084,
                2.5616518707077685,
                5.092453584379162,
                -1.1414545486146292,
                -5.283527057627409
              ],
              "metrics": {
                "initial_rmse_K": 3.495898394679787,
                "observation_residual_rms_K": 0.012276661270111905,
                "future_predictive_rmse_K": 0.0187455520612834
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.566512096732737,
                2.7775664695824647,
                -0.06755437342713377,
                -0.036930951115682016,
                0.0677942476218711,
                0.028255367623008967,
                -0.008705248412467424,
                0.004541107724545862
              ],
              "initial_K": [
                0.7001658132416799,
                1.3270049964545438,
                1.831887499409273,
                2.1946480436408353,
                2.4094420253180733,
                2.471525860757257,
                2.3764929844933156,
                2.1303240176885394,
                1.7629516110824075,
                1.3339390164347515,
                0.9179787414988995,
                0.573717183369123,
                0.32180485027473027,
                0.15302313025684344,
                0.05253472107401702,
                0.008472627800740706
              ],
              "metrics": {
                "initial_rmse_K": 0.06313359197246529,
                "observation_residual_rms_K": 0.023458705192914025,
                "future_predictive_rmse_K": 0.023235230836866398
              }
            },
            "learned": {
              "coefficients_K": [
                5.634002737852157,
                2.845324929225847,
                -0.07020119396531291,
                -0.034987921101290335,
                0.02116926617486049,
                0.002794614622138513,
                -0.0013575280755356313,
                -0.0012259696303784334
              ],
              "initial_K": [
                0.6926609908970316,
                1.329488149124103,
                1.8605385615343981,
                2.248060242619175,
                2.4700901171403906,
                2.5194079301870227,
                2.4018628916592224,
                2.1386857793681715,
                1.7697832099017101,
                1.3502668400978355,
                0.9384415470588444,
                0.5821341648402764,
                0.31046017230118117,
                0.13198708643040613,
                0.037041046804831446,
                0.002852792888543343
              ],
              "metrics": {
                "initial_rmse_K": 0.04971123366837682,
                "observation_residual_rms_K": 0.014674760064166265,
                "future_predictive_rmse_K": 0.018508459699780728
              }
            }
          }
        },
        {
          "split": "test",
          "index": 23,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.3073933628624665,
            -0.12895218170690614,
            -0.5797098359900882,
            -0.004750410625855255,
            0.04804790973107032,
            0.020260473845860535,
            0.01728589544363994,
            -0.008473803232893842
          ],
          "initial_K": [
            0.29795725439702275,
            0.5960873620178911,
            0.9034863110307689,
            1.2348503172798584,
            1.590327977921797,
            1.9352009913882426,
            2.2073713024985793,
            2.353536438451543,
            2.3573809740751153,
            2.23254447914464,
            2.000699011401208,
            1.6882629835973466,
            1.3348003324484605,
            0.9822361975301281,
            0.6489044805611504,
            0.32545496363917653
          ],
          "observed_K": [
            0.3144664365732007,
            0.5975322675773075,
            0.9041876095552913,
            1.2243646409199362,
            1.528336176156823,
            1.7301852105945106,
            1.8860143209418945,
            2.019589959087378,
            2.038031723961231,
            1.9481413207685951,
            1.81545077576751,
            1.5976473838989318,
            1.3114599150082829,
            1.0157120410542424,
            0.6732063361609103,
            0.3097847875074002
          ],
          "future_observed_K": [
            0.2971471634652938,
            0.5688229107110707,
            0.8812282237978878,
            1.2021504978774649,
            1.4557893163682813,
            1.6926188188317066,
            1.7892923375390257,
            1.894405183344111,
            1.8749480381574604,
            1.8628893524398336,
            1.6758666278462573,
            1.487728398657565,
            1.2732958996122636,
            0.9290245202407656,
            0.6243473376151959,
            0.2979698844608273
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.318228056482201,
                -0.20699662642086084,
                -0.5057512712247364,
                0.0059474456672050065,
                -0.3460897501630025,
                -0.09117790128272286,
                -1.8197009812541036,
                16.05768483083377
              ],
              "initial_K": [
                5.043809199245951,
                1.1261110897898885,
                -4.007943043004023,
                -0.08710123973389106,
                6.552292500973476,
                4.259831162315213,
                -2.5116246106410025,
                -1.0242270228988213,
                6.4573475052527005,
                6.4196044094269515,
                -1.3992360832820472,
                -3.2117740365379053,
                3.972632719050617,
                6.69939191271099,
                -0.7564629446928959,
                -5.820144210514112
              ],
              "metrics": {
                "initial_rmse_K": 4.044097007413402,
                "observation_residual_rms_K": 0.010894088173594371,
                "future_predictive_rmse_K": 0.027490081171333967
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.242184417769513,
                -0.2025358838794063,
                -0.4775324087732247,
                0.00481457850957893,
                -0.14477978138304806,
                -0.0069105518251680485,
                -0.01139419575816001,
                0.005236708753357771
              ],
              "initial_K": [
                0.2394879735892344,
                0.5302772063255657,
                0.8865583251535558,
                1.274110172767096,
                1.6336746537654518,
                1.9193144448488868,
                2.117285167215308,
                2.232304306390921,
                2.263943039013728,
                2.2009705043505257,
                2.033187801984096,
                1.7626384600481864,
                1.408587150112767,
                1.0108794070664802,
                0.6237137507798254,
                0.2881198562085597
              ],
              "metrics": {
                "initial_rmse_K": 0.06079154559951773,
                "observation_residual_rms_K": 0.022546434701274314,
                "future_predictive_rmse_K": 0.028627968215489154
              }
            },
            "learned": {
              "coefficients_K": [
                6.31786718303076,
                -0.20747672675912415,
                -0.496242412627386,
                0.004561271452269359,
                -0.045208580909851324,
                -0.0006834924052424701,
                -0.0017768522972530505,
                -0.0014137620783694527
              ],
              "initial_K": [
                0.27027660297929185,
                0.5685525011752952,
                0.90416406983405,
                1.2626116862657037,
                1.6136061540903897,
                1.922309232744955,
                2.1571765052210177,
                2.294645928694103,
                2.3215223890305268,
                2.234596368782979,
                2.0395788030714668,
                1.7527002312637656,
                1.402956130595421,
                1.0280547797179715,
                0.6618748762323459,
                0.32096877099915877
              ],
              "metrics": {
                "initial_rmse_K": 0.03781367028935466,
                "observation_residual_rms_K": 0.015045435536759083,
                "future_predictive_rmse_K": 0.028731183476691617
              }
            }
          }
        },
        {
          "split": "test",
          "index": 24,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.714850767936276,
            -0.7122801141751662,
            -0.36390482425410486,
            0.10663356330007517,
            -0.19171585434582544,
            0.022988197840341743,
            0.049432722517613964,
            0.007037053860749392
          ],
          "initial_K": [
            0.20415243457210236,
            0.4206072874313576,
            0.679157150021953,
            0.9953922896417096,
            1.3303696423986238,
            1.6127747784409132,
            1.808052441550762,
            1.9438950748134727,
            2.0550540912832247,
            2.1189088346155622,
            2.0648216365696386,
            1.8451482694748593,
            1.485398391600072,
            1.065717759773858,
            0.6634789830914641,
            0.31245822419369396
          ],
          "observed_K": [
            0.25135596174499225,
            0.5131477616806412,
            0.7643863412647746,
            0.9891751020786553,
            1.2109004245309822,
            1.4460325314711733,
            1.6804896265679679,
            1.7589358277920926,
            1.8732885582019894,
            1.833886405173056,
            1.716401393706243,
            1.5546247579770618,
            1.3331241204528388,
            1.026445485989087,
            0.684907752747086,
            0.3695726198952619
          ],
          "future_observed_K": [
            0.2479614048402281,
            0.5023768037421505,
            0.7194464240956262,
            0.9802976398960803,
            1.2208637018822204,
            1.426928168446563,
            1.5787793935941687,
            1.7128677628239442,
            1.7540001729597614,
            1.696832313158539,
            1.6471747359920288,
            1.477428702079926,
            1.2610776138077904,
            0.9914439559586123,
            0.6646649887105173,
            0.32458795383516703
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.712316888984827,
                -0.7043003222017237,
                -0.33977098796710503,
                0.16075937702672077,
                0.34449469430281277,
                0.6831605835231115,
                -1.2670806479076628,
                -4.469809616224695
              ],
              "initial_K": [
                -1.3920027410658937,
                0.2857599564223805,
                2.5101803173902173,
                1.6518587863595044,
                -0.4676963863977588,
                0.2947022442643643,
                3.1079977524957654,
                3.607548860230618,
                1.4237262545555696,
                0.5474832775715797,
                2.231217454036696,
                3.115591493838709,
                1.4557716516047743,
                -0.008428722898394359,
                0.6908820776360534,
                1.3419053560801033
              ],
              "metrics": {
                "initial_rmse_K": 1.1859146005470782,
                "observation_residual_rms_K": 0.014812763947169806,
                "future_predictive_rmse_K": 0.015975849866155252
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.643565752141533,
                -0.6891227685211254,
                -0.32081314975695163,
                0.13013799287213687,
                0.1441125214060529,
                0.05177807945710068,
                -0.007933921612597126,
                -0.0014576877918403644
              ],
              "initial_K": [
                0.294676160818066,
                0.5461616580983527,
                0.7504013897003685,
                0.9486350683994108,
                1.192019331342463,
                1.491594959166401,
                1.7977581150568889,
                2.029855777917271,
                2.1295976795211566,
                2.0903694676967297,
                1.9424063433654903,
                1.718528432516635,
                1.4367510526715932,
                1.1078985602586933,
                0.747586204398801,
                0.3745040131904535
              ],
              "metrics": {
                "initial_rmse_K": 0.08838828206174743,
                "observation_residual_rms_K": 0.022881068002766056,
                "future_predictive_rmse_K": 0.026380068186476282
              }
            },
            "learned": {
              "coefficients_K": [
                5.711990622903099,
                -0.7059338503841615,
                -0.33338279981240715,
                0.12329110649298052,
                0.04500022393921826,
                0.005121142994410418,
                -0.001237244571076717,
                0.00039353414888399407
              ],
              "initial_K": [
                0.25444116972710057,
                0.5004149293339089,
                0.7399297029421485,
                0.9858357321272614,
                1.2505032196647694,
                1.5307963884407776,
                1.8004445270946108,
                2.016044146339857,
                2.1339131188928557,
                2.1278056269109915,
                1.9971866415085213,
                1.7629324157279767,
                1.4559720663705777,
                1.1068386882840293,
                0.7395939351517254,
                0.36898570885365617
              ],
              "metrics": {
                "initial_rmse_K": 0.06135085497642243,
                "observation_residual_rms_K": 0.017260537321944443,
                "future_predictive_rmse_K": 0.015647300275133346
              }
            }
          }
        },
        {
          "split": "test",
          "index": 25,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            4.986804801747439,
            1.409274362677173,
            -0.12718695672699243,
            0.03689907187329964,
            0.12627846114006258,
            -0.1106416293018512,
            0.08567935609441617,
            0.01678757000823148
          ],
          "initial_K": [
            0.509065992664648,
            0.944993307678865,
            1.2970869050704315,
            1.5864694936775365,
            1.8004718716335195,
            1.9021318480005827,
            1.8938817977872537,
            1.820834389282905,
            1.7000520672301658,
            1.4923760093169012,
            1.1763471629653488,
            0.8225061549732091,
            0.5503460976345522,
            0.40861419871791843,
            0.3269436556282219,
            0.19925654600422413
          ],
          "observed_K": [
            0.39752209197383365,
            0.777242768868332,
            1.0627975324702663,
            1.3373471929013139,
            1.5726793285300371,
            1.6233587448229336,
            1.6448656979222083,
            1.6437971424862166,
            1.5134956050894874,
            1.3407467868014507,
            1.1465261139877942,
            0.9125295648694425,
            0.6981970193010676,
            0.4958030550352788,
            0.3257428185648261,
            0.1532872541526289
          ],
          "future_observed_K": [
            0.3928815626760937,
            0.7393761081345529,
            0.9651659707712464,
            1.1996087017213384,
            1.425441359469643,
            1.5787752285564822,
            1.5509941438189088,
            1.5305889721806856,
            1.4412178310647648,
            1.2747573433868753,
            1.0901952927069598,
            0.887625540798451,
            0.67283792577372,
            0.516269738706745,
            0.3657414032355708,
            0.17697150082438554
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                4.985736183115924,
                1.3926483157113352,
                -0.17150819018609773,
                0.09744609428945136,
                0.10564878085325062,
                -0.4919477838160219,
                0.5159857924159585,
                11.660908512396613
              ],
              "initial_K": [
                4.509027165818372,
                1.6484890082531138,
                -2.6261686979882586,
                0.12686401000428038,
                5.475739883946191,
                4.087074901516852,
                -1.3832351090073332,
                -1.0570991989962384,
                4.358266029149665,
                4.893304685151717,
                -0.7002027664935542,
                -2.7959980032808214,
                1.7284034309755878,
                4.097230518215894,
                -0.2622487718803269,
                -3.5442192707909963
              ],
              "metrics": {
                "initial_rmse_K": 2.91464453233933,
                "observation_residual_rms_K": 0.01441449107573216,
                "future_predictive_rmse_K": 0.028450981150889048
              }
            },
            "tikhonov": {
              "coefficients_K": [
                4.925729877924603,
                1.3626369783548127,
                -0.1619387312375337,
                0.0788845998199554,
                0.04419607164937739,
                -0.037285686635796435,
                0.0032308841879971303,
                0.0038028384740567103
              ],
              "initial_K": [
                0.47128593547145936,
                0.907612308395173,
                1.2799045620504472,
                1.5671068276198952,
                1.758381709525949,
                1.856505962431076,
                1.8736696620698763,
                1.8169095013323757,
                1.6799183913496085,
                1.457572954997816,
                1.1704654234242087,
                0.8682250510049228,
                0.6027306313579248,
                0.39776562167878815,
                0.24391632521388557,
                0.11745327741724618
              ],
              "metrics": {
                "initial_rmse_K": 0.04180358020450522,
                "observation_residual_rms_K": 0.021470655464993896,
                "future_predictive_rmse_K": 0.029771905320424143
              }
            },
            "learned": {
              "coefficients_K": [
                4.985451416594633,
                1.395878372833597,
                -0.1682835870628712,
                0.07473428306685222,
                0.013800557384267541,
                -0.0036877639130067316,
                0.0005038358225055026,
                -0.0010266579788953227
              ],
              "initial_K": [
                0.47651096143494764,
                0.9176997553577804,
                1.2939312964027072,
                1.5861018091075458,
                1.7866209658826515,
                1.8950938154923527,
                1.9126578404015737,
                1.8406053581233472,
                1.6840304848652463,
                1.4564145687692527,
                1.181535536961518,
                0.8915256120233797,
                0.6205139783863612,
                0.39470013252815733,
                0.2236922383470128,
                0.09902600135657466
              ],
              "metrics": {
                "initial_rmse_K": 0.04674688796698569,
                "observation_residual_rms_K": 0.01594818412654867,
                "future_predictive_rmse_K": 0.028514238399486046
              }
            }
          }
        },
        {
          "split": "test",
          "index": 26,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.5287372691079035,
            -0.056908109949892954,
            -0.585948894231754,
            -0.03780142717700538,
            -0.08439024445458593,
            -0.012358905128850904,
            0.020233371164114115,
            -0.04275300105504225
          ],
          "initial_K": [
            0.2550691555772773,
            0.5727083445459744,
            0.9506698802624346,
            1.3448294949131172,
            1.7223065127618422,
            2.0555572743139305,
            2.295252085346513,
            2.4003877910879545,
            2.382898366623391,
            2.2776277672809275,
            2.0802711646359175,
            1.766745616460929,
            1.3697174154078802,
            0.9765430935526446,
            0.6369842178073036,
            0.323434047999801
          ],
          "observed_K": [
            0.31915992780816205,
            0.6375597236409252,
            0.9727744023523057,
            1.260401956374614,
            1.5503907127927823,
            1.7995964138569271,
            2.0242641033221944,
            2.120908775797193,
            2.1112974976196335,
            1.9891501310375463,
            1.8392037260370588,
            1.618777493064311,
            1.3044674426074803,
            0.9694968313925305,
            0.6950561505933865,
            0.33189456254420263
          ],
          "future_observed_K": [
            0.31677972812107197,
            0.6265086146308673,
            0.9398201849215433,
            1.2067057654109856,
            1.4927815114875023,
            1.7541373305260417,
            1.9110491907622538,
            1.955474805404016,
            1.970860954560547,
            1.9071252123621014,
            1.740718333048909,
            1.5084880336178121,
            1.2675791873644704,
            0.9762344294650006,
            0.6482719887263294,
            0.35576405706434283
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.5161239458661955,
                -0.08216309885011851,
                -0.6518734074258096,
                -0.05344169907204489,
                0.2895167370531677,
                0.6741652692626096,
                0.05642705503302695,
                -24.126033663543897
              ],
              "initial_K": [
                -7.664557347034276,
                -0.6603334314824724,
                8.853696418977991,
                3.993180746344965,
                -5.973375635511231,
                -2.2834806476211824,
                9.16110709325822,
                8.212094797317866,
                -3.1841329861705105,
                -4.509981948340691,
                6.271794507894507,
                9.188344407012734,
                -1.4778070492853175,
                -6.900138584383205,
                2.0861945960290793,
                8.44623406678477
              ],
              "metrics": {
                "initial_rmse_K": 6.024025994371092,
                "observation_residual_rms_K": 0.01024049666798349,
                "future_predictive_rmse_K": 0.01578832001129409
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.437698512229279,
                -0.08039249786634556,
                -0.6155015245130862,
                -0.0432621448374776,
                0.12111358362259851,
                0.051096306960625705,
                0.0003533222863130372,
                -0.007867946905215507
              ],
              "initial_K": [
                0.3209127060066731,
                0.6288369652845059,
                0.9299816769711244,
                1.2510793632751716,
                1.6115729148523739,
                1.9847256296589053,
                2.2920953934675006,
                2.450176756112112,
                2.427500974796238,
                2.2553517641625853,
                1.9903698423711484,
                1.6774389620256471,
                1.3432100934718778,
                1.0042815034739676,
                0.6685612991759782,
                0.3348256890472403
              ],
              "metrics": {
                "initial_rmse_K": 0.06000693697703095,
                "observation_residual_rms_K": 0.024208083698865762,
                "future_predictive_rmse_K": 0.022489765870911668
              }
            },
            "learned": {
              "coefficients_K": [
                6.515751769344972,
                -0.08235366491021702,
                -0.6396172403981432,
                -0.04098601483359896,
                0.037818631801894605,
                0.0050537118636942375,
                5.509836143164532e-05,
                0.002124121369569325
              ],
              "initial_K": [
                0.28813866799962073,
                0.5919218310917143,
                0.9252135741158456,
                1.2910715701783608,
                1.6710279667784984,
                2.0241680792825347,
                2.2986182328277893,
                2.4482691094171587,
                2.4476497695624175,
                2.3009007924424245,
                2.0401890834478262,
                1.7115954346912463,
                1.3563519097727998,
                1.000260789146565,
                0.6549435999271774,
                0.3229341649267764
              ],
              "metrics": {
                "initial_rmse_K": 0.036542663359869366,
                "observation_residual_rms_K": 0.016643656480645523,
                "future_predictive_rmse_K": 0.016206970992936623
              }
            }
          }
        },
        {
          "split": "test",
          "index": 27,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.957312760882661,
            -2.3510480167926078,
            -0.35876480690229295,
            -0.33014295349320666,
            0.04855441761960698,
            0.06140967563426924,
            0.013760287624349882,
            -0.005853890030697762
          ],
          "initial_K": [
            -0.022225986887687954,
            0.00690321083042833,
            0.1418194080734232,
            0.4220935683995457,
            0.8384588286430119,
            1.3171593639604615,
            1.7524311555804308,
            2.069295586817411,
            2.2589529774167096,
            2.353579124262073,
            2.3732715262205692,
            2.3024475966668776,
            2.1087020296321395,
            1.7701540366202622,
            1.286073495746904,
            0.679250973902292
          ],
          "observed_K": [
            0.08769485114709019,
            0.2558669709422912,
            0.4106498053931285,
            0.6145936978223419,
            0.9674311721354603,
            1.2254762006109392,
            1.5320799506912828,
            1.801368238168151,
            1.9833576331202187,
            2.1299674140971154,
            2.0704282550711253,
            1.960681372583968,
            1.7440440030026103,
            1.3714964392570157,
            0.9908551278866613,
            0.5448618286360106
          ],
          "future_observed_K": [
            0.12501982843231807,
            0.27160290732628856,
            0.48253220124474266,
            0.6970724573091521,
            0.9603121635944568,
            1.2463089698555132,
            1.4631662669071757,
            1.710385863216248,
            1.8725868649956376,
            1.9753890834500374,
            1.9669142565606117,
            1.8559707856219831,
            1.6502314662222866,
            1.304156208068469,
            0.9376240245639311,
            0.49959070394742966
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.932927140773089,
                -2.3531732871815576,
                -0.45810392938836864,
                -0.12915719515310012,
                0.12470145801916754,
                -0.7199461843273421,
                3.2504940564059575,
                1.4622233229828911
              ],
              "initial_K": [
                1.3546240269884602,
                0.5297498302228212,
                -1.0157245622385602,
                -0.5304720147935995,
                1.5917820888007987,
                2.505173424520069,
                1.442395044975413,
                0.7258089490191197,
                1.926185036999459,
                3.5051277172433504,
                3.358522458945552,
                1.8671379247224984,
                0.9805134740847368,
                1.3740452032006276,
                1.9153043601466129,
                1.440757845935615
              ],
              "metrics": {
                "initial_rmse_K": 0.9116905401695079,
                "observation_residual_rms_K": 0.019816681972350043,
                "future_predictive_rmse_K": 0.02669128975759267
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.861520828122063,
                -2.302462797976757,
                -0.4325435946795646,
                -0.10455538241744701,
                0.052166381181930906,
                -0.05456613223306153,
                0.02035321515510754,
                0.0004768581371160715
              ],
              "initial_K": [
                -0.013720606019129888,
                0.03169031026446201,
                0.18013460860318709,
                0.4453750481649923,
                0.8063174944220518,
                1.219464227803741,
                1.6370882849141455,
                2.0129303623627743,
                2.2971743761010597,
                2.44190386585426,
                2.4242770876963684,
                2.2622297723742055,
                1.995408109828655,
                1.6446977641444267,
                1.1970064685684543,
                0.6383545918926876
              ],
              "metrics": {
                "initial_rmse_K": 0.0713340114252072,
                "observation_residual_rms_K": 0.02832611576954398,
                "future_predictive_rmse_K": 0.04059267860496524
              }
            },
            "learned": {
              "coefficients_K": [
                5.932588274262527,
                -2.3586311504844653,
                -0.44949091003421865,
                -0.09905446137246926,
                0.01628934677141048,
                -0.005396897079756284,
                0.003173954342406215,
                -0.00012873810302784736
              ],
              "initial_K": [
                -0.01858769100933716,
                0.02267443767397115,
                0.1680638929930448,
                0.4339282812816584,
                0.8037693848086368,
                1.2335697072103389,
                1.6651877402810955,
                2.041276462822132,
                2.31592740494119,
                2.459747901878057,
                2.460794735371212,
                2.3218239902720597,
                2.0539268807159416,
                1.6699056018673553,
                1.1833507364835096,
                0.6150842826736638
              ],
              "metrics": {
                "initial_rmse_K": 0.06516849406871361,
                "observation_residual_rms_K": 0.021683181945655616,
                "future_predictive_rmse_K": 0.026204012766709618
              }
            }
          }
        },
        {
          "split": "test",
          "index": 28,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.655962654569335,
            2.779093117337611,
            -0.08398405134231095,
            0.16092454576813897,
            -0.18006023287756892,
            -0.020780863434476177,
            -0.020572540460693223,
            0.06688472410583254
          ],
          "initial_K": [
            0.6832248693314179,
            1.3075672552743929,
            1.8516081303642962,
            2.280662198521159,
            2.511044185283134,
            2.4935720629843487,
            2.298422269685895,
            2.0457627073067015,
            1.7737490023443212,
            1.4444396617103263,
            1.0593731719206438,
            0.6848175634349857,
            0.36493120142069635,
            0.09844687734351176,
            -0.08377164226844147,
            -0.11275873960000488
          ],
          "observed_K": [
            0.5236164307300847,
            1.0663802063185832,
            1.5085908805454227,
            1.8089355862428997,
            2.010623349843362,
            2.0475010317724416,
            2.0401959784525165,
            1.8550646893361324,
            1.6148173378606432,
            1.3537035689462364,
            1.1499150353055132,
            0.8157083089003675,
            0.5036440363146538,
            0.3188412254565672,
            0.17931209748754703,
            0.059604015398626864
          ],
          "future_observed_K": [
            0.48277734112276344,
            0.9737503237136281,
            1.3587439720609515,
            1.658234528896085,
            1.8631755783916177,
            1.944011083294021,
            1.9215096099050295,
            1.8352801058346533,
            1.5945960384188136,
            1.3214870417732065,
            1.0665616178633708,
            0.8146611861633325,
            0.5876873960978183,
            0.3698428558149328,
            0.22801282418273622,
            0.10595213087026488
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.646183806144818,
                2.7493224729903405,
                -0.08602483995463023,
                0.3186200184818232,
                -0.5352334524907134,
                -0.2580179911095248,
                3.2651787954191205,
                -30.07118934245146
              ],
              "initial_K": [
                -8.664263537671188,
                -0.13557905930905312,
                11.037511073737782,
                5.145414262265097,
                -6.400519529885145,
                -1.8364755301934204,
                10.794907547739244,
                7.9346005147315495,
                -6.137261858662818,
                -6.288083421003064,
                7.792208468844979,
                10.247302395178465,
                -4.39489801341335,
                -10.698911452652043,
                2.307934105093108,
                11.206287245240556
              ],
              "metrics": {
                "initial_rmse_K": 7.580022896144843,
                "observation_residual_rms_K": 0.01719769931980123,
                "future_predictive_rmse_K": 0.03007768309721279
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.578228620351959,
                2.6900750353508975,
                -0.08122500401904378,
                0.25792940020671734,
                -0.22390429709057424,
                -0.019555689199944177,
                0.020445164762596432,
                -0.00980677240290049
              ],
              "initial_K": [
                0.6659239262511933,
                1.299787173696616,
                1.8480472635025291,
                2.2435869749018638,
                2.436954891101242,
                2.423607038025899,
                2.2500114947042507,
                1.9939275631981899,
                1.721287906690565,
                1.4449238762538155,
                1.1295362149411015,
                0.7521550276889191,
                0.358237289207882,
                0.045998933533627606,
                -0.10767645946822979,
                -0.10119790760593345
              ],
              "metrics": {
                "initial_rmse_K": 0.045326726332427236,
                "observation_residual_rms_K": 0.030240972172736292,
                "future_predictive_rmse_K": 0.042385231927915566
              }
            },
            "learned": {
              "coefficients_K": [
                5.6458613173363466,
                2.755699150099048,
                -0.08440744799631165,
                0.24435908720216315,
                -0.06991580892294277,
                -0.001934167543431889,
                0.003188293298376947,
                0.0026475489830384263
              ],
              "initial_K": [
                0.7207275805810534,
                1.3710130930851334,
                1.89345536203796,
                2.250038826223585,
                2.4252448985153023,
                2.429968223125497,
                2.299251533726202,
                2.0762015886433822,
                1.7913192136630625,
                1.4569131335656258,
                1.0821542488510763,
                0.6927410472778097,
                0.3362870649099503,
                0.06897630460103454,
                -0.06872589410972307,
                -0.07571312768396732
              ],
              "metrics": {
                "initial_rmse_K": 0.03936114887255154,
                "observation_residual_rms_K": 0.025270367732831662,
                "future_predictive_rmse_K": 0.02843191843963397
              }
            }
          }
        },
        {
          "split": "test",
          "index": 29,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.608043060768968,
            0.29341304963263093,
            -0.5652863008777103,
            0.29211979222911494,
            0.08191861570761154,
            -0.09064712211537529,
            -0.013020152688873845,
            -0.01960056688216214
          ],
          "initial_K": [
            0.40186272394278105,
            0.8114007369206384,
            1.1955006738578815,
            1.512390362690192,
            1.7688773707080119,
            2.010344937185019,
            2.25188397793415,
            2.442536336458542,
            2.501618338619069,
            2.3764960131968342,
            2.072004526627692,
            1.6509180340149265,
            1.2104804528416047,
            0.8310470338531757,
            0.5283559087710069,
            0.2632013708606279
          ],
          "observed_K": [
            0.334142192344652,
            0.7049012716094022,
            1.0633160094076661,
            1.3753737407106141,
            1.6448483200731514,
            1.8475642763378253,
            2.0338862333416223,
            2.121854246403055,
            2.110027585478128,
            2.028236430200196,
            1.7818036875108818,
            1.5485825739698706,
            1.245922515116521,
            0.9273087724865305,
            0.6143125575666237,
            0.32204169207402933
          ],
          "future_observed_K": [
            0.385054354428485,
            0.7225044350461249,
            1.0891035099718271,
            1.3571834411716874,
            1.5944075124937453,
            1.8086737374157666,
            1.9291995738575034,
            1.9853452526229258,
            1.9778050842153858,
            1.8761326374701415,
            1.7305147612995035,
            1.4740298918030204,
            1.187509298264897,
            0.9520955433185245,
            0.6039333970667979,
            0.2870904144660344
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.56042315454237,
                0.23734245491135986,
                -0.6002820628810691,
                0.17872474828861762,
                0.1674535821074311,
                -1.1453327669332665,
                -3.067130965503355,
                -7.7040005451060285
              ],
              "initial_K": [
                -3.5730701160428513,
                -0.5531756358608656,
                4.4446072970634445,
                3.6878747633169895,
                -0.5839103130149119,
                -0.5610688084950448,
                3.6390695308061236,
                4.895799680404903,
                1.7633709323639322,
                0.22800723268792633,
                2.492891742240504,
                3.5255642931463504,
                0.8384003903548005,
                -1.026503045113604,
                0.8131486160795377,
                2.2511949927844173
              ],
              "metrics": {
                "initial_rmse_K": 2.084417913779365,
                "observation_residual_rms_K": 0.00983111310151717,
                "future_predictive_rmse_K": 0.030824440185940924
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.481464553538003,
                0.23222776486146607,
                -0.5667887670095034,
                0.1446813271426934,
                0.07005088419377833,
                -0.08680701498505791,
                -0.01920507324932825,
                -0.0025124174197865977
              ],
              "initial_K": [
                0.3536895588833061,
                0.7278581576286652,
                1.1070684185037207,
                1.4531983791001606,
                1.748504176327083,
                2.007659437378251,
                2.239813735308178,
                2.4090070509749335,
                2.4457753761565852,
                2.302714619623279,
                1.998410437451669,
                1.6089522108984204,
                1.218435304183333,
                0.8726592018456736,
                0.5695445025725343,
                0.2842989185803407
              ],
              "metrics": {
                "initial_rmse_K": 0.05122985184764694,
                "observation_residual_rms_K": 0.023292985430750077,
                "future_predictive_rmse_K": 0.039734745598213196
              }
            },
            "learned": {
              "coefficients_K": [
                6.5600484478167616,
                0.23789293824462693,
                -0.5889958880769223,
                0.13706927945186362,
                0.02187391799896625,
                -0.008585701542382047,
                -0.002994908920846258,
                0.000678281080812754
              ],
              "initial_K": [
                0.37084310183854596,
                0.738130840305638,
                1.097631585785995,
                1.4442549133855243,
                1.7708861820920043,
                2.0641862095480916,
                2.2990445088892466,
                2.4386300780519563,
                2.4460245253630117,
                2.3035413731291112,
                2.026277153228001,
                1.6590381160613612,
                1.258983299208612,
                0.8758757502832817,
                0.5391752642468721,
                0.2533531250931884
              ],
              "metrics": {
                "initial_rmse_K": 0.05052224221525362,
                "observation_residual_rms_K": 0.015081722536472036,
                "future_predictive_rmse_K": 0.03075352864495215
              }
            }
          }
        },
        {
          "split": "test",
          "index": 30,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.022028047866522,
            -1.3518810968495025,
            -0.3362361886406321,
            -0.01624701096388649,
            -0.04467320659660451,
            0.09172452114367745,
            -0.04042773839908142,
            -0.006286635853356148
          ],
          "initial_K": [
            0.14802113806900288,
            0.32765810602114964,
            0.5531028781478615,
            0.8277712050695261,
            1.1532013276091881,
            1.5122574316071133,
            1.8504934397237065,
            2.099827152952207,
            2.2301773177725353,
            2.262625035780819,
            2.2211450368197734,
            2.0855656871931223,
            1.812208476008304,
            1.3995701020447804,
            0.9141088560476243,
            0.43850730361187956
          ],
          "observed_K": [
            0.19826179231038674,
            0.43639772705601865,
            0.6771130463393472,
            0.8959554580043327,
            1.1807445542076784,
            1.3930768538395653,
            1.6778254123402245,
            1.881526686450013,
            1.9518326997136237,
            1.995530340213618,
            1.9447250205025979,
            1.7646802620490525,
            1.555259296730394,
            1.2430719499056009,
            0.7975842429232611,
            0.4387213429117321
          ],
          "future_observed_K": [
            0.23245850409737007,
            0.42388320394309836,
            0.7013403051673927,
            0.9384970670139918,
            1.1364558327456502,
            1.4322487500277619,
            1.6055555809214046,
            1.7295200882312898,
            1.8456393641727873,
            1.8749967930118292,
            1.8199695717763957,
            1.6853290793653946,
            1.4468912770801163,
            1.1077674842476473,
            0.8236265772451052,
            0.3748185959296608
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.024493885804008,
                -1.3618319362497349,
                -0.33602509637496497,
                0.08876886427008816,
                0.09459686567563214,
                0.9031229259211093,
                -4.014952827490035,
                -6.742341857209881
              ],
              "initial_K": [
                -3.1533020199089576,
                -0.512567492058701,
                3.686091205085771,
                2.5937506650464925,
                -1.4221272905638513,
                -1.0297428495284076,
                3.454429385705192,
                4.920668101252161,
                1.6721993066228895,
                -0.3071523632120161,
                1.9853981231566842,
                4.066172195819891,
                2.4378538878307943,
                0.1389612619875975,
                0.4116483047182248,
                1.1940396007910787
              ],
              "metrics": {
                "initial_rmse_K": 1.9662811763494155,
                "observation_residual_rms_K": 0.017874716081260553,
                "future_predictive_rmse_K": 0.023050088460765006
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.951985512826102,
                -1.3324846866960658,
                -0.3172762636693176,
                0.07186020522913733,
                0.03957272217853643,
                0.0684494564611989,
                -0.025139931751133868,
                -0.00219880269128113
              ],
              "initial_K": [
                0.1921457998623655,
                0.38381487617945864,
                0.584027243329091,
                0.8162195171050588,
                1.105692659914905,
                1.4494073251562396,
                1.7975907313657258,
                2.0764908010218077,
                2.2365243625726197,
                2.2749585988589462,
                2.2101019547372314,
                2.043810399046962,
                1.7619576621434754,
                1.3701139108690072,
                0.9133446433883732,
                0.4486068855773049
              ],
              "metrics": {
                "initial_rmse_K": 0.03648121974485342,
                "observation_residual_rms_K": 0.02696618477907009,
                "future_predictive_rmse_K": 0.029922629154882252
              }
            },
            "learned": {
              "coefficients_K": [
                6.02414978934495,
                -1.3649905189984315,
                -0.32970733642380756,
                0.06807945950278993,
                0.012356881571040318,
                0.006770035854997279,
                -0.003920412325090739,
                0.0005936140444619413
              ],
              "initial_K": [
                0.1711147985176263,
                0.35828314685768364,
                0.5764871970718042,
                0.8365534664582468,
                1.1396064099534258,
                1.4710958094183102,
                1.7986458776636194,
                2.0777113082824363,
                2.2644701377576646,
                2.3290907973738735,
                2.2613670538912607,
                2.067586395060773,
                1.764967350744988,
                1.3786723560443976,
                0.938831541331377,
                0.4733469230139005
              ],
              "metrics": {
                "initial_rmse_K": 0.03462274946785305,
                "observation_residual_rms_K": 0.020933300778352888,
                "future_predictive_rmse_K": 0.022811732093381814
              }
            }
          }
        },
        {
          "split": "test",
          "index": 31,
          "scenario": "smooth",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.377356295188499,
            0.7716874304292267,
            -1.1237860672550566,
            -0.24010557718598957,
            0.019814182809407426,
            -0.003852254828625139,
            -0.0564822158563766,
            0.04301894278658247
          ],
          "initial_K": [
            0.17642749503288802,
            0.41554399494937866,
            0.7599238282098529,
            1.1931060799661073,
            1.6343433249125352,
            1.9957398848396755,
            2.227909024659861,
            2.296584926823459,
            2.1610847818172205,
            1.8279680797885427,
            1.400286833220606,
            1.010272127251759,
            0.7043754304123903,
            0.4453892485518376,
            0.21960228221239542,
            0.06914168026504514
          ],
          "observed_K": [
            0.27956083083799127,
            0.5694537533742229,
            0.8433098881018456,
            1.1629479870011934,
            1.4481768969018514,
            1.6183234505596333,
            1.8174582619839261,
            1.8919486683623883,
            1.7791907623820378,
            1.5883357928505513,
            1.3744602062317002,
            1.1113321852020948,
            0.848679373684854,
            0.5822425844988092,
            0.37320133843808795,
            0.15537343588027872
          ],
          "future_observed_K": [
            0.28079735809241746,
            0.570836195707769,
            0.8657026723294704,
            1.1363645826299924,
            1.3656478495796784,
            1.586215997424402,
            1.6807613206438572,
            1.7286743579591288,
            1.679380804788249,
            1.5595371644501441,
            1.3145413305999885,
            1.0776778351779903,
            0.8581623195422048,
            0.634614074186956,
            0.37932885070614303,
            0.1901853771675993
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.367816904522193,
                0.7043095454334899,
                -1.128296683079251,
                -0.18726397629830854,
                0.23055814680631484,
                0.7929710765870527,
                -4.128323973384467,
                -6.420420476991955
              ],
              "initial_K": [
                -3.0695855538448598,
                -0.4395083030473001,
                3.799543660584513,
                2.9201216453258545,
                -0.897853643267911,
                -0.5504891483785169,
                3.7474747193579807,
                5.100684557154977,
                1.7119281661277168,
                -0.6782847105629544,
                1.062486052037013,
                2.878916409778112,
                1.3948002674079465,
                -0.6667248258359737,
                -0.26189102182344376,
                0.7410625652104195
              ],
              "metrics": {
                "initial_rmse_K": 1.9209816538547804,
                "observation_residual_rms_K": 0.015316678328805584,
                "future_predictive_rmse_K": 0.01882154798370286
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.3032120302260575,
                0.6891317929937957,
                -1.0653423204985941,
                -0.1515940062934343,
                0.09644942699105497,
                0.06010083192880531,
                -0.02584981378282778,
                -0.002093818160357771
              ],
              "initial_K": [
                0.22784188985342302,
                0.4809299445397698,
                0.7786451904966982,
                1.130601557512811,
                1.525200460093238,
                1.9100258718466485,
                2.19067634530436,
                2.272928688555849,
                2.1258245332992063,
                1.806520965288491,
                1.4186105903345256,
                1.044822898787993,
                0.718122348920853,
                0.4446474122189893,
                0.23335834968909552,
                0.09165138697675868
              ],
              "metrics": {
                "initial_rmse_K": 0.04776193452271116,
                "observation_residual_rms_K": 0.024715594233738578,
                "future_predictive_rmse_K": 0.0306586896577728
              }
            },
            "learned": {
              "coefficients_K": [
                5.367510314985425,
                0.7059430950079512,
                -1.107083066375374,
                -0.14361826520549498,
                0.03011706249436601,
                0.005944309978616455,
                -0.004031113909087194,
                0.0005652712139503758
              ],
              "initial_K": [
                0.20160518005401523,
                0.45008987536198364,
                0.7726194555346015,
                1.1630935131651468,
                1.5790947160990516,
                1.9509184851618342,
                2.201419188790247,
                2.2719985042353,
                2.1455381504128685,
                1.8545387377724138,
                1.468022790817594,
                1.0638438183184986,
                0.7030517895851497,
                0.41886003682614525,
                0.2186129508876552,
                0.08900260595013526
              ],
              "metrics": {
                "initial_rmse_K": 0.034245078948532515,
                "observation_residual_rms_K": 0.019227603865029492,
                "future_predictive_rmse_K": 0.019403103122838005
              }
            }
          }
        }
      ],
      "high-frequency": [
        {
          "split": "test",
          "index": 0,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.064136750230109,
            1.768324303923217,
            0.2456775890493475,
            0.005338822758752014,
            0.08703779952503056,
            6.008671880120627,
            -0.009365291777447502,
            -0.002943137637902704
          ],
          "initial_K": [
            2.5115164315543548,
            2.908765798168476,
            1.358500980894104,
            0.07804278632857509,
            0.8530359079267317,
            3.0493610056977345,
            4.318764018396351,
            3.2157689272752914,
            0.8229239107204327,
            -0.4224942970128369,
            0.596895895354381,
            2.4669346798555587,
            2.833318174568957,
            1.0251490960268048,
            -1.2011026485079768,
            -1.6169354454115703
          ],
          "observed_K": [
            0.6034705665422802,
            1.0310706763058097,
            1.389803905928652,
            1.6700973689403815,
            1.880791185730425,
            2.0462925556396647,
            2.0683535339177794,
            1.9786782734678787,
            1.7643635084254665,
            1.5214788457494777,
            1.3344738164377665,
            1.195144145280449,
            0.9223035527894834,
            0.63468973485659,
            0.4273864211523684,
            0.16721082976720014
          ],
          "future_observed_K": [
            0.4797287279329672,
            0.8924185176929295,
            1.257217564687762,
            1.5623647048857352,
            1.7441426408622749,
            1.8917893656757698,
            1.920689088425938,
            1.7749583909186892,
            1.6965476740026721,
            1.5185202919464562,
            1.3144166352881164,
            1.1554866620173767,
            0.9368288343222407,
            0.6556164681617255,
            0.4272601958819062,
            0.2208783697896571
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.110819678615166,
                1.801780974166862,
                0.2228236936016799,
                0.037373020120454604,
                0.21941131555390067,
                5.591787561161967,
                2.8456679416074073,
                -8.242750501403444
              ],
              "initial_K": [
                0.557824226476769,
                2.8519665206987668,
                3.479454064947635,
                0.3539969231164204,
                -1.430640668711556,
                2.468754270459633,
                6.810747201236399,
                4.32530715973432,
                -1.7213060017165613,
                -2.1489229292150887,
                3.09805556290088,
                5.039963770763178,
                0.7654135045744225,
                -2.3812103270940734,
                -0.02839129202958235,
                2.2906246793757212
              ],
              "metrics": {
                "initial_rmse_K": 2.182913800602311,
                "observation_residual_rms_K": 0.01768506392884992,
                "future_predictive_rmse_K": 0.025806303199984854
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.037272323292616,
                1.7629528967202843,
                0.21039103842425078,
                0.03025422165723828,
                0.09178637126323246,
                0.42381253783105094,
                0.017818365722399608,
                -0.0026881137696487156
              ],
              "initial_K": [
                0.8041317284975983,
                1.3796875646768854,
                1.6929808801750972,
                1.895141353467959,
                2.1257346235504313,
                2.349888267540466,
                2.405613628981881,
                2.2003390224716846,
                1.8313205908692924,
                1.4965734234782024,
                1.3006934454150634,
                1.1709680109639562,
                0.9660793646599894,
                0.6454783231763107,
                0.3125996217641621,
                0.09485545434462134
              ],
              "metrics": {
                "initial_rmse_K": 1.3962904404522243,
                "observation_residual_rms_K": 0.04534748944869351,
                "future_predictive_rmse_K": 0.025529799185502806
              }
            },
            "learned": {
              "coefficients_K": [
                6.1104706515511165,
                1.805959958482361,
                0.21863428446887279,
                0.028662471134541588,
                0.028660988102316313,
                0.04191744135382651,
                0.002778660709288486,
                0.0007257140866265154
              ],
              "initial_K": [
                0.6768637709827459,
                1.2728252437335648,
                1.7403790871931677,
                2.070481599119095,
                2.271173701464044,
                2.346888277703819,
                2.2989048933235035,
                2.1405161041361156,
                1.9051734171650563,
                1.6360852857980825,
                1.3665041138283218,
                1.1088661966367728,
                0.8611124459734455,
                0.6214524243824241,
                0.3955813413901061,
                0.18984665796400257
              ],
              "metrics": {
                "initial_rmse_K": 1.491864729258992,
                "observation_residual_rms_K": 0.04420845029734951,
                "future_predictive_rmse_K": 0.027876388796131166
              }
            }
          }
        },
        {
          "split": "test",
          "index": 1,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.184809778754638,
            -2.9132134703184316,
            0.12478018733153877,
            0.44910633776766584,
            -0.04817235905362789,
            -5.937025133703197,
            0.022310270053648815,
            -0.0271975656568205
          ],
          "initial_K": [
            -1.6828611733981678,
            -1.3537938829545273,
            0.7598677500337363,
            2.4605207475800857,
            2.047590613959569,
            0.22376447078799067,
            -0.6728832581952751,
            0.745273850855928,
            3.3552460554102908,
            4.6954529050458484,
            3.595958336690852,
            1.4048315703170666,
            0.46980305907998676,
            1.5366344686399311,
            2.9393470536110016,
            2.4958744565449242
          ],
          "observed_K": [
            0.09380366807060793,
            0.2720939564050037,
            0.44957482442827346,
            0.7323810486815221,
            0.8959681307231662,
            1.151748864881143,
            1.3920589452799574,
            1.7401897434536586,
            2.135782844344176,
            2.2789375124310585,
            2.284849656754142,
            2.149580532091112,
            1.8879553773801738,
            1.5898755286803568,
            1.1465623669672163,
            0.6217865156766976
          ],
          "future_observed_K": [
            0.15569462840299658,
            0.29763308187752224,
            0.4797902666695665,
            0.7311332665744388,
            0.9350036674234561,
            1.2300449440822747,
            1.435353114870793,
            1.697635092833165,
            1.8862465463327363,
            2.0811513780545656,
            2.092537038904202,
            1.972917222033743,
            1.7634252618288697,
            1.4636622360184937,
            1.0448275967695106,
            0.5395762347507728
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.201054259012771,
                -2.8509822712210418,
                0.030036920422251458,
                0.5620970260892715,
                0.36098441491694727,
                -6.055782143460637,
                -3.0211522541207834,
                15.830995085298639
              ],
              "initial_K": [
                2.822469147113168,
                -0.7754947894172199,
                -3.6897435686599787,
                1.4015687902103737,
                6.605386282205464,
                1.9292049202670032,
                -5.401626294339592,
                -1.9552099161477137,
                8.046690742332963,
                8.77607491637859,
                -0.3555485203367199,
                -3.8306633915844217,
                3.2055582316229505,
                7.435329549323077,
                1.4777742739242754,
                -3.825733672975689
              ],
              "metrics": {
                "initial_rmse_K": 4.038504755564524,
                "observation_residual_rms_K": 0.017625536917471513,
                "future_predictive_rmse_K": 0.02212821633916303
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.126420876758335,
                -2.7895440819999697,
                0.028360982517419434,
                0.45502900127870133,
                0.15101066890813156,
                -0.45897959654223625,
                -0.018917174059517452,
                0.0051627810242208284
              ],
              "initial_K": [
                0.046682492007556475,
                0.1997110580301662,
                0.43426043744896037,
                0.6287045556624695,
                0.7328577759955189,
                0.8683030156337881,
                1.2201725956120952,
                1.8183072951095187,
                2.4508301462793227,
                2.823322601866666,
                2.807504399359537,
                2.522454323813027,
                2.1752374208135614,
                1.8437077678814586,
                1.4286978628059872,
                0.8059886532972067
              ],
              "metrics": {
                "initial_rmse_K": 1.3711181295412243,
                "observation_residual_rms_K": 0.04945621472314572,
                "future_predictive_rmse_K": 0.028114522896807027
              }
            },
            "learned": {
              "coefficients_K": [
                6.200700078088466,
                -2.8575947343150685,
                0.029472182684067625,
                0.4310887836511148,
                0.04715422262948238,
                -0.04539566106072041,
                -0.0029500128748549247,
                -0.0013938036989910383
              ],
              "initial_K": [
                0.1391879784797797,
                0.2667670381860755,
                0.3801438629070967,
                0.4996422669274764,
                0.6740941266614291,
                0.9598240555594935,
                1.3779642388888291,
                1.8819222834385052,
                2.3647028889213026,
                2.7048929446956533,
                2.820360495862697,
                2.6951100911001262,
                2.366936815774645,
                1.8922918927106398,
                1.3179723623795718,
                0.676927990075772
              ],
              "metrics": {
                "initial_rmse_K": 1.4733983488334759,
                "observation_residual_rms_K": 0.048376788641841376,
                "future_predictive_rmse_K": 0.022648866010223256
              }
            }
          }
        },
        {
          "split": "test",
          "index": 2,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.475793918696814,
            -0.03163023368275662,
            0.3355965009422605,
            0.11297519515169935,
            0.19505591894691615,
            5.966869824714086,
            0.11145245560602077,
            0.05838141932070094
          ],
          "initial_K": [
            2.370055238469367,
            2.5341855825237767,
            0.7276533916485021,
            -0.6916661190390603,
            0.08910207608206555,
            2.35705756970171,
            3.736548137263643,
            2.8367626371917076,
            0.7409144486004602,
            -0.22647163440967555,
            0.9491831916334562,
            2.8725171499883473,
            3.2671484822086585,
            1.4758813250125473,
            -0.8022004283134284,
            -1.3783138394393706
          ],
          "observed_K": [
            0.39680096203267406,
            0.7033334473781279,
            0.9508340949545669,
            1.157253927188342,
            1.3431579923784032,
            1.5428759633359033,
            1.6816823522495614,
            1.668889352609104,
            1.6371287269835433,
            1.5420631331900228,
            1.5294323376726557,
            1.4387392784526172,
            1.2219135897447153,
            0.9577473059277576,
            0.6200348817244977,
            0.29074516907084963
          ],
          "future_observed_K": [
            0.3303651355257104,
            0.6376208589051292,
            0.8402066533450739,
            1.1203991036035383,
            1.3047167155047859,
            1.4634083648745628,
            1.5552131459950471,
            1.618737242610587,
            1.60557800543524,
            1.5363810096536687,
            1.4663628717056922,
            1.310819738780253,
            1.1149109768010035,
            0.8435949474749389,
            0.6219849123626865,
            0.28876056195640554
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.517670107088665,
                0.011193117124321169,
                0.3621996286256284,
                0.06310106187480273,
                -0.11943984742097975,
                5.388230214141185,
                1.6887877467463936,
                -11.466863746639703
              ],
              "initial_K": [
                -1.3083629952789548,
                1.8366930883823347,
                4.179033707065883,
                0.5281879179378269,
                -3.0711670439345666,
                0.8550504308755396,
                6.899917744063119,
                4.881582293336222,
                -2.3494674737348227,
                -3.023269214188833,
                3.696324114507939,
                6.475950179860227,
                1.2261795219836111,
                -2.749107343442951,
                0.28412154942746193,
                3.1835608083748177
              ],
              "metrics": {
                "initial_rmse_K": 2.912899937693739,
                "observation_residual_rms_K": 0.010649653995616619,
                "future_predictive_rmse_K": 0.02080169957548079
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.451261660225343,
                0.010951907329788447,
                0.3419903635546298,
                0.0510815959377748,
                -0.04996529076602123,
                0.4083845275764721,
                0.010574472607663747,
                -0.003739556878105141
              ],
              "initial_K": [
                0.53240570651293,
                0.8973909049001323,
                1.085312167153458,
                1.2317338697358882,
                1.4510857236617247,
                1.7034215762655847,
                1.8443199333646485,
                1.7996966900033897,
                1.66176677131798,
                1.5907313355702912,
                1.6312789087070985,
                1.6533385058780117,
                1.4863423294091531,
                1.099632929688065,
                0.6343445298894637,
                0.25785913203994054
              ],
              "metrics": {
                "initial_rmse_K": 1.3914272426267844,
                "observation_residual_rms_K": 0.040687670794748575,
                "future_predictive_rmse_K": 0.024470426718904776
              }
            },
            "learned": {
              "coefficients_K": [
                5.517354958499906,
                0.01121907802721377,
                0.3553897494447543,
                0.048394064989025994,
                -0.015602039654304957,
                0.0403915244511266,
                0.0016490216899872684,
                0.001009573751983207
              ],
              "initial_K": [
                0.4334980811664122,
                0.8181362373405264,
                1.1291154805375818,
                1.3679453329767297,
                1.5456039450787977,
                1.6681025564181355,
                1.7379792981071371,
                1.7636490549339583,
                1.7601074035941315,
                1.7366079562527503,
                1.6835175774045783,
                1.5737250867399288,
                1.3810826038089832,
                1.1014910047859174,
                0.7576558828047557,
                0.38285938779958456
              ],
              "metrics": {
                "initial_rmse_K": 1.4830499827293497,
                "observation_residual_rms_K": 0.04028904546653779,
                "future_predictive_rmse_K": 0.021503632467970882
              }
            }
          }
        },
        {
          "split": "test",
          "index": 3,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.6585834541058055,
            1.133465957070806,
            0.1259019836794421,
            -0.2656798847535495,
            -0.13024952652174732,
            -6.005406078317735,
            0.03481519825014512,
            0.01213347660713752
          ],
          "initial_K": [
            -1.405494011400434,
            -0.7687437784229864,
            1.690344593512818,
            3.7049250648465364,
            3.424468559291502,
            1.4274460491461889,
            0.065664572641011,
            0.8587300278835263,
            2.8243540052084986,
            3.601931772660852,
            2.1154656914318455,
            -0.20220270195349532,
            -0.9952218823083565,
            0.39076935557474635,
            2.1749426233334246,
            2.1158998853716136
          ],
          "observed_K": [
            0.33828004581685917,
            0.7421139719451194,
            1.151001310410975,
            1.521261572007,
            1.6910371293382271,
            1.80495866677788,
            1.750466931666231,
            1.743777599304454,
            1.7049561663356054,
            1.6222545441807108,
            1.3506812772489132,
            1.1183934625839267,
            0.8812715164338311,
            0.7322126366990649,
            0.5479334169176162,
            0.2837176762508135
          ],
          "future_observed_K": [
            0.34893767412961535,
            0.7473607483436833,
            1.0611128406431427,
            1.3612325038976247,
            1.5659766504759016,
            1.6837972506555354,
            1.6910098245619316,
            1.686036444182531,
            1.6206463956682453,
            1.4593639478831384,
            1.3169510244521219,
            1.1474474732429942,
            0.9341725441081014,
            0.7270260453749862,
            0.4691703445795883,
            0.23222203649517015
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.654059473951639,
                1.0947223892814417,
                0.10043358399737737,
                -0.3082679420201481,
                -0.257964512189674,
                -6.734800827387154,
                -0.7504737599723804,
                15.060021807717044
              ],
              "initial_K": [
                3.1963664979769195,
                -0.23579774106712303,
                -3.095466904294926,
                2.3212901233317806,
                8.197934701984448,
                3.8191587862431975,
                -4.397198513983249,
                -2.5647481804234844,
                6.613014323044936,
                7.862879292664619,
                -0.7531969034849424,
                -4.996205287505534,
                0.9007294910295633,
                5.488823834981806,
                1.2573777108996127,
                -3.083783069247136
              ],
              "metrics": {
                "initial_rmse_K": 3.7716701680376263,
                "observation_residual_rms_K": 0.015080660291783201,
                "future_predictive_rmse_K": 0.017006279294912677
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.5860094998048355,
                1.0711313056131413,
                0.09482979878993503,
                -0.2495491832781748,
                -0.1079143362720662,
                -0.5104437533117752,
                -0.004699148387882097,
                0.004911352343570429
              ],
              "initial_K": [
                0.2581011512127735,
                0.7076753182495201,
                1.319861954475861,
                1.8555643987659147,
                2.095188364529376,
                2.045629640883887,
                1.9078989937216644,
                1.8498058773115826,
                1.839553926552407,
                1.7191959420550924,
                1.4193195655282231,
                1.0594106762670499,
                0.8197875721635587,
                0.7376154726528507,
                0.6619253995153502,
                0.41809084291110926
              ],
              "metrics": {
                "initial_rmse_K": 1.3740246910182925,
                "observation_residual_rms_K": 0.050344351021933874,
                "future_predictive_rmse_K": 0.022523983888639014
              }
            },
            "learned": {
              "coefficients_K": [
                5.653736535314608,
                1.097261448001799,
                0.0985452867196592,
                -0.23641977451592583,
                -0.03369706706339757,
                -0.05048575533742926,
                -0.0007328022780512261,
                -0.0013259251227975318
              ],
              "initial_K": [
                0.43002975942818145,
                0.8784362379018882,
                1.3263246864766345,
                1.7163955307852685,
                1.9871385928479257,
                2.109080757448054,
                2.09403835274144,
                1.9779266587794238,
                1.7986476082435763,
                1.586364303466995,
                1.365399388394198,
                1.1552618721975625,
                0.9630528877038426,
                0.7747076106906795,
                0.560630928728475,
                0.2992872521199496
              ],
              "metrics": {
                "initial_rmse_K": 1.489017756113199,
                "observation_residual_rms_K": 0.05101469093333823,
                "future_predictive_rmse_K": 0.017331468077492286
              }
            }
          }
        },
        {
          "split": "test",
          "index": 4,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.497192439893651,
            -1.1318418722730608,
            0.05168256978725702,
            -0.18610872515166946,
            0.08827460384575889,
            6.105883179340385,
            0.048580982748094505,
            -0.0148131148411177
          ],
          "initial_K": [
            2.145446583999134,
            2.2040472130469384,
            0.41212691827598735,
            -0.9261745432725665,
            0.002449724408195575,
            2.4932914304430023,
            4.085279897384262,
            3.2734230994611657,
            1.1581131448509436,
            0.20089359807446394,
            1.4823579352755405,
            3.512976352318643,
            3.8954429569000264,
            1.968927085219904,
            -0.4864543558956469,
            -1.2274253355309188
          ],
          "observed_K": [
            0.3175596320262785,
            0.6182579553862911,
            0.8414314893391205,
            1.0497397153963353,
            1.3453047264717504,
            1.6569446871199562,
            1.8938419229325452,
            1.9971999509760126,
            1.9919752553093673,
            1.9884477864859582,
            1.9822472659759833,
            1.8907042631438895,
            1.6923845467504357,
            1.370269383483653,
            0.86953263199655,
            0.42070002714422683
          ],
          "future_observed_K": [
            0.2721056234754819,
            0.5359264651608739,
            0.791564015639997,
            1.0606801303336821,
            1.3024306162461634,
            1.5881008302758965,
            1.7765570181999688,
            1.858521114583616,
            1.934094637920106,
            1.9299812905012135,
            1.8916141673234963,
            1.7277301498382804,
            1.5155100989878183,
            1.2092858359567633,
            0.8757602658432658,
            0.43831854371234286
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.523282563076323,
                -1.0958701023776256,
                0.13248700716250764,
                -0.29448397396857273,
                -0.05672579409316786,
                6.957759012701622,
                -0.60784332666954,
                0.8419902822637457
              ],
              "initial_K": [
                2.4390358769230973,
                2.324199095344287,
                0.22318091511165905,
                -1.0520424083862363,
                0.12541393463364758,
                2.6113837296492304,
                4.080935234072867,
                3.3623579759940467,
                1.303992705064604,
                0.004163021742897843,
                0.9887311790153572,
                3.440621030762095,
                4.533062568417103,
                2.48992482942818,
                -0.883247151420189,
                -2.0010367308111743
              ],
              "metrics": {
                "initial_rmse_K": 0.34748846208947665,
                "observation_residual_rms_K": 0.012142230931879038,
                "future_predictive_rmse_K": 0.022725261811148714
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.444770971216573,
                -1.072254285684821,
                0.12509477140464648,
                -0.2383907801465956,
                -0.023730110654015535,
                0.5273421911216506,
                -0.003806057108124848,
                0.0002745886426233833
              ],
              "initial_K": [
                0.3950863336818009,
                0.6436012320541945,
                0.7765600253048515,
                0.9736819763444945,
                1.3549450819210374,
                1.8256329104472628,
                2.154892731376447,
                2.210709271012938,
                2.096480665645089,
                2.0356648237645145,
                2.1245511730940096,
                2.219879282652296,
                2.0841660914863978,
                1.632163451406368,
                1.0132618221281577,
                0.4469577724453288
              ],
              "metrics": {
                "initial_rmse_K": 1.3953059276893907,
                "observation_residual_rms_K": 0.0510872138352252,
                "future_predictive_rmse_K": 0.025150791257972017
              }
            },
            "learned": {
              "coefficients_K": [
                6.522909977681777,
                -1.098411823061394,
                0.12999605896569208,
                -0.22584844297449946,
                -0.007409906391994309,
                0.052157105787540556,
                -0.0005935303780615428,
                -7.413110569553177e-05
              ],
              "initial_K": [
                0.2600610191815446,
                0.5289028203316892,
                0.8190884879798601,
                1.1378115659101997,
                1.470371456422866,
                1.7764034173240029,
                2.0101946068402152,
                2.150987310415452,
                2.2146061890246402,
                2.2325077463477303,
                2.215798185299443,
                2.137700678689934,
                1.9509652453215074,
                1.6237608324186725,
                1.1622619306249165,
                0.6046564998020276
              ],
              "metrics": {
                "initial_rmse_K": 1.513870896848453,
                "observation_residual_rms_K": 0.05105968352833223,
                "future_predictive_rmse_K": 0.02403490129133178
              }
            }
          }
        },
        {
          "split": "test",
          "index": 5,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.522111901523194,
            -0.9107309638742822,
            0.0861641534473814,
            0.14234900537895906,
            -0.05158663102566782,
            -6.021699515731568,
            0.04003948010891521,
            0.02107881625588748
          ],
          "initial_K": [
            -1.5589634930854115,
            -1.1078643361630167,
            1.1427837404295498,
            2.9785254394574645,
            2.614101669389015,
            0.6771091665773838,
            -0.4669740512582796,
            0.6635500551643057,
            2.9979790373776094,
            4.074100586545465,
            2.754221909989536,
            0.4705338402488555,
            -0.3852622688936058,
            0.8789816890305597,
            2.5096310828447623,
            2.284326334979423
          ],
          "observed_K": [
            0.17670864154668037,
            0.4481155210668689,
            0.7128774153607308,
            1.0152122093004476,
            1.1979082020605358,
            1.364171097123968,
            1.4423864073035477,
            1.6588373042804907,
            1.7658253535966482,
            1.8404147242244848,
            1.7399238557536882,
            1.5710115225904009,
            1.3273026105077683,
            1.0944082443901404,
            0.8314685314081932,
            0.45180374371921855
          ],
          "future_observed_K": [
            0.24179543337056367,
            0.473677413042659,
            0.7167768550771559,
            0.9317812783275835,
            1.1417499539060507,
            1.3316298089582925,
            1.4250949308026657,
            1.587502738763666,
            1.6787624781417985,
            1.6846256063195277,
            1.610818594240237,
            1.4636403806780907,
            1.2524829140795992,
            1.0103254397846628,
            0.7080352251164038,
            0.38461485302994936
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.5511193910425405,
                -0.9660579337139248,
                0.05801967241200246,
                0.039778783911166724,
                -0.11116671829175502,
                -6.2154087443227155,
                0.7011100366455724,
                -1.2803703923560874
              ],
              "initial_K": [
                -1.8949579422919638,
                -1.1960633916579848,
                1.37476802884307,
                2.9851093449411374,
                2.326001784024303,
                0.6870319354048717,
                -0.06117184597633085,
                0.758480167925973,
                2.5429528190124544,
                3.8567543201827306,
                3.2447507854855946,
                0.8915649147242362,
                -0.7782796710405888,
                0.31796905744374593,
                2.7871563133334734,
                3.017376112240865
              ],
              "metrics": {
                "initial_rmse_K": 0.36971886663559883,
                "observation_residual_rms_K": 0.014710792776826935,
                "future_predictive_rmse_K": 0.01708836926815243
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.484308362119589,
                -0.9452395474583646,
                0.05478241084010118,
                0.03220173648864808,
                -0.046504391314018546,
                -0.47107800945165723,
                0.004390053688955428,
                -0.0004175525246526527
              ],
              "initial_K": [
                0.0898021981385751,
                0.3454109632759569,
                0.7506232097839127,
                1.12399453441719,
                1.3151734923739764,
                1.364889908184554,
                1.4529075053298168,
                1.6909968170940766,
                1.9880524196110227,
                2.1355854552625404,
                2.0204828432933386,
                1.7330251580137739,
                1.4546743483037028,
                1.2537892433007547,
                1.018196131436734,
                0.5987230505848858
              ],
              "metrics": {
                "initial_rmse_K": 1.3880493303364136,
                "observation_residual_rms_K": 0.04640441735657004,
                "future_predictive_rmse_K": 0.019720605920573835
              }
            },
            "learned": {
              "coefficients_K": [
                5.550802331956338,
                -0.9682985728430622,
                0.0569288182862297,
                0.0305075223234893,
                -0.014521347644674368,
                -0.04659226207729345,
                0.0006846009273360369,
                0.00011272727831251531
              ],
              "initial_K": [
                0.22917841372172384,
                0.47450681326275684,
                0.7337097029763625,
                0.9872226441125247,
                1.2172563187856953,
                1.4234536602517363,
                1.6170924524289363,
                1.799114172504733,
                1.9456072988991142,
                2.017394977739911,
                1.9851688638384397,
                1.8455617082148041,
                1.6140769520543272,
                1.3058200152829136,
                0.9266606802546966,
                0.4835673696859678
              ],
              "metrics": {
                "initial_rmse_K": 1.494213198138516,
                "observation_residual_rms_K": 0.046623180869261344,
                "future_predictive_rmse_K": 0.020524412652633557
              }
            }
          }
        },
        {
          "split": "test",
          "index": 6,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.822054874763854,
            2.859774744073671,
            0.01098550497731065,
            0.20400532732130353,
            0.19347015101728815,
            5.95744950344682,
            -0.0029728544021611013,
            0.015425310860645847
          ],
          "initial_K": [
            2.65681250444495,
            3.1501740805157588,
            1.633008864547794,
            0.33659453570737763,
            1.0634241459761908,
            3.197591934125679,
            4.414189271929392,
            3.2721246484093256,
            0.8179194805011214,
            -0.5541835526445062,
            0.2847698783551329,
            1.9939685327530126,
            2.292047907313608,
            0.526328354074049,
            -1.5740868741160063,
            -1.815017842377055
          ],
          "observed_K": [
            0.6114866774503327,
            1.1597120351150767,
            1.5973032388678963,
            1.8102127792640823,
            2.024216641077208,
            2.180169557074401,
            2.153069985198667,
            1.9701356221750437,
            1.647662545860124,
            1.3454305988375395,
            1.0766566356949405,
            0.841223598326765,
            0.6717294591149133,
            0.3689311700127092,
            0.16778520461797952,
            0.003290071215011979
          ],
          "future_observed_K": [
            0.5623676726798132,
            1.028059230442574,
            1.4211296539629195,
            1.6874541720876066,
            1.9095622060043445,
            2.010813781106732,
            1.952064879452521,
            1.8264398899071432,
            1.6248217159149088,
            1.3710319100982808,
            1.0826999278871472,
            0.879222490474916,
            0.652515719201144,
            0.4333819532324567,
            0.2438900490853707,
            0.13014205601813275
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.856219147045664,
                2.862813631308268,
                0.04211079711788796,
                0.10528559014273771,
                0.020936210853742483,
                7.077306998657703,
                -4.755115821781557,
                -5.078264936851367
              ],
              "initial_K": [
                -0.36865249141777623,
                2.2014529709586967,
                4.310293215355506,
                2.0997570534924734,
                -0.9678511015339923,
                0.875384684234515,
                5.6261420003522815,
                5.9129536185843286,
                0.6754320502910645,
                -2.9573544586031684,
                -0.5422667943104692,
                3.5704990869215116,
                3.5422021000157393,
                0.03609634975610598,
                -2.4277642328498596,
                -2.0039542572425857
              ],
              "metrics": {
                "initial_rmse_K": 1.7646579465790582,
                "observation_residual_rms_K": 0.01881707807811239,
                "future_predictive_rmse_K": 0.01731455146196686
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.785736060797554,
                2.8011204782639836,
                0.039761186035911764,
                0.08523083152565895,
                0.008758248486026004,
                0.5364029672628153,
                -0.02977451849740864,
                -0.0016561163534368967
              ],
              "initial_K": [
                0.8953012907899248,
                1.5497009159365733,
                1.9163652987815898,
                2.1406804519341387,
                2.367968402972818,
                2.5665068546238956,
                2.559676981824134,
                2.2369670213424313,
                1.710527348315892,
                1.2331417531327962,
                0.9569827089736522,
                0.7994653804743079,
                0.5700932223664849,
                0.21612489073727026,
                -0.0964964505961432,
                -0.16649464962599342
              ],
              "metrics": {
                "initial_rmse_K": 1.356525178041785,
                "observation_residual_rms_K": 0.054810527527945165,
                "future_predictive_rmse_K": 0.030673046399826886
              }
            },
            "learned": {
              "coefficients_K": [
                5.855884661807542,
                2.8694535356223674,
                0.04131905295826177,
                0.08074662359699841,
                0.002734829280212259,
                0.05305326745954098,
                -0.004643146626108812,
                0.00044710420382942115
              ],
              "initial_K": [
                0.7663879258004589,
                1.443511498873072,
                1.9725331459769282,
                2.3329414124869254,
                2.5266926043596927,
                2.5585957784151914,
                2.433252851708837,
                2.1687833143625315,
                1.8081427861034625,
                1.4105989870983122,
                1.0277242211511144,
                0.6868112970059002,
                0.3978470052835039,
                0.17324674011290164,
                0.033134508641636806,
                -0.01489196112192448
              ],
              "metrics": {
                "initial_rmse_K": 1.477240945494417,
                "observation_residual_rms_K": 0.05459063836921141,
                "future_predictive_rmse_K": 0.021204618135495637
              }
            }
          }
        },
        {
          "split": "test",
          "index": 7,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.719353124787714,
            -0.11954545828251328,
            -0.014730721284114578,
            -0.03840727740350079,
            -0.09190249194734669,
            -5.978097974626972,
            -0.030855775710861892,
            -0.05555103725941407
          ],
          "initial_K": [
            -1.4926694977748731,
            -0.8884062550868543,
            1.5518717518042016,
            3.5105442783210155,
            3.198656870475313,
            1.303929475655305,
            0.17421483671856208,
            1.2106026717987919,
            3.349348264307398,
            4.246838088789302,
            2.8455235049436443,
            0.5349900645854819,
            -0.3611134292356175,
            0.856108400772726,
            2.472700766876543,
            2.263662325977463
          ],
          "observed_K": [
            0.3130234766879545,
            0.6930231345380038,
            1.0710542158214456,
            1.4054253253259457,
            1.700280782225044,
            1.8313880308527213,
            1.920717198625542,
            2.0300878060176943,
            2.115384106389551,
            2.0701946336514534,
            1.950649464829416,
            1.6554964554568579,
            1.395773832269519,
            1.098885812122593,
            0.7938598808920672,
            0.4521000158639279
          ],
          "future_observed_K": [
            0.3408999714191556,
            0.6928325043583973,
            1.0452746069562524,
            1.3460612461504788,
            1.5814716409776588,
            1.7811402013361066,
            1.883834044727892,
            1.9298270036986278,
            1.9735755894820284,
            1.9070272639401018,
            1.8097769996812232,
            1.5895613031217732,
            1.3605155453230109,
            1.0470488763671097,
            0.7447814262096002,
            0.3880270648683601
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.714832949967142,
                -0.14249669010309643,
                -0.02393386981199125,
                0.06857114627037908,
                -0.38530925177653597,
                -5.702821095060808,
                2.8216470270856453,
                3.8600075567335628
              ],
              "initial_K": [
                0.8098171724560776,
                -0.12016479390993973,
                -0.4344571186785243,
                2.1070636893023456,
                4.587997412305613,
                3.0446927830207633,
                -0.5049346606532108,
                -0.5285593051756645,
                3.349759894964218,
                5.597152111819348,
                3.1871962861717673,
                -0.29912763925010033,
                -0.6104583678339454,
                1.443521313637126,
                2.5342187687914297,
                1.6787623042611217
              ],
              "metrics": {
                "initial_rmse_K": 1.215584028928801,
                "observation_residual_rms_K": 0.012872038273365518,
                "future_predictive_rmse_K": 0.018368981560275475
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.63401593508597,
                -0.1394259103587591,
                -0.02259845729088885,
                0.055509740766696215,
                -0.1611864818614215,
                -0.4322279869645012,
                0.017667956943610928,
                0.0012588200337298701
              ],
              "initial_K": [
                0.23901196129441313,
                0.6335739441686,
                1.1653078107256205,
                1.648771512096377,
                1.9134550921946738,
                1.971798866639038,
                1.9956529877727622,
                2.1248695148930015,
                2.312872198223466,
                2.376021280595195,
                2.1914069519841104,
                1.8249676994721162,
                1.4521367446848013,
                1.1668858094069683,
                0.8965510782427004,
                0.5124705403529105
              ],
              "metrics": {
                "initial_rmse_K": 1.3870746212740985,
                "observation_residual_rms_K": 0.044518599883287165,
                "future_predictive_rmse_K": 0.02555170069125071
              }
            },
            "learned": {
              "coefficients_K": [
                6.714449423934077,
                -0.14282719166876354,
                -0.02348387829110293,
                0.05258923400631135,
                -0.05033169712783927,
                -0.04274977655873291,
                0.0027552054176829955,
                -0.00033984552340015516
              ],
              "initial_K": [
                0.3872870982561632,
                0.781869746386794,
                1.1708468863375914,
                1.5220398523069054,
                1.805476330986757,
                2.0138438666706473,
                2.1612719897478003,
                2.2615939001430565,
                2.3079106979637167,
                2.2741598977015682,
                2.1374477945879637,
                1.8991580496199734,
                1.584680788886289,
                1.2241516795963658,
                0.8354010841380445,
                0.4248606693104771
              ],
              "metrics": {
                "initial_rmse_K": 1.484149322955684,
                "observation_residual_rms_K": 0.04351051665447418,
                "future_predictive_rmse_K": 0.021405874509859337
              }
            }
          }
        },
        {
          "split": "test",
          "index": 8,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.741946397165456,
            -0.7547739471050924,
            -0.10218431985307472,
            -0.1775817626729975,
            0.05262716988903501,
            6.026150007209081,
            -0.07053828811899616,
            0.002862834288456887
          ],
          "initial_K": [
            2.0512553591403013,
            2.09928968510517,
            0.36361622677349126,
            -0.94636571578338,
            -0.07196410882601456,
            2.332362755324905,
            3.8880676043004536,
            3.0921289332130364,
            0.968365169112652,
            -0.06311321155939464,
            1.134010466056185,
            3.1451466298250113,
            3.5683856853797895,
            1.6858119690042945,
            -0.7298781684049348,
            -1.3821099840849929
          ],
          "observed_K": [
            0.3059548922183466,
            0.5250937448169035,
            0.7625147104157997,
            0.948111968905711,
            1.1848098715869997,
            1.4972291245720541,
            1.7207202826470618,
            1.7769889149620113,
            1.8143492491617137,
            1.7899139500784096,
            1.6894216570869225,
            1.6289565275771372,
            1.4145380790882187,
            1.0553996343450136,
            0.7281380522977934,
            0.34690858099904226
          ],
          "future_observed_K": [
            0.2438456057328643,
            0.48701394961600525,
            0.7519781847139173,
            1.022326668867998,
            1.1844522298772215,
            1.422721787144488,
            1.5841651647404693,
            1.6570353637594553,
            1.7357282605408146,
            1.6804299928258362,
            1.6266594232887817,
            1.4892370178274368,
            1.2570942148301765,
            1.0349769449179511,
            0.6773600131620826,
            0.3475625565243001
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.743778821891298,
                -0.7645910228121419,
                -0.18952616898321842,
                -0.09166989887244632,
                0.20478938413141387,
                5.329605434145502,
                1.74252012135256,
                -8.785748426620708
              ],
              "initial_K": [
                -0.5214560825627703,
                1.7327822944450233,
                2.897811660252084,
                -0.233197131959467,
                -2.5762227858086355,
                1.2182419388248376,
                6.282645086223049,
                4.565822191400727,
                -1.3455405279701504,
                -1.9476427397378542,
                3.4283862900446995,
                5.753365199172419,
                1.6399423042640668,
                -1.7075823464470938,
                0.33859523327766883,
                2.4388582229174185
              ],
              "metrics": {
                "initial_rmse_K": 2.250698579787914,
                "observation_residual_rms_K": 0.017939026519779612,
                "future_predictive_rmse_K": 0.020598891789371784
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.674649021942185,
                -0.7481142146571242,
                -0.17895138015362622,
                -0.07420865187894461,
                0.08566957631698366,
                0.4039412406100061,
                0.01091092194803367,
                -0.002865195460938375
              ],
              "initial_K": [
                0.3655886062777441,
                0.5905739783861348,
                0.6970917320526169,
                0.8503822695758743,
                1.1748805033906242,
                1.606786952248166,
                1.9466348159428903,
                2.0560837481678633,
                1.9847955171007752,
                1.8937432454549594,
                1.868301832196375,
                1.8301339876789897,
                1.6365624552785947,
                1.2461426379559573,
                0.7662350315409364,
                0.3391803441498756
              ],
              "metrics": {
                "initial_rmse_K": 1.4061948315916708,
                "observation_residual_rms_K": 0.043059826762445366,
                "future_predictive_rmse_K": 0.021571658325649185
              }
            },
            "learned": {
              "coefficients_K": [
                5.743450758822153,
                -0.7663643870211743,
                -0.1859628016841214,
                -0.07030434848105283,
                0.026750972652680907,
                0.039952058403736314,
                0.0017014888229060126,
                0.0007735210951332081
              ],
              "initial_K": [
                0.23761853942275854,
                0.4735610708047292,
                0.7191534055263923,
                0.9914712594566013,
                1.290886786897487,
                1.588096508762711,
                1.836293672120374,
                1.9981270579063415,
                2.0632356697338663,
                2.0430116478175506,
                1.9510642800870166,
                1.7891392591051647,
                1.5503645302626254,
                1.2337935711290462,
                0.8537914253010679,
                0.43496034506641124
              ],
              "metrics": {
                "initial_rmse_K": 1.497062170750643,
                "observation_residual_rms_K": 0.04241817039933275,
                "future_predictive_rmse_K": 0.020100519077762537
              }
            }
          }
        },
        {
          "split": "test",
          "index": 9,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.532372949943475,
            1.3849097516507591,
            -0.09422401342588824,
            -0.03524605733377563,
            -0.025646583943571666,
            -6.083156678460301,
            -0.01762022259597104,
            0.07964854294653081
          ],
          "initial_K": [
            -1.3582734158312852,
            -0.7071511370274339,
            1.740355824390714,
            3.730405177711061,
            3.403657553841403,
            1.355849303365636,
            0.004604006757412904,
            0.8923702139827945,
            2.9426833800705996,
            3.6816406195933173,
            2.0531472512767843,
            -0.38309361551509724,
            -1.2051109211550026,
            0.19497349463062452,
            1.996981260371236,
            1.9959424138097779
          ],
          "observed_K": [
            0.388802258056002,
            0.7718585088666218,
            1.1690034714083937,
            1.5063477217096568,
            1.7595775575388142,
            1.7831763914138816,
            1.759591120617043,
            1.7510564840118872,
            1.7005444172193502,
            1.531486659167968,
            1.298902961795458,
            0.9776190006826116,
            0.7502708427320446,
            0.5821924201680764,
            0.4450892384154048,
            0.20430896337249943
          ],
          "future_observed_K": [
            0.3794693314985072,
            0.751358430992338,
            1.1087410702796887,
            1.3952983388062081,
            1.5462098473576598,
            1.700921587632356,
            1.7122105470014408,
            1.707342972168677,
            1.6175240026630677,
            1.4609632909333023,
            1.2482620250732865,
            1.053445823872962,
            0.8242860748482985,
            0.6066801231627968,
            0.4514629342941117,
            0.19037067054628923
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.50312862673379,
                1.4420111223290093,
                -0.14042620543412726,
                -0.07152804197199836,
                -0.0767264085990372,
                -6.075685826411974,
                0.7614736426646651,
                27.54928289543401
              ],
              "initial_K": [
                8.257384603755861,
                1.1330022972320581,
                -7.522260344303262,
                0.09214184550283755,
                11.914374037588729,
                6.616244770650747,
                -7.39597517810172,
                -5.669432304462683,
                9.057124136041953,
                11.27090498197763,
                -2.6636019340921417,
                -8.788172171570931,
                1.9343672400901655,
                9.04275203899707,
                0.36886003947013224,
                -7.153998213426574
              ],
              "metrics": {
                "initial_rmse_K": 6.870216656401261,
                "observation_residual_rms_K": 0.012793754066373364,
                "future_predictive_rmse_K": 0.022928023837690856
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.436895195249553,
                1.4109360247786498,
                -0.13259099472642644,
                -0.05790340811511484,
                -0.032096970967915514,
                -0.46048813567959174,
                0.00476802498794103,
                0.008984331951155746
              ],
              "initial_K": [
                0.33463226410315844,
                0.8039988443102384,
                1.3747695244527427,
                1.853410147684193,
                2.068102388716203,
                2.0366040701871806,
                1.9356693672458276,
                1.9003422935373218,
                1.8785911504110564,
                1.7100446744827948,
                1.3368717483161314,
                0.8979140614849551,
                0.5953368091145643,
                0.4879274760283593,
                0.44243972880968063,
                0.2883869586361616
              ],
              "metrics": {
                "initial_rmse_K": 1.4060520208003253,
                "observation_residual_rms_K": 0.04680991335688125,
                "future_predictive_rmse_K": 0.03471310626943211
              }
            },
            "learned": {
              "coefficients_K": [
                5.5028143086997625,
                1.4453556697237193,
                -0.13778598877663467,
                -0.05485696450875279,
                -0.010022521757544655,
                -0.045544864057742794,
                0.0007435431453874792,
                -0.00242551350671979
              ],
              "initial_K": [
                0.47103871670402747,
                0.9389794315271092,
                1.377577151129588,
                1.7409402865366916,
                1.9891276201213264,
                2.1084653336107926,
                2.109629262725107,
                2.0118015471436794,
                1.8313453815093508,
                1.5837647452783854,
                1.2931939956266545,
                0.9961022691472003,
                0.7299269646965356,
                0.5127068339608991,
                0.3337159296594242,
                0.16784257088530347
              ],
              "metrics": {
                "initial_rmse_K": 1.509695407338596,
                "observation_residual_rms_K": 0.04677199164095193,
                "future_predictive_rmse_K": 0.02449670439003068
              }
            }
          }
        },
        {
          "split": "test",
          "index": 10,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.857473922033986,
            0.046136057016025515,
            -0.07095537977773908,
            0.12194996194946563,
            0.006794916496936428,
            6.027784206927364,
            -0.02724361969343163,
            -0.030469329332704697
          ],
          "initial_K": [
            2.2865077685764104,
            2.525512374179934,
            0.8988144337464201,
            -0.389056894143502,
            0.45515306984567205,
            2.812872246378101,
            4.3136736579390895,
            3.4582558982254397,
            1.2917687382655156,
            0.23783268103450084,
            1.385338916915885,
            3.27321132159003,
            3.533680414019126,
            1.5434287615874807,
            -0.8750907587683376,
            -1.4619952686394488
          ],
          "observed_K": [
            0.4519265821763294,
            0.8613893629693732,
            1.1398899422546465,
            1.3590124230478058,
            1.613529869823228,
            1.935677203870164,
            2.124647846165758,
            2.1686142132322153,
            2.1125731346441383,
            2.0328222920078614,
            1.906300579996472,
            1.7503771380160884,
            1.451219100839719,
            1.0932309333968409,
            0.6556883818264265,
            0.3455420993097314
          ],
          "future_observed_K": [
            0.4134926348202783,
            0.7685422515125842,
            1.072855653204716,
            1.3636964284900508,
            1.6169295194681417,
            1.837060970039966,
            1.9458394229572118,
            2.04211294945524,
            2.00158508145669,
            1.9514221748356189,
            1.8435962546905513,
            1.611926996284698,
            1.3930674062672677,
            1.0550762587095617,
            0.7041857165584506,
            0.33767843764308414
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.8706842345645205,
                0.039409965812908815,
                -0.13786793000221922,
                0.3961978179112717,
                0.32870828780865835,
                6.746155485806244,
                3.227768918615373,
                -16.31450960921231
              ],
              "initial_K": [
                -1.841235624883368,
                2.4629761058936666,
                5.56596618682294,
                0.33380638743551017,
                -4.671880693599412,
                0.9148264262003081,
                9.374252657441618,
                6.550881718672301,
                -3.331913363568158,
                -3.935904983600191,
                5.374553509148039,
                8.581304575413164,
                0.6652114174791598,
                -4.589193509965005,
                0.5375113774938847,
                4.9671558364347685
              ],
              "metrics": {
                "initial_rmse_K": 4.15680668379266,
                "observation_residual_rms_K": 0.013901081314101619,
                "future_predictive_rmse_K": 0.017688844374999797
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.787991456625592,
                0.0385606876671796,
                -0.1301754606510577,
                0.3207302103112971,
                0.13750859141398827,
                0.5113043451257817,
                0.020210919980634078,
                -0.005320464075447015
              ],
              "initial_K": [
                0.6826818792994349,
                1.108178670710428,
                1.2627394416818267,
                1.3672359590947085,
                1.6311987871470728,
                2.034643895628935,
                2.3652034473734345,
                2.454206827933969,
                2.341720344823703,
                2.1960628247943994,
                2.100369615435963,
                1.9611485056792535,
                1.6365116782661262,
                1.1244211836890572,
                0.5920418506999805,
                0.21455427516583842
              ],
              "metrics": {
                "initial_rmse_K": 1.3806571427577876,
                "observation_residual_rms_K": 0.05160873874286182,
                "future_predictive_rmse_K": 0.028460993624687486
              }
            },
            "learned": {
              "coefficients_K": [
                6.870291806891553,
                0.039501371833600446,
                -0.13527581263922014,
                0.3038557890919535,
                0.04293809689000443,
                0.05057087270341804,
                0.003151764315745481,
                0.0014363736276857039
              ],
              "initial_K": [
                0.5124965466381037,
                0.9512998142240272,
                1.2905611334556248,
                1.5575895515631881,
                1.7962139430707713,
                2.02621872173495,
                2.2316044521939817,
                2.377026979940414,
                2.4297473999681465,
                2.3701731551546583,
                2.192029765501557,
                1.902371303561258,
                1.526029023306362,
                1.1072851108213815,
                0.6976246934324237,
                0.3302447958132324
              ],
              "metrics": {
                "initial_rmse_K": 1.4951538923889973,
                "observation_residual_rms_K": 0.051436309939479535,
                "future_predictive_rmse_K": 0.021310353576300494
              }
            }
          }
        },
        {
          "split": "test",
          "index": 11,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.064394954021725,
            -2.411669180940734,
            -0.2575990270640851,
            0.06749840108382132,
            -0.006010335171964219,
            -5.976562505631167,
            -0.008668201445281585,
            -0.00471828157506624
          ],
          "initial_K": [
            -1.7886726009764047,
            -1.5016459152728627,
            0.6645284633413382,
            2.4874320728151655,
            2.2013043770037957,
            0.4529047337152552,
            -0.43735788010406473,
            0.9182807645935727,
            3.395133525367534,
            4.554831881582274,
            3.3004277958603145,
            1.057736787168062,
            0.18171118900359162,
            1.3520623069024864,
            2.8391804141510395,
            2.451060220461088
          ],
          "observed_K": [
            0.09358298276099399,
            0.21150904753023278,
            0.4441743307223852,
            0.7155771431698212,
            0.9942789737134443,
            1.2271222767989833,
            1.4732681980675186,
            1.8071046376083706,
            2.0449738813399025,
            2.1848776207946345,
            2.1463893836469983,
            1.9885842048318347,
            1.7279447315246852,
            1.443490153837755,
            1.0927314236999428,
            0.5765397887898158
          ],
          "future_observed_K": [
            0.16144086246025666,
            0.3121961171226529,
            0.5098056012701478,
            0.7260883275658997,
            1.0137544076823213,
            1.273464364988776,
            1.496459111158389,
            1.6985577075729335,
            1.8982629762343566,
            1.9763387245689672,
            1.973052422005734,
            1.8374687748526646,
            1.6286939056418681,
            1.3129474447309706,
            0.927757508987173,
            0.4912282473902038
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.052894587528757,
                -2.4326536435793646,
                -0.3018205821853771,
                -0.0928043649089537,
                0.252132226351576,
                -5.680002397632898,
                1.1555737265335388,
                7.251807598964824
              ],
              "initial_K": [
                1.1871269180566668,
                -0.7423428820717217,
                -2.052658858388803,
                1.0543667047100822,
                4.359416792399385,
                2.1842970904644052,
                -2.109932332314387,
                -0.9151907817877456,
                4.771099494941248,
                6.561305014855532,
                2.2435029766699195,
                -1.1472047827417784,
                0.7770961818912485,
                3.5608043826915,
                2.6406383831895512,
                0.36733262390127075
              ],
              "metrics": {
                "initial_rmse_K": 1.840438767834299,
                "observation_residual_rms_K": 0.010898745528106706,
                "future_predictive_rmse_K": 0.017079686021201315
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.9800443951860185,
                -2.380230366040165,
                -0.28498022215405316,
                -0.0751270252622163,
                0.1054745151903798,
                -0.43049851316723264,
                0.0072357125641792355,
                0.00236494891581414
              ],
              "initial_K": [
                -0.08695844163882877,
                -0.0037981702178799814,
                0.2688178570715456,
                0.6066375971658299,
                0.8944890684248044,
                1.1525231675792948,
                1.491837550534278,
                1.9478225748946496,
                2.385794762605118,
                2.6006295598441715,
                2.5118036338575758,
                2.237443266812142,
                1.9585068095359461,
                1.7188852364349776,
                1.382917469459096,
                0.8003496767011018
              ],
              "metrics": {
                "initial_rmse_K": 1.3874606513551906,
                "observation_residual_rms_K": 0.0437137864191591,
                "future_predictive_rmse_K": 0.0206917658895141
              }
            },
            "learned": {
              "coefficients_K": [
                6.052548868928308,
                -2.4382958506885055,
                -0.296145916789439,
                -0.07117440393602298,
                0.03293521449169659,
                -0.0425787218824343,
                0.0011283633145162686,
                -0.0006384687886862433
              ],
              "initial_K": [
                0.00552423092750981,
                0.07064708400812969,
                0.23031497006968282,
                0.4881224327863738,
                0.8269103464260702,
                1.2204900652299138,
                1.6346202905091347,
                2.0222575475640916,
                2.327051145326262,
                2.5001888953947367,
                2.519119915239787,
                2.3907259668717575,
                2.1343639851376697,
                1.7607912727027974,
                1.2695154557136965,
                0.6692337679596685
              ],
              "metrics": {
                "initial_rmse_K": 1.4839844641626658,
                "observation_residual_rms_K": 0.0422817505755967,
                "future_predictive_rmse_K": 0.01780078599588563
              }
            }
          }
        },
        {
          "split": "test",
          "index": 12,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.219832099640153,
            2.6671383183638744,
            -0.18560462213307943,
            -0.05593799433153152,
            -0.014870897683554967,
            5.873693205502208,
            0.05443173497232211,
            0.048045278628120774
          ],
          "initial_K": [
            2.4467604255695736,
            2.802665056737327,
            1.28226665232937,
            0.10503368534667579,
            0.9617549812349406,
            3.1213651655798706,
            4.262417953304239,
            3.0490255982672227,
            0.6000082152070438,
            -0.7209448111354273,
            0.15146227410268076,
            1.8667897617444642,
            2.1776575444747452,
            0.4471471870670775,
            -1.6132703664973451,
            -1.828048413568742
          ],
          "observed_K": [
            0.5763255612710079,
            1.0197385167803494,
            1.400494593093174,
            1.6009941359452833,
            1.8379331933552776,
            1.9763488554343138,
            2.0178576525833427,
            1.7700708627343518,
            1.4685553213074065,
            1.1947276143413323,
            0.9497186539719751,
            0.720940930270655,
            0.5152041643452009,
            0.2926941093492845,
            0.10417453534871027,
            0.010194731849856517
          ],
          "future_observed_K": [
            0.45770230719170896,
            0.8683421212753294,
            1.2394974493192144,
            1.4998285402912923,
            1.7044865995954641,
            1.813029141281897,
            1.757390644025135,
            1.6495366749222775,
            1.4925035613647657,
            1.193770791989856,
            0.9609254119406159,
            0.7893700773248862,
            0.5110853154688809,
            0.343047214028541,
            0.2067573460027903,
            0.10111247946087865
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.226964914098198,
                2.685889061180446,
                -0.1692706775672663,
                -0.07420577921069707,
                0.06815078861258238,
                7.021315160530224,
                3.481642033943146,
                -8.63171423866222
              ],
              "initial_K": [
                0.9895655283924252,
                3.219957895681132,
                3.299385239103364,
                -0.2540107441278474,
                -1.767344877037922,
                2.859946746121552,
                7.467627191434387,
                4.3498227793448265,
                -2.5318882181902245,
                -3.0692354584881727,
                2.717851007481033,
                4.979136355517868,
                0.4143877598121406,
                -3.1195547863964554,
                -0.7263203519335888,
                1.9426904207231288
              ],
              "metrics": {
                "initial_rmse_K": 2.3506505408148377,
                "observation_residual_rms_K": 0.016126945062290697,
                "future_predictive_rmse_K": 0.021566163802346595
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.164055277418688,
                2.6280086029140612,
                -0.1598260627158242,
                -0.06007109099699927,
                0.0285095304664899,
                0.5321592361204789,
                0.02180056575407593,
                -0.002814962056254178
              ],
              "initial_K": [
                0.7857782406143763,
                1.3363572171986695,
                1.634201430881825,
                1.8562549373390278,
                2.139329389857287,
                2.4010734047716977,
                2.4205605323081696,
                2.0890284678871582,
                1.5493994850855728,
                1.0695789081814207,
                0.791915724055168,
                0.6313243512529813,
                0.419143146794522,
                0.11850889579397927,
                -0.12811591692750435,
                -0.1625698565705127
              ],
              "metrics": {
                "initial_rmse_K": 1.3356375436948273,
                "observation_residual_rms_K": 0.0527350338692712,
                "future_predictive_rmse_K": 0.02394152191301518
              }
            },
            "learned": {
              "coefficients_K": [
                5.226666369497996,
                2.692118613174152,
                -0.1660881429316794,
                -0.05691060015454002,
                0.008902316348897953,
                0.0526335386044423,
                0.00339965945501724,
                0.0007599595078930608
              ],
              "initial_K": [
                0.6398182386906872,
                1.2172656384441858,
                1.694782967014305,
                2.05804813866021,
                2.2937118678033417,
                2.3766736261039645,
                2.285000210188603,
                2.027732108568533,
                1.6556282098987931,
                1.2423130577357593,
                0.85204530456577,
                0.5207391966239405,
                0.2612379810621649,
                0.07990579037488887,
                -0.01693618485028181,
                -0.03385380457938242
              ],
              "metrics": {
                "initial_rmse_K": 1.4554035854944387,
                "observation_residual_rms_K": 0.053061830526332704,
                "future_predictive_rmse_K": 0.02256461824823098
              }
            }
          }
        },
        {
          "split": "test",
          "index": 13,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.026781424113795,
            0.3370523805996143,
            -0.11418621892443814,
            -0.04510213638445195,
            0.024253871011956536,
            -6.0023616910011,
            0.02941545941533061,
            -0.012254116718890413
          ],
          "initial_K": [
            -1.440234487427634,
            -0.8562431294697794,
            1.518921441351089,
            3.441967457402864,
            3.1316346763624496,
            1.2232943683808548,
            0.04786653004973851,
            1.0412645955211157,
            3.1495685393230417,
            3.991763712583114,
            2.5008902981838794,
            0.12648258159262937,
            -0.7460137027179392,
            0.5719460235282913,
            2.3062447957218977,
            2.1913670313285425
          ],
          "observed_K": [
            0.3222211956573597,
            0.6876502573493365,
            1.043338291083404,
            1.3787877526369687,
            1.605499904922767,
            1.7234143393714942,
            1.757205672375577,
            1.83838500167694,
            1.8907224473092905,
            1.8306007251149772,
            1.6350157290174945,
            1.381552340678763,
            1.1177148495005538,
            0.9085087994473547,
            0.6461760496477262,
            0.3945859848495375
          ],
          "future_observed_K": [
            0.2854060812989507,
            0.705289858569599,
            0.9591011955211326,
            1.2566200139380115,
            1.453703964360265,
            1.6948300868286041,
            1.7732934695242917,
            1.8029712918120118,
            1.7590756877216198,
            1.7023768298315107,
            1.567483620582716,
            1.325263269586173,
            1.130466656450412,
            0.8851114042505375,
            0.5752165091066961,
            0.33179548541261106
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.010678856873694,
                0.315670223986874,
                -0.029005403026029362,
                0.049587024376378394,
                0.0256024870421849,
                -6.313736851082857,
                2.377866642718631,
                9.952332274074694
              ],
              "initial_K": [
                2.6761345875751634,
                0.16260134552409977,
                -2.2457709902813723,
                1.6069817306887093,
                6.392644380423437,
                3.7383271146937176,
                -2.5528219079051597,
                -2.0066121053429002,
                4.845446269696408,
                7.124600199957703,
                1.568760809181354,
                -2.8271298731971672,
                -0.3144555833384932,
                3.304001834520953,
                2.1847023147818376,
                -0.34600779892072575
              ],
              "metrics": {
                "initial_rmse_K": 2.5607872264560116,
                "observation_residual_rms_K": 0.01090666918021765,
                "future_predictive_rmse_K": 0.03004811019720533
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.9383367559992,
                0.3088675836658392,
                -0.02738701959347745,
                0.04014170709165532,
                0.010710292561637686,
                -0.478530489362657,
                0.014889192396468466,
                0.0032456400835503183
              ],
              "initial_K": [
                0.2788926843891548,
                0.687905664532985,
                1.1956978061556736,
                1.6236890091390799,
                1.8255362877886205,
                1.8402276375666664,
                1.847048989083749,
                1.963729122208391,
                2.109054966433566,
                2.0888035418511754,
                1.81504081513027,
                1.4130930563116417,
                1.0927180955976168,
                0.9258765416403313,
                0.7792979288954198,
                0.4754382944593955
              ],
              "metrics": {
                "initial_rmse_K": 1.3815019743823491,
                "observation_residual_rms_K": 0.04665299209029383,
                "future_predictive_rmse_K": 0.036130487433415626
              }
            },
            "learned": {
              "coefficients_K": [
                6.010335549477191,
                0.3164023778578633,
                -0.028460059313366474,
                0.03802975114815172,
                0.0033443697953923677,
                -0.04732935421526704,
                0.0023218747751425216,
                -0.0008762302977451479
              ],
              "initial_K": [
                0.4085076674718693,
                0.810585324763273,
                1.1862416146400596,
                1.5059173953700267,
                1.7487957472376792,
                1.9152543893470972,
                2.0194352504395896,
                2.069400185150376,
                2.0556285250253827,
                1.9603757048976558,
                1.7791819597230552,
                1.5324296700166473,
                1.2535539846499104,
                0.9645833172411843,
                0.6644028259432733,
                0.34218696468914056
              ],
              "metrics": {
                "initial_rmse_K": 1.4890993005968056,
                "observation_residual_rms_K": 0.04663304637159718,
                "future_predictive_rmse_K": 0.02947770822160796
              }
            }
          }
        },
        {
          "split": "test",
          "index": 14,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.311080076657534,
            -1.3591251807694569,
            -0.38326473334367095,
            0.12561504020200748,
            -0.022651107013994504,
            6.06272293803486,
            0.055553774881321766,
            -0.037699810452175825
          ],
          "initial_K": [
            2.049920461859596,
            2.052794140755961,
            0.24042698961905618,
            -1.1112489105748022,
            -0.19238192431571632,
            2.31704375459797,
            3.973032602502923,
            3.2619295775856196,
            1.2575264427854034,
            0.3790997818379951,
            1.6551712608499471,
            3.574788078717275,
            3.7921764409654215,
            1.7456068063949939,
            -0.7190843276564849,
            -1.3685551355713164
          ],
          "observed_K": [
            0.2730120262976014,
            0.49261424228642664,
            0.7039838461475174,
            0.9102126531261219,
            1.2030724548861027,
            1.526162240535396,
            1.8433611307715028,
            1.969707304151033,
            2.0225806847881422,
            2.017350758134985,
            1.9748223067998965,
            1.8618149612528703,
            1.6880724266347162,
            1.283936994092518,
            0.8246349595707592,
            0.3729638098948113
          ],
          "future_observed_K": [
            0.24434085063283273,
            0.4986930962244057,
            0.7082298266961852,
            0.9692740163532533,
            1.2197481314711343,
            1.4954151124120563,
            1.6504106264975595,
            1.842875881029713,
            1.9291170552345447,
            1.957503086922318,
            1.8479101298239813,
            1.7214602770368732,
            1.502610606767381,
            1.157056542585193,
            0.8071028987717034,
            0.4079046815008245
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.307038379439731,
                -1.3471089764322544,
                -0.33755020859410184,
                -0.08405550359989684,
                0.022266524547559608,
                6.958120448960689,
                -3.9938015221997705,
                5.102923793823254
              ],
              "initial_K": [
                2.7179768845522077,
                1.8502210009835176,
                -0.6094602234881519,
                -0.8059263453019709,
                0.9549101670414291,
                2.031169285088536,
                2.4275077453374454,
                3.3681798357100057,
                3.3626955901189275,
                0.9030231081260571,
                -0.8539423596208107,
                1.895504318710606,
                5.980406420592697,
                4.507806814255073,
                -1.9221451491216928,
                -4.667815418081334
              ],
              "metrics": {
                "initial_rmse_K": 1.652143606391103,
                "observation_residual_rms_K": 0.01157193798230959,
                "future_predictive_rmse_K": 0.017140373851810862
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.231129415156444,
                -1.3180790041904409,
                -0.31871628083406,
                -0.06804464368214767,
                0.00931475882957419,
                0.5273695850840542,
                -0.025007491248270706,
                0.001664158063902189
              ],
              "initial_K": [
                0.31292233222900867,
                0.48940627570808426,
                0.5660898303011336,
                0.7299760524849999,
                1.1174184740654507,
                1.6499012526641277,
                2.0893602110444767,
                2.2631913689742356,
                2.2227949772150706,
                2.1642544809253947,
                2.19527960562086,
                2.2052259020547504,
                1.9872652695071722,
                1.4803153622169305,
                0.8561269536977557,
                0.34601983255411023
              ],
              "metrics": {
                "initial_rmse_K": 1.385165731758079,
                "observation_residual_rms_K": 0.051428664486883685,
                "future_predictive_rmse_K": 0.020497545846981758
              }
            },
            "learned": {
              "coefficients_K": [
                6.306678145100608,
                -1.3502334112911478,
                -0.3312037743177139,
                -0.06446464422372976,
                0.0029086038408113204,
                0.052159815204346344,
                -0.00389975907173644,
                -0.00044927523640666097
              ],
              "initial_K": [
                0.17085273949277105,
                0.36021697695290456,
                0.5915499877716037,
                0.8849703471790048,
                1.2379747325219694,
                1.6133292669419301,
                1.9507541934068975,
                2.1975811062769033,
                2.3327605056105583,
                2.3629023865829746,
                2.2971970178870786,
                2.1299696558799455,
                1.849701510888517,
                1.4622657957768372,
                0.9997654804050087,
                0.5035228988885239
              ],
              "metrics": {
                "initial_rmse_K": 1.503566255354965,
                "observation_residual_rms_K": 0.05146127296796552,
                "future_predictive_rmse_K": 0.01761656060732705
              }
            }
          }
        },
        {
          "split": "test",
          "index": 15,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            4.884268549802298,
            0.6877274449795013,
            -0.25992970679231264,
            0.35035125405665124,
            0.11789004813219005,
            -6.0268493879993175,
            0.07154517271454933,
            0.03169186925118979
          ],
          "initial_K": [
            -1.3567091283526853,
            -0.7918965836629202,
            1.467673094777386,
            3.255549682647636,
            2.8349613217043474,
            0.844861665255021,
            -0.3627451351795501,
            0.6748835730470626,
            2.866134658551562,
            3.7381361012488616,
            2.1816066785207764,
            -0.29706197849710336,
            -1.227080651506495,
            0.11478022131359922,
            1.9462707983118261,
            1.990251589975773
          ],
          "observed_K": [
            0.2644726182048358,
            0.6092583028228419,
            0.9215680458846239,
            1.2197952114924868,
            1.3648103977104715,
            1.439424358458464,
            1.4574629387334894,
            1.5527032493808874,
            1.56182650471919,
            1.5268495466652048,
            1.3163986292082652,
            1.0255522569824755,
            0.7968325832821187,
            0.599959092100202,
            0.422619580434483,
            0.23967743263071709
          ],
          "future_observed_K": [
            0.3204006054699737,
            0.5500067291122135,
            0.8469639474261179,
            1.1045082310929502,
            1.3166652642544519,
            1.396437973016723,
            1.4619372035059428,
            1.438762642527323,
            1.4537100715581135,
            1.350848045433154,
            1.208500984013625,
            1.0480916494472898,
            0.801574162623387,
            0.6307289092477416,
            0.4127837110765027,
            0.1973436787044488
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                4.910539980485876,
                0.6261196272059117,
                -0.27981729764083424,
                0.5081208845175128,
                -0.0709604301801434,
                -6.620925594299876,
                -1.1335936789411565,
                5.096023189086207
              ],
              "initial_K": [
                -0.23185523371946443,
                -0.8784348744010704,
                0.11167316455159748,
                3.2176953706967346,
                4.471641289106032,
                1.2581431381586108,
                -2.1593671841275257,
                -0.3386438541158787,
                4.454496054856005,
                5.238833340775533,
                1.0510504549398463,
                -1.9471997688862255,
                -0.37972466207668054,
                1.976840581048757,
                1.4672908643995626,
                -0.03701516255594833
              ],
              "metrics": {
                "initial_rmse_K": 1.3114442157105288,
                "observation_residual_rms_K": 0.011003879857775416,
                "future_predictive_rmse_K": 0.024488591691941633
              }
            },
            "tikhonov": {
              "coefficients_K": [
                4.85143870639097,
                0.6126268543747329,
                -0.26420463133045796,
                0.41133421434279877,
                -0.029684888279671664,
                -0.5018129262277804,
                -0.0070980828285131725,
                0.0016619076487513966
              ],
              "initial_K": [
                0.26504017614505204,
                0.6537185679603129,
                1.1154942302159951,
                1.456772933237836,
                1.5491815170662337,
                1.4807744259992317,
                1.4712896667882964,
                1.6335728771803908,
                1.8402706907428832,
                1.8463250508679203,
                1.5405559979291854,
                1.060576889895425,
                0.6557701665852029,
                0.451957781396841,
                0.36412359244739634,
                0.2301431491173042
              ],
              "metrics": {
                "initial_rmse_K": 1.382148416409912,
                "observation_residual_rms_K": 0.04757233214562053,
                "future_predictive_rmse_K": 0.027682130468419105
              }
            },
            "learned": {
              "coefficients_K": [
                4.910259508889195,
                0.6275718259688214,
                -0.27455632595822016,
                0.38969288910558064,
                -0.00926933070882898,
                -0.04963211804302578,
                -0.001106900833339092,
                -0.00044866768846946886
              ],
              "initial_K": [
                0.40940989288045493,
                0.7853443624958669,
                1.0945873119266585,
                1.3168314468616118,
                1.461106208080362,
                1.5636923094175559,
                1.6594719961204085,
                1.7474647054472072,
                1.782644529840883,
                1.7057952231846414,
                1.4897207626789195,
                1.1650975128777228,
                0.8061771794875947,
                0.48932605516516375,
                0.2563513477137486,
                0.10457877924162448
              ],
              "metrics": {
                "initial_rmse_K": 1.494900980593822,
                "observation_residual_rms_K": 0.04882649543982068,
                "future_predictive_rmse_K": 0.02571814800171626
              }
            }
          }
        },
        {
          "split": "test",
          "index": 16,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.125696078420558,
            1.6783579303051732,
            -0.14240359145815265,
            0.04012788816479341,
            -0.09569853536567843,
            5.907441712409014,
            0.010008089659754228,
            -0.0006444199244397005
          ],
          "initial_K": [
            2.3682908199092374,
            2.7039792428474043,
            1.1974758425298468,
            0.017667734076920683,
            0.8735680540339028,
            3.0933334571781144,
            4.35750309955557,
            3.2746224455306203,
            0.9393584150545471,
            -0.25949705409400936,
            0.7373288694275042,
            2.5111953684250055,
            2.763788349747532,
            0.8890820045804754,
            -1.3329472046526307,
            -1.6933513964890468
          ],
          "observed_K": [
            0.490122353456659,
            0.9905602355274143,
            1.338898650516434,
            1.6199069046257553,
            1.8619775237553535,
            2.0278954571102537,
            2.130161262189801,
            2.021782027138602,
            1.8382757995633339,
            1.568593089552038,
            1.3573502641686463,
            1.181773986988631,
            0.9406757541411833,
            0.6387293399079463,
            0.3355088553152398,
            0.1741768183984868
          ],
          "future_observed_K": [
            0.45546416120582595,
            0.8537256547590888,
            1.2238501007736502,
            1.57078910258167,
            1.7484008246560379,
            1.9110270014981134,
            1.9128018117778223,
            1.8898585314934988,
            1.7377819998125767,
            1.54735008653554,
            1.4105998514790712,
            1.126399944511537,
            0.9113838046413391,
            0.6396423231587881,
            0.38966988310738215,
            0.17714809289834382
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.143425781999812,
                1.719109388937573,
                -0.14817108347454885,
                -0.038849949879370425,
                -0.017667761026725657,
                5.54989235153391,
                -4.389678225320631,
                -17.798261165521243
              ],
              "initial_K": [
                -5.263219849722436,
                0.6985902342601273,
                8.109961372137288,
                3.6890778860440347,
                -4.780464001104516,
                -1.6422475749611816,
                8.605474385312911,
                8.57120076168037,
                -1.8848433716565656,
                -5.573553952078024,
                2.443177297006904,
                7.565618294191957,
                1.7709814240361417,
                -3.9682824250307305,
                -0.864077490292818,
                3.0780845124623224
              ],
              "metrics": {
                "initial_rmse_K": 4.584311409764935,
                "observation_residual_rms_K": 0.013856524287540683,
                "future_predictive_rmse_K": 0.022650948885929122
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.069485992798104,
                1.6820628702708567,
                -0.13990374009499704,
                -0.0314498264051124,
                -0.0073909573391657294,
                0.42063721778871715,
                -0.027486303260750574,
                -0.005804342968611702
              ],
              "initial_K": [
                0.6744981558653291,
                1.1943943558335457,
                1.5368425523243856,
                1.8084395290344586,
                2.10639853446356,
                2.386560248336627,
                2.4894295824428037,
                2.3115480085194826,
                1.9371415240871854,
                1.572173142411014,
                1.3428469600890294,
                1.183166698203077,
                0.9395414643661287,
                0.5703353080017816,
                0.20896899958611875,
                0.017862317473855194
              ],
              "metrics": {
                "initial_rmse_K": 1.372100514804182,
                "observation_residual_rms_K": 0.0447247924372534,
                "future_predictive_rmse_K": 0.02863134693887541
              }
            },
            "learned": {
              "coefficients_K": [
                6.1430748925976255,
                1.7230966278284259,
                -0.14538525185901227,
                -0.029795172116325538,
                -0.0023078822863042154,
                0.041603384359818425,
                -0.004286314025883074,
                0.0015670071347030608
              ],
              "initial_K": [
                0.57879768343778,
                1.1144587259975007,
                1.5780356922251193,
                1.9541525768108303,
                2.2286752818837616,
                2.3813020133261875,
                2.3935990111978485,
                2.265937612729471,
                2.0270557888724423,
                1.7254813799744668,
                1.4074834133442067,
                1.0992690392247932,
                0.8087546295798934,
                0.542510772237559,
                0.3155066537963445,
                0.13894938711955768
              ],
              "metrics": {
                "initial_rmse_K": 1.466803327481569,
                "observation_residual_rms_K": 0.0434549611618198,
                "future_predictive_rmse_K": 0.023734559439133707
              }
            }
          }
        },
        {
          "split": "test",
          "index": 17,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.66936998021999,
            -2.9652521436342125,
            -0.4790226749520172,
            -0.25661258666649445,
            0.0812490107136822,
            -5.900865937422526,
            -0.00947824150363086,
            -0.03526847257965021
          ],
          "initial_K": [
            -1.8975857920774917,
            -1.6858516965849026,
            0.4557625840721048,
            2.3204303638977164,
            2.158630517658068,
            0.5914333222839876,
            -0.1474376340442416,
            1.2509590264301211,
            3.6758186095125147,
            4.7772080129495205,
            3.520430786928179,
            1.3170182219553026,
            0.47607333540019225,
            1.6500531718609408,
            3.0946155331425285,
            2.6035029652867316
          ],
          "observed_K": [
            0.02285971845557374,
            0.12260142942173495,
            0.38411202574735775,
            0.7510297252230161,
            0.9985272313836319,
            1.3012130076309114,
            1.613883652202908,
            1.9628933330406875,
            2.2875157254878404,
            2.459351539686324,
            2.4234261013800835,
            2.2245476440706597,
            1.9585545657449743,
            1.6251901262334847,
            1.2408581036741853,
            0.6359840963105758
          ],
          "future_observed_K": [
            0.09037612120325605,
            0.32683400476601,
            0.5018388739234287,
            0.7454733652919207,
            1.018848590956731,
            1.3445237518895723,
            1.6457153301512821,
            1.92401727745379,
            2.0969219376353774,
            2.2252794833556684,
            2.1941552548598824,
            2.077465003797977,
            1.8539535416455346,
            1.5143580521062845,
            1.086149837746479,
            0.5421122739461833
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.64517127081374,
                -2.986826460992954,
                -0.5186063674037921,
                -0.23283298838264238,
                -0.11617291497778418,
                -7.712715343626678,
                -2.0397366754865027,
                3.6191919850317955
              ],
              "initial_K": [
                -1.9354487649636218,
                -2.3952015092427827,
                -0.20898579506082804,
                3.1020790968062038,
                3.6158935467938207,
                0.3603347908273151,
                -2.0405709050460947,
                0.5749353151345957,
                5.35163343561635,
                6.144665397730082,
                2.4460932493486185,
                -0.2843650259813526,
                0.9796014131308644,
                3.168388028935853,
                2.9102146970032106,
                1.1763664730101362
              ],
              "metrics": {
                "initial_rmse_K": 1.1402299000426237,
                "observation_residual_rms_K": 0.014413998484316305,
                "future_predictive_rmse_K": 0.023734894661982097
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.565192675741778,
                -2.9224608522926245,
                -0.4896702429076408,
                -0.18848305052527187,
                -0.048598634386581296,
                -0.5845618109768941,
                -0.01277196595210623,
                0.0011802856107690962
              ],
              "initial_K": [
                -0.27689886817833637,
                -0.25484084374761884,
                0.10268686168268715,
                0.5784255050764924,
                0.9574735429347582,
                1.2435315566020209,
                1.6045926561278823,
                2.1256949574075197,
                2.6590144887700515,
                2.9441779426039165,
                2.863461242010886,
                2.5467858863610546,
                2.2130180660562164,
                1.9275790733172915,
                1.5443862642338109,
                0.8925828167521851
              ],
              "metrics": {
                "initial_rmse_K": 1.3299137271402353,
                "observation_residual_rms_K": 0.05738259513862661,
                "future_predictive_rmse_K": 0.03173319179976462
              }
            },
            "learned": {
              "coefficients_K": [
                6.644791723594095,
                -2.9937539960888206,
                -0.5088558143238436,
                -0.17856648424926294,
                -0.015175290871321167,
                -0.05781644770282518,
                -0.001991706788623967,
                -0.00031864346801424554
              ],
              "initial_K": [
                -0.10796425889353262,
                -0.10689806680148506,
                0.060278056256768076,
                0.38490901311482806,
                0.8186595249910856,
                1.3073491711555671,
                1.803122170830201,
                2.256257636223908,
                2.6101051569356915,
                2.8139195747826666,
                2.8428589362803995,
                2.7029493087458816,
                2.414128446754426,
                1.9889289099409466,
                1.430333513019264,
                0.752163289859721
              ],
              "metrics": {
                "initial_rmse_K": 1.4611682008885518,
                "observation_residual_rms_K": 0.05696457982157455,
                "future_predictive_rmse_K": 0.02295296344634807
              }
            }
          }
        },
        {
          "split": "test",
          "index": 18,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.807302046901371,
            0.0017489550590784845,
            -0.3149889416754652,
            -0.1285277374178691,
            -0.061114877660351924,
            5.987554857301268,
            -0.0513899601285698,
            0.014605475623798663
          ],
          "initial_K": [
            2.089365697880037,
            2.189725567156408,
            0.5284863656149807,
            -0.7021058066720602,
            0.2128569184878184,
            2.586893172407625,
            4.059150716660609,
            3.1764105618734977,
            0.9888070214918459,
            -0.10231842988508899,
            1.0120833667120799,
            2.9234757570327545,
            3.267150278992216,
            1.3621478391490633,
            -1.002929464887277,
            -1.5384644049880793
          ],
          "observed_K": [
            0.3381840274142367,
            0.6557458263799447,
            0.9161748141832443,
            1.1338287303693342,
            1.409587237309419,
            1.6338732575368582,
            1.852230355402673,
            1.8349073263144928,
            1.8154826888090807,
            1.6981641458927659,
            1.6023704150959337,
            1.5155723923396323,
            1.2219748292604844,
            0.8964919495261472,
            0.5637709620396052,
            0.26565143885962095
          ],
          "future_observed_K": [
            0.2836118926908448,
            0.6049996439149784,
            0.8836297930271627,
            1.099918865062276,
            1.340159128085376,
            1.5892842285027613,
            1.6684812234752018,
            1.7322396116563867,
            1.744170435525881,
            1.6681238362242654,
            1.5387723518871335,
            1.388345958284228,
            1.1250350015143502,
            0.8768714559919422,
            0.5650125291012956,
            0.29871540434197585
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.820162981892468,
                0.01317847365895795,
                -0.2888609625291902,
                0.03414151714504976,
                -0.41809484839659616,
                5.580372455243462,
                0.9581453235151549,
                -21.3241424737135
              ],
              "initial_K": [
                -5.043692088916113,
                0.8657174572629948,
                7.3756462885210725,
                1.854971108843283,
                -6.078166485712073,
                -0.9375388276508909,
                9.813786887110224,
                7.624157245530545,
                -4.239262615808517,
                -5.655369001903355,
                5.3956795589416195,
                9.599109119412269,
                0.23930408383031154,
                -6.017541690932335,
                0.46934539129937536,
                6.076325057113044
              ],
              "metrics": {
                "initial_rmse_K": 5.342529818222469,
                "observation_residual_rms_K": 0.016042553580670534,
                "future_predictive_rmse_K": 0.018474361715409032
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.750113853072256,
                0.012894479764475681,
                -0.2727436965271037,
                0.027638254122668748,
                -0.17490168581915064,
                0.42294736458260124,
                0.005999499639426052,
                -0.006954198237564084
              ],
              "initial_K": [
                0.4027320911163206,
                0.6998557921681535,
                0.9092209666101535,
                1.1512714910070703,
                1.4996217535920104,
                1.8707216271415237,
                2.089923740738317,
                2.073859285105418,
                1.923130293743387,
                1.8095303906306057,
                1.7795995359916443,
                1.700831003736271,
                1.416320142906101,
                0.9348971724291156,
                0.44435804952789903,
                0.1317916176062126
              ],
              "metrics": {
                "initial_rmse_K": 1.3921909339519274,
                "observation_residual_rms_K": 0.044700125741205535,
                "future_predictive_rmse_K": 0.02370283502670473
              }
            },
            "learned": {
              "coefficients_K": [
                5.819830556047049,
                0.013209039324548056,
                -0.2834299568090601,
                0.026184136216592765,
                -0.05461437321627486,
                0.04183187085822864,
                0.0009355837781748358,
                0.0018774352779172196
              ],
              "initial_K": [
                0.32215276803207316,
                0.6397964131248552,
                0.9550389522482015,
                1.2689443073938789,
                1.5671235195853033,
                1.8182143058478628,
                1.9902685839330518,
                2.0688574613616146,
                2.0594420683727424,
                1.974031246504725,
                1.8172153442044179,
                1.586043735176187,
                1.2846873010315798,
                0.9391051645405962,
                0.5926693956378216,
                0.27980800054965743
              ],
              "metrics": {
                "initial_rmse_K": 1.4870226982983779,
                "observation_residual_rms_K": 0.044562675948304695,
                "future_predictive_rmse_K": 0.020294611559957338
              }
            }
          }
        },
        {
          "split": "test",
          "index": 19,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.955620357912321,
            1.1049016266397764,
            -0.15437426852275474,
            0.15907621310153364,
            0.022577552990945143,
            -6.042911330097955,
            -0.0173039345769594,
            0.012378956026638271
          ],
          "initial_K": [
            -1.3295640788531689,
            -0.6487699957154821,
            1.7890102969298636,
            3.714611414204171,
            3.3381872048801737,
            1.3306474639124102,
            0.0831466219733834,
            1.0525735783568317,
            3.1407145202570774,
            3.916315195510278,
            2.323766770323925,
            -0.1337290098867825,
            -1.0442505319438555,
            0.26988366310441925,
            2.0384809048183654,
            2.025470143949261
          ],
          "observed_K": [
            0.37053688767738985,
            0.7895856314398104,
            1.1625438391876042,
            1.5600723121854798,
            1.7335790057559886,
            1.7894251748823191,
            1.8435794754573294,
            1.8653340031481258,
            1.8515930396648157,
            1.7165365300657371,
            1.4753719082581225,
            1.1669978150265297,
            0.9044048326834454,
            0.6812772173803577,
            0.5089953573189832,
            0.30025240029382755
          ],
          "future_observed_K": [
            0.39351642723149044,
            0.7136770106217917,
            1.1408284618893674,
            1.3657624056762043,
            1.6189801891580469,
            1.7588272035222627,
            1.8121946561959676,
            1.7871547206790972,
            1.7310885161297576,
            1.6148314850389673,
            1.430209204343423,
            1.1833937568600708,
            0.9532102019481209,
            0.7224031483943165,
            0.4882095120747052,
            0.26703973771270717
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.900430141514306,
                1.1010727288096651,
                -0.17288566290883506,
                0.18678188465657924,
                0.18903399138912907,
                -6.788305054342771,
                -0.6804069230848941,
                -3.102115763831289
              ],
              "initial_K": [
                -2.7962256121092417,
                -1.1178530492065504,
                3.027443769472713,
                4.502580875037224,
                2.4318508723995738,
                0.3850182954666681,
                0.5862628363700122,
                1.8538607733891723,
                2.7791656473793607,
                3.241997803496031,
                2.7079657666848007,
                0.540520997414576,
                -1.5207760851498524,
                -0.6534216649731863,
                2.352882938778141,
                3.132094049401998
              ],
              "metrics": {
                "initial_rmse_K": 0.8188129128432632,
                "observation_residual_rms_K": 0.013159172289965118,
                "future_predictive_rmse_K": 0.023575508862448913
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.829414949609285,
                1.0773447963908511,
                -0.16323934658886094,
                0.15120374328174913,
                0.0790786203127746,
                -0.5144989435282713,
                -0.004260419572612198,
                -0.001011657467780861
              ],
              "initial_K": [
                0.3682778752402606,
                0.8571893870579572,
                1.412551498818175,
                1.8367238704420137,
                1.9948063738365958,
                1.9614887602932778,
                1.9379841193187353,
                2.0267417765594993,
                2.1137442077205164,
                1.992657834527702,
                1.5993406551547882,
                1.101415750919596,
                0.7420440259035319,
                0.6026839519716253,
                0.5377929473172447,
                0.34805529519704415
              ],
              "metrics": {
                "initial_rmse_K": 1.3825635852865759,
                "observation_residual_rms_K": 0.04978790110835903,
                "future_predictive_rmse_K": 0.03596702243815215
              }
            },
            "learned": {
              "coefficients_K": [
                5.900093131110263,
                1.1036265162732313,
                -0.16963516129738426,
                0.14324853491019815,
                0.02469289682922588,
                -0.05088683643556881,
                -0.0006643853120951035,
                0.00027311867656011575
              ],
              "initial_K": [
                0.5020812878605208,
                0.977026157793941,
                1.3918082374648488,
                1.7153895413964149,
                1.9355328277396175,
                2.0648821726336526,
                2.124972630248456,
                2.1213652020817033,
                2.036253174547893,
                1.849294863973378,
                1.5677460588810823,
                1.2353985155244387,
                0.9099731271658902,
                0.6294431879649199,
                0.39695795164348646,
                0.1934512533562292
              ],
              "metrics": {
                "initial_rmse_K": 1.4980894862769214,
                "observation_residual_rms_K": 0.050209713395781855,
                "future_predictive_rmse_K": 0.025548045831109166
              }
            }
          }
        },
        {
          "split": "test",
          "index": 20,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            7.180732206431159,
            -1.189659729794893,
            -0.5444413310804779,
            0.16352564588851226,
            -0.16319068955682428,
            6.015665053162014,
            -0.03842669357752824,
            -0.026288524616383802
          ],
          "initial_K": [
            2.02536189534468,
            2.087672539372787,
            0.40832171984883603,
            -0.8258000055589529,
            0.13120208246409604,
            2.6247050411391535,
            4.276439764706119,
            3.5895406069897304,
            1.595438509414337,
            0.6829786787431058,
            1.9026153085340165,
            3.7714929660719596,
            3.928868951390625,
            1.7902806513521479,
            -0.7640974042969364,
            -1.4315268524433098
          ],
          "observed_K": [
            0.33129537377991936,
            0.5783016802722927,
            0.8561122017067938,
            1.137154349727123,
            1.454676557128507,
            1.800223641654795,
            2.1138860010267204,
            2.286559928613804,
            2.2880375339779864,
            2.2964132687876946,
            2.232715592815479,
            2.0713626305144306,
            1.7710093175034725,
            1.3453579650096172,
            0.9048880564775923,
            0.378227479017479
          ],
          "future_observed_K": [
            0.302811066996243,
            0.5825340541543055,
            0.8822105175759312,
            1.1460492423128887,
            1.4821410056640536,
            1.7348207091363501,
            1.9625398935853144,
            2.1313417892468007,
            2.17335020765222,
            2.161581736923744,
            2.0830808769859734,
            1.896763630529616,
            1.6503245503596808,
            1.2826043856988156,
            0.8726959664613319,
            0.45599288620907774
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                7.194963317426302,
                -1.1914959045558844,
                -0.5206264887594028,
                0.06795363558295209,
                -0.2648203123872156,
                5.672768482191042,
                -0.7322575751876521,
                -7.644565312689038
              ],
              "initial_K": [
                -0.9556510017014711,
                1.3308701293934833,
                3.0749436915102706,
                0.4658042676895717,
                -2.1141888012270686,
                1.0270390980001367,
                6.1804160596325435,
                5.455463688182851,
                0.04094215539089241,
                -1.4073624710852735,
                3.0790529541801375,
                6.012537790167606,
                3.1196456974919005,
                -0.5594647873817495,
                -0.3067629604481613,
                1.0464500544128357
              ],
              "metrics": {
                "initial_rmse_K": 1.914702264754714,
                "observation_residual_rms_K": 0.016661395397878094,
                "future_predictive_rmse_K": 0.015376860179041215
              }
            },
            "tikhonov": {
              "coefficients_K": [
                7.108367647537483,
                -1.16581936788318,
                -0.4915776497138026,
                0.055009853276926424,
                -0.11078232428193487,
                0.42995024053914466,
                -0.0045850863647573055,
                -0.00249303448849016
              ],
              "initial_K": [
                0.32683213410226886,
                0.5593757879071051,
                0.7337934910807632,
                0.993195616663753,
                1.4276665728109987,
                1.9531269614802313,
                2.3712455968767765,
                2.5550805492530184,
                2.5592455064282404,
                2.5309875970123814,
                2.5219879736780593,
                2.416980991711832,
                2.0656618354721155,
                1.4721327510770346,
                0.8255296787567266,
                0.3279910252407916
              ],
              "metrics": {
                "initial_rmse_K": 1.3969843262078903,
                "observation_residual_rms_K": 0.0460858387521053,
                "future_predictive_rmse_K": 0.023049814580064904
              }
            },
            "learned": {
              "coefficients_K": [
                7.194552368150313,
                -1.1942594161971496,
                -0.5108379544633647,
                0.05211564685181858,
                -0.03459261799429442,
                0.042524494638824656,
                -0.0007150150316215278,
                0.0006730482419200098
              ],
              "initial_K": [
                0.22885153335279484,
                0.47656889220760124,
                0.7651722003175226,
                1.1104186442066188,
                1.5047298497623438,
                1.9102570616639793,
                2.2719779273786362,
                2.541082589394878,
                2.689489303673627,
                2.706584560633589,
                2.587642049767691,
                2.3307704580290265,
                1.9478345554193432,
                1.4758137798479227,
                0.9695347727376793,
                0.4741422782221438
              ],
              "metrics": {
                "initial_rmse_K": 1.493963859623628,
                "observation_residual_rms_K": 0.04406940130456513,
                "future_predictive_rmse_K": 0.01788091904757473
              }
            }
          }
        },
        {
          "split": "test",
          "index": 21,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.656457177825757,
            -0.8046586944460525,
            -0.3496565046537763,
            -0.0662370360402944,
            0.12229509305188335,
            -5.962933445708799,
            -0.037136746228791595,
            0.03332413208248
          ],
          "initial_K": [
            -1.6198870175115465,
            -1.211474557125957,
            1.0253035783543214,
            2.884753372695803,
            2.5954607116499266,
            0.786627618452975,
            -0.22063332651693046,
            0.9680367356735919,
            3.221842565410434,
            4.120609902499771,
            2.6490611886700677,
            0.32621834781955905,
            -0.48338763372301097,
            0.8260394275231425,
            2.465763709189038,
            2.2490641273537544
          ],
          "observed_K": [
            0.1947392109491142,
            0.4235423732625151,
            0.7061632037744746,
            1.0336994638527663,
            1.2470237015414891,
            1.406402335620961,
            1.563696345410767,
            1.7542751999183148,
            1.8567607380657483,
            1.8552156356292324,
            1.7178746901794193,
            1.5289612249368925,
            1.289578121812346,
            1.0515159584862768,
            0.7494585517697702,
            0.43722832785076493
          ],
          "future_observed_K": [
            0.23067590572458485,
            0.51101872280766,
            0.7267006743685218,
            0.9661455059285794,
            1.1709028389123943,
            1.405464484598776,
            1.5367508444323692,
            1.700352787184029,
            1.7460214519391783,
            1.712772638177119,
            1.6508636875338307,
            1.4777592603919043,
            1.243891051360774,
            0.962949211760643,
            0.633798508423087,
            0.3566444238910003
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.650781809888639,
                -0.7956803953773995,
                -0.30088621449655295,
                -0.10735210548551426,
                0.14632183724391698,
                -5.20286788437471,
                -2.7691475132637717,
                1.6319919644517715
              ],
              "initial_K": [
                -1.7351812545161487,
                -1.385748945653774,
                1.0914069792196133,
                3.2829293575239284,
                2.7451634257779705,
                0.24204510408313884,
                -0.7345207127674611,
                1.4786735947474752,
                4.185503475799651,
                3.934223107992915,
                1.3067578898265158,
                -0.17529045300316315,
                0.8115001589607229,
                2.0597565677301226,
                1.6978237703888275,
                0.5918087698729122
              ],
              "metrics": {
                "initial_rmse_K": 0.8140209004228197,
                "observation_residual_rms_K": 0.012211136650885808,
                "future_predictive_rmse_K": 0.025400032207120744
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.582771284381486,
                -0.7785336164639841,
                -0.28409798837925004,
                -0.08690371782269724,
                0.06121083793369414,
                -0.3943355533374934,
                -0.017339227254581254,
                0.0005322228388269085
              ],
              "initial_K": [
                0.0741535894967755,
                0.3040825155423734,
                0.6844643112497628,
                1.0652053000386834,
                1.321039099019642,
                1.4787722008819473,
                1.6604155988413185,
                1.9143454747346873,
                2.133597091293915,
                2.1578508313509417,
                1.9451572982252694,
                1.6207679401176711,
                1.347897571788538,
                1.1607627467666388,
                0.9390501802545541,
                0.5490333063909256
              ],
              "metrics": {
                "initial_rmse_K": 1.3925093847439398,
                "observation_residual_rms_K": 0.0402191618709192,
                "future_predictive_rmse_K": 0.03212376428103617
              }
            },
            "learned": {
              "coefficients_K": [
                5.650459058459466,
                -0.79752586713013,
                -0.29522911657050854,
                -0.08233149514793314,
                0.019113546745617757,
                -0.03900200195904175,
                -0.0027039421152503205,
                -0.00014368499418516623
              ],
              "initial_K": [
                0.17728874389649524,
                0.39219763696503734,
                0.657534792804128,
                0.9575668471619416,
                1.2640796198075164,
                1.5521812117947087,
                1.801188661056244,
                1.9867573041648376,
                2.080902162714614,
                2.0652032543093677,
                1.9441690976677786,
                1.742623801502066,
                1.4869398333953248,
                1.1873371623649127,
                0.838382526928131,
                0.43702141328973565
              ],
              "metrics": {
                "initial_rmse_K": 1.4813259288846012,
                "observation_residual_rms_K": 0.03944494009135272,
                "future_predictive_rmse_K": 0.024080630439986345
              }
            }
          }
        },
        {
          "split": "test",
          "index": 22,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.616317898180286,
            2.8494047653427668,
            -0.14949376274781773,
            -0.15241351632198927,
            -0.08747961663688894,
            5.919992133876744,
            -0.005665201640811569,
            0.02009165091951631
          ],
          "initial_K": [
            2.4435280283275977,
            2.848152460582047,
            1.4069412042179519,
            0.28245792320171326,
            1.1540341723949084,
            3.3194849932696373,
            4.458849795904781,
            3.204942395669027,
            0.6794038309679937,
            -0.6965062704927998,
            0.18476934854068472,
            1.9425309223202603,
            2.266363425106762,
            0.5001022556925583,
            -1.6079403947709583,
            -1.8411987899146287
          ],
          "observed_K": [
            0.6240144934925267,
            1.1058165357495175,
            1.482961878777784,
            1.7731870050914376,
            1.974071836078815,
            2.112973987087423,
            2.1079588092093395,
            1.9089561980288217,
            1.5884921521225057,
            1.3120251382065022,
            1.0053009595030287,
            0.7747102032995462,
            0.5935184754518603,
            0.35625297914933013,
            0.12387933773582176,
            0.024393984510928158
          ],
          "future_observed_K": [
            0.47464975545724086,
            0.949220672598993,
            1.3357192037438739,
            1.6537339677272413,
            1.8317701545494405,
            1.9422361000686452,
            1.9203520868520547,
            1.7374925464037787,
            1.562594651567154,
            1.3187809497813932,
            1.0490975486040295,
            0.7988006130124661,
            0.558833570290862,
            0.4084648200100997,
            0.2397362831006501,
            0.08170303752764832
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.634324549304429,
                2.8387408584130447,
                -0.0715463696492029,
                -0.045620779630393904,
                0.16205919084699613,
                6.372801649566539,
                -1.390264781687907,
                13.924714941778232
              ],
              "initial_K": [
                6.981543941352449,
                3.740928146709741,
                -2.8020846297276787,
                -1.1811235436142398,
                5.137949817996476,
                5.318190684977331,
                0.6049412187726408,
                0.495821165790602,
                4.2606093155895906,
                2.8215971119200534,
                -2.8738046189011817,
                -2.3571934409438136,
                4.541072714202823,
                5.470606972293059,
                -2.7837604533895277,
                -7.125757912894239
              ],
              "metrics": {
                "initial_rmse_K": 3.4958983946797706,
                "observation_residual_rms_K": 0.012276661270111872,
                "future_predictive_rmse_K": 0.018745552061283356
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.566512096732737,
                2.777566469582464,
                -0.06755437342713365,
                -0.03693095111568333,
                0.06779424762187014,
                0.48300712619265973,
                -0.008705248412467372,
                0.004541107724545841
              ],
              "initial_K": [
                0.8397921000956583,
                1.4514785795054947,
                1.8032265130487846,
                2.044623858719368,
                2.3043599446513414,
                2.527871817962791,
                2.5318061737989472,
                2.2124361517460107,
                1.6808394770249353,
                1.1786258271291195,
                0.8616327842933659,
                0.6787992640358558,
                0.4718290351961979,
                0.18168411661733175,
                -0.07193886197693411,
                -0.13115365905323806
              ],
              "metrics": {
                "initial_rmse_K": 1.3604424522229395,
                "observation_residual_rms_K": 0.04818956580309626,
                "future_predictive_rmse_K": 0.022383012696383413
              }
            },
            "learned": {
              "coefficients_K": [
                5.634002737852157,
                2.8453249292258467,
                -0.07020119396531277,
                -0.03498792110129158,
                0.021169266174860188,
                0.04777211875155083,
                -0.0013575280755356233,
                -0.0012259696303784278
              ],
              "initial_K": [
                0.7064708152137138,
                1.3417992858930643,
                1.8577038289399894,
                2.233222007758818,
                2.4596969089162357,
                2.524980861957224,
                2.4172242387715865,
                2.1468071308067262,
                1.7616618584631554,
                1.3349054929854716,
                0.9328686152886431,
                0.5925273730644318,
                0.3252984071615389,
                0.13482181902481505,
                0.024729910035869995,
                -0.01095703142813903
              ],
              "metrics": {
                "initial_rmse_K": 1.4687505524097821,
                "observation_residual_rms_K": 0.04752710453566603,
                "future_predictive_rmse_K": 0.01745967679536653
              }
            }
          }
        },
        {
          "split": "test",
          "index": 23,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.3073933628624665,
            -0.12895218170690614,
            -0.5797098359900882,
            -0.004750410625855255,
            0.04804790973107032,
            -5.979739526154139,
            0.01728589544363994,
            -0.008473803232893842
          ],
          "initial_K": [
            -1.5442736008698328,
            -1.0462185427570168,
            1.281639698944689,
            3.214271160774923,
            2.9767821743464746,
            1.191771775640813,
            0.1581672735469004,
            1.2701479851678148,
            3.440769427358842,
            4.281748508096319,
            2.7441282271486376,
            0.30180878717267134,
            -0.6446205110466052,
            0.6040828096162076,
            2.2912103853360564,
            2.167685818906033
          ],
          "observed_K": [
            0.26171057145963844,
            0.5505016424307313,
            0.9150167676208983,
            1.2810492082877285,
            1.568039989804064,
            1.708895668453077,
            1.8273313762759376,
            1.9885650226937528,
            2.069056660354856,
            2.0068242654345516,
            1.8367403179089437,
            1.5579435702516908,
            1.2547753476404906,
            1.0048828829886352,
            0.7202369613074864,
            0.36254065262096247
          ],
          "future_observed_K": [
            0.2882195763281854,
            0.5608641746879778,
            0.8830607831170102,
            1.2117429178560952,
            1.462508176067544,
            1.6890161058031619,
            1.7793617430764062,
            1.8891550026773525,
            1.8801982188242188,
            1.8728199469024531,
            1.679469340874802,
            1.4810095389583022,
            1.2637034796336333,
            0.9271919609216432,
            0.6323060736382888,
            0.3068974715979357
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.318228056482201,
                -0.20699662642086022,
                -0.5057512712247356,
                0.00594744566720518,
                -0.3460897501630054,
                -6.091177901282723,
                -1.819700981254119,
                16.05768483083373
              ],
              "initial_K": [
                3.2015783439790755,
                -0.5161948149850255,
                -3.6297896550900837,
                1.8923196037611842,
                7.938746697398141,
                3.5164019465677705,
                -4.560828639592673,
                -2.107615476182536,
                7.540735958536421,
                8.468808438378616,
                -0.655806867534614,
                -4.598228232962569,
                1.9932118755555515,
                6.321238524797058,
                0.8858429600820095,
                -3.977913355247248
              ],
              "metrics": {
                "initial_rmse_K": 4.0440970074133915,
                "observation_residual_rms_K": 0.010894088173594385,
                "future_predictive_rmse_K": 0.027490081171334006
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.242184417769513,
                -0.2025358838794057,
                -0.477532408773224,
                0.00481457850957907,
                -0.14477978138304926,
                -0.46166231039481936,
                -0.011394195758160105,
                0.005236708753357757
              ],
              "initial_K": [
                0.09986168673525497,
                0.4058036232746139,
                0.915219311514044,
                1.424134357688564,
                1.738756734432185,
                1.8629684876433537,
                1.9619719779096763,
                2.1501921723334485,
                2.346055173071199,
                2.3562836936561573,
                2.0895337591896292,
                1.6575563793814543,
                1.2585629651912997,
                0.9822184207059923,
                0.748187333830777,
                0.42774614306253866
              ],
              "metrics": {
                "initial_rmse_K": 1.3808414030652691,
                "observation_residual_rms_K": 0.046176966583659856,
                "future_predictive_rmse_K": 0.02946845941458362
              }
            },
            "learned": {
              "coefficients_K": [
                6.31786718303076,
                -0.20747672675912354,
                -0.4962424126273853,
                0.004561271452269492,
                -0.045208580909851706,
                -0.04566099653465484,
                -0.0017768522972530655,
                -0.001413762078369449
              ],
              "initial_K": [
                0.25646677866260936,
                0.5562413644063335,
                0.9069988024284587,
                1.277449921126062,
                1.6239993623145454,
                1.916736300974754,
                2.1418151581086535,
                2.2865245772555487,
                2.329643740469081,
                2.2499577158953428,
                2.0451517348416672,
                1.7423070230396105,
                1.3881178957350637,
                1.025220047123563,
                0.6741860130013078,
                0.3347785953158413
              ],
              "metrics": {
                "initial_rmse_K": 1.4839922364297566,
                "observation_residual_rms_K": 0.04581719132409055,
                "future_predictive_rmse_K": 0.02969190662301884
              }
            }
          }
        },
        {
          "split": "test",
          "index": 24,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.714850767936276,
            -0.7122801141751662,
            -0.36390482425410486,
            0.10663356330007517,
            -0.19171585434582544,
            6.022988197840342,
            0.049432722517613964,
            0.007037053860749392
          ],
          "initial_K": [
            2.046383289838958,
            2.0629131922062656,
            0.3010037621080329,
            -0.9840285538533546,
            -0.056084554026053945,
            2.356203994188343,
            3.857256470502441,
            3.0272835280972012,
            0.9716656379994975,
            0.06970480566388315,
            1.3213924208222094,
            3.2316024658995346,
            3.4648192350951375,
            1.4438711476877788,
            -0.9788269216834421,
            -1.5297726310731625
          ],
          "observed_K": [
            0.30411182685855453,
            0.5601783868272174,
            0.7535571831991674,
            0.9324905347108632,
            1.1711966108837413,
            1.467322073612607,
            1.7391725712339245,
            1.7899607641857174,
            1.8422636218083646,
            1.775203460507099,
            1.6951118515648094,
            1.5943285716243027,
            1.3898086878206308,
            1.037274644054694,
            0.6378771276005099,
            0.3168167547816996
          ],
          "future_observed_K": [
            0.2568889919773365,
            0.5103355397652435,
            0.7176138647765037,
            0.9707052199174501,
            1.2141448421829575,
            1.4305308814751079,
            1.5887099880567883,
            1.7181179434907023,
            1.7487499922930032,
            1.6869017186959194,
            1.6435720229634838,
            1.4841475617791888,
            1.2706700337864205,
            0.9932765152777349,
            0.6567062526874242,
            0.3156603666980586
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.712316888984827,
                -0.7043003222017236,
                -0.33977098796710625,
                0.16075937702672022,
                0.3444946943028138,
                6.68316058352312,
                -1.2670806479076318,
                -4.469809616224743
              ],
              "initial_K": [
                0.4502281142009581,
                1.928065861197293,
                2.1320269294763055,
                -0.32756205713556663,
                -1.8541505828224516,
                1.038131460011797,
                5.157201781447464,
                4.690937313514351,
                0.3403378012718221,
                -1.5017207513801116,
                1.4877882382892844,
                4.502045690263403,
                3.4351924950998267,
                0.3697246650155035,
                -0.951423827138846,
                -0.5003254991867283
              ],
              "metrics": {
                "initial_rmse_K": 1.185914600547088,
                "observation_residual_rms_K": 0.014812763947169787,
                "future_predictive_rmse_K": 0.015975849866155262
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.643565752141533,
                -0.6891227685211253,
                -0.3208131497569528,
                0.13013799287213643,
                0.14411252140605338,
                0.5065298380267527,
                -0.007933921612596932,
                -0.0014576877918403802
              ],
              "initial_K": [
                0.43430244767204534,
                0.6706352411493046,
                0.72174040333988,
                0.7986108834779428,
                1.0869372506757302,
                1.5479409163719344,
                1.9530713043625212,
                2.1119679119747428,
                2.047485545463685,
                1.9350562783910976,
                1.8860603861599565,
                1.8236105131833669,
                1.5867752375930602,
                1.1365595466191807,
                0.623112621347849,
                0.23487772633647414
              ],
              "metrics": {
                "initial_rmse_K": 1.3819253731833478,
                "observation_residual_rms_K": 0.049583422345071015,
                "future_predictive_rmse_K": 0.028771278699753246
              }
            },
            "learned": {
              "coefficients_K": [
                5.711990622903099,
                -0.7059338503841613,
                -0.33338279981240837,
                0.12329110649298011,
                0.045000223939218396,
                0.050098647123822844,
                -0.0012372445710766868,
                0.0003935341488839983
              ],
              "initial_K": [
                0.268250994043783,
                0.5127260661028703,
                0.7370949703477397,
                0.9709974972669035,
                1.2401100114406138,
                1.5363693202109787,
                1.8158058742069747,
                2.024165497778412,
                2.125791767454302,
                2.1124442797986283,
                1.9916137097383202,
                1.7733256239521316,
                1.4708103012309348,
                1.1096734208784373,
                0.7272827983827632,
                0.3551758845369734
              ],
              "metrics": {
                "initial_rmse_K": 1.4944755181984233,
                "observation_residual_rms_K": 0.050293540253809145,
                "future_predictive_rmse_K": 0.019770158200212776
              }
            }
          }
        },
        {
          "split": "test",
          "index": 25,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            4.986804801747439,
            1.409274362677173,
            -0.12718695672699243,
            0.03689907187329964,
            0.12627846114006258,
            -6.110641629301851,
            0.08567935609441617,
            0.01678757000823148
          ],
          "initial_K": [
            -1.3331648626022075,
            -0.697312597096043,
            1.6752402929843515,
            3.565890337172601,
            3.186926068058197,
            1.158702632253153,
            -0.1553222311644249,
            0.7374459359991767,
            2.7834405205138926,
            3.54158003826858,
            1.9197763787127782,
            -0.5639480414514659,
            -1.4290747458605135,
            0.030460810803997873,
            1.969249560403128,
            2.04148740127108
          ],
          "observed_K": [
            0.3447662268602714,
            0.7302121437217559,
            1.0736266905358733,
            1.3940317602691061,
            1.6123831421772783,
            1.6020692026815,
            1.5861827532562514,
            1.6127722060925915,
            1.5445205414831122,
            1.3994297314674073,
            1.1678156561292279,
            0.8728257512222015,
            0.6415124519332754,
            0.4849738969696716,
            0.3727734437114022,
            0.20604311926619118
          ],
          "future_observed_K": [
            0.3839539755389853,
            0.73141737211146,
            0.9669985300903688,
            1.2092011216999685,
            1.4321602191689056,
            1.5751725155279372,
            1.5410635493562892,
            1.5253387915139274,
            1.446468011731523,
            1.2846879378494949,
            1.0937980057355046,
            0.8809066810991882,
            0.6632455057950898,
            0.5144371793876225,
            0.37370013925866374,
            0.18589908796149396
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                4.9857361831159235,
                1.3926483157113354,
                -0.17150819018609817,
                0.09744609428945195,
                0.10564878085324722,
                -6.491947783816029,
                0.5159857924159599,
                11.660908512396698
              ],
              "initial_K": [
                2.666796310551543,
                0.006183103478208496,
                -2.248015310074367,
                2.1062848534993366,
                6.862194080370897,
                3.3436456857694377,
                -3.4324391379590384,
                -2.1404876522799894,
                5.441654482433412,
                6.942508714103422,
                0.043226449253861654,
                -4.182452199705523,
                -0.25101741251946974,
                3.719077130302,
                1.3800571328945743,
                -1.7019884155241676
              ],
              "metrics": {
                "initial_rmse_K": 2.9146445323393513,
                "observation_residual_rms_K": 0.014414491075732193,
                "future_predictive_rmse_K": 0.02845098115088904
              }
            },
            "tikhonov": {
              "coefficients_K": [
                4.925729877924601,
                1.3626369783548127,
                -0.1619387312375341,
                0.07888459981995587,
                0.044196071649375966,
                -0.4920374452054483,
                0.003230884187997139,
                0.003802838474056738
              ],
              "initial_K": [
                0.33165964861747954,
                0.7831387253442204,
                1.3085655484109346,
                1.7171310125413626,
                1.8634637901926818,
                1.8001600052255426,
                1.7183564727642433,
                1.7347973672749029,
                1.762030525407079,
                1.6128861443034477,
                1.2268113806297425,
                0.7631429703381901,
                0.45270644643645697,
                0.36910463531829946,
                0.36838990826483664,
                0.2570795642712249
              ],
              "metrics": {
                "initial_rmse_K": 1.4051532948469494,
                "observation_residual_rms_K": 0.04791144591682557,
                "future_predictive_rmse_K": 0.029773326099355592
              }
            },
            "learned": {
              "coefficients_K": [
                4.985451416594632,
                1.3958783728335973,
                -0.1682835870628716,
                0.07473428306685266,
                0.013800557384267097,
                -0.04866526804241915,
                0.0005038358225055039,
                -0.00102665797889533
              ],
              "initial_K": [
                0.4627011371182649,
                0.9053886185888183,
                1.2967660289971152,
                1.6009400439679027,
                1.7970141741068064,
                1.889520883722151,
                1.8972964932892096,
                1.8324840066847925,
                1.6921518363038004,
                1.4717759158816164,
                1.1871084687317186,
                0.8811324037992241,
                0.6056757435260034,
                0.39186539993374847,
                0.2360033751159743,
                0.11283582567325695
              ],
              "metrics": {
                "initial_rmse_K": 1.5159791105853853,
                "observation_residual_rms_K": 0.048682734601840034,
                "future_predictive_rmse_K": 0.028588838214252225
              }
            }
          }
        },
        {
          "split": "test",
          "index": 26,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.5287372691079035,
            -0.056908109949892954,
            -0.585948894231754,
            -0.03780142717700538,
            -0.08439024445458593,
            5.987641094871149,
            0.020233371164114115,
            -0.04275300105504225
          ],
          "initial_K": [
            2.0973000108441324,
            2.215014249320882,
            0.5725164923485146,
            -0.6345913485819474,
            0.3358523163371643,
            2.79898649006136,
            4.3444561142981915,
            3.483776244371683,
            1.299509913339664,
            0.22842373832924823,
            1.3368419488884884,
            3.153199812885604,
            3.349138258902946,
            1.3546964814665652,
            -1.0053216869676023,
            -1.518796807267055
          ],
          "observed_K": [
            0.37191579292172433,
            0.6845903487875014,
            0.9619452442866986,
            1.2037173890068218,
            1.510686899145541,
            1.8208859559983606,
            2.0829470479881516,
            2.151933712190818,
            2.0802725612260087,
            1.9304671863715894,
            1.8179141838956254,
            1.658481306711552,
            1.3611520099752725,
            0.9803259894581376,
            0.6480255254468104,
            0.27913869743064035
          ],
          "future_observed_K": [
            0.32570731525818036,
            0.6344673506539603,
            0.9379876256024208,
            1.1971133454323555,
            1.4860626517882396,
            1.7577400435545867,
            1.9209797852248731,
            1.9607249860707743,
            1.965610773893789,
            1.897194617899482,
            1.7371156200203641,
            1.5152068933170748,
            1.2771716073431005,
            0.9780669887841231,
            0.6403132527032365,
            0.34683646992723444
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.5161239458661955,
                -0.08216309885011819,
                -0.6518734074258102,
                -0.05344169907204456,
                0.28951673705316994,
                6.674165269262618,
                0.056427055033035266,
                -24.12603366354405
              ],
              "initial_K": [
                -5.822326491767466,
                0.9819724732924306,
                8.475543031064118,
                2.0137599028499134,
                -7.359829831935959,
                -1.5400514318737775,
                11.210311122209944,
                9.29548325060163,
                -4.267521439454276,
                -6.5591859772924135,
                5.528365292147106,
                10.574798603437458,
                0.5016137942097292,
                -6.521985196469336,
                0.4438886912541823,
                6.604003211517966
              ],
              "metrics": {
                "initial_rmse_K": 6.02402599437113,
                "observation_residual_rms_K": 0.010240496667983505,
                "future_predictive_rmse_K": 0.015788320011294113
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.437698512229279,
                -0.08039249786634525,
                -0.6155015245130868,
                -0.04326214483747733,
                0.12111358362259945,
                0.5058480655302776,
                0.0003533222863130892,
                -0.007867946905215558
              ],
              "initial_K": [
                0.4605389928606528,
                0.7533105483354583,
                0.9013206906106367,
                1.1010551783537041,
                1.5064908341856407,
                2.0410715868644385,
                2.4474085827731327,
                2.532288890169584,
                2.345388840738767,
                2.100038574856953,
                1.9340238851656149,
                1.7825210426923788,
                1.4932342783933445,
                1.032942489834455,
                0.5440877161250262,
                0.19519940219326085
              ],
              "metrics": {
                "initial_rmse_K": 1.3716696388971248,
                "observation_residual_rms_K": 0.050162516560698554,
                "future_predictive_rmse_K": 0.02404137893715354
              }
            },
            "learned": {
              "coefficients_K": [
                6.515751769344972,
                -0.0823536649102167,
                -0.6396172403981438,
                -0.040986014833598705,
                0.037818631801894896,
                0.05003121599310667,
                5.509836143165344e-05,
                0.0021241213695693383
              ],
              "initial_K": [
                0.30194849231630355,
                0.6042329678606763,
                0.9223788415214371,
                1.2762333353180033,
                1.6606347585543428,
                2.0297410110527356,
                2.3139795799401535,
                2.4563904608557134,
                2.4395284181238637,
                2.285539445330061,
                2.0346161516776253,
                1.7219886429154017,
                1.371190144633157,
                1.0030955217409727,
                0.6426324631582153,
                0.30912434061009364
              ],
              "metrics": {
                "initial_rmse_K": 1.4848458197411971,
                "observation_residual_rms_K": 0.05003074413420519,
                "future_predictive_rmse_K": 0.0185630282634698
              }
            }
          }
        },
        {
          "split": "test",
          "index": 27,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.957312760882661,
            -2.3510480167926078,
            -0.35876480690229295,
            -0.33014295349320666,
            0.04855441761960698,
            -5.938590324365731,
            0.013760287624349882,
            -0.005853890030697762
          ],
          "initial_K": [
            -1.8644568421545435,
            -1.6354026939444797,
            0.5199727959873433,
            2.4015144118946106,
            2.22491302506769,
            0.5737301482130317,
            -0.296772873371248,
            0.9859071335336824,
            3.342341430700437,
            4.402783153213752,
            3.116700741967999,
            0.9159934002422024,
            0.12928118613707373,
            1.3920006487063414,
            2.92837940052181,
            2.5214818291691485
          ],
          "observed_K": [
            0.03493898603352791,
            0.20883634579571503,
            0.42147896345873553,
            0.671278265190134,
            1.0071349857827014,
            1.2041866584695056,
            1.4733970060253259,
            1.7703433017745263,
            2.0143825695138435,
            2.188650358763072,
            2.0917177972125587,
            1.920977558936727,
            1.687359435634818,
            1.3606672811914087,
            1.0378857530332373,
            0.5976176937495729
          ],
          "future_observed_K": [
            0.11609224129520963,
            0.26364417130319556,
            0.4843647605638651,
            0.7066648772877824,
            0.9670310232937197,
            1.2427062568269682,
            1.4532356724445563,
            1.7051356825494899,
            1.8778370456623958,
            1.985319677912657,
            1.9705169695891567,
            1.8492519259227203,
            1.6406390462436564,
            1.3023236487493466,
            0.9455827605870242,
            0.5085182910845382
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.93292714077309,
                -2.3531732871815576,
                -0.4581039293883676,
                -0.12915719515309948,
                0.12470145801916563,
                -6.719946184327347,
                3.2504940564059503,
                1.4622233229829495
              ],
              "initial_K": [
                -0.48760682827837964,
                -1.1125560745520855,
                -0.6375711743246572,
                1.4489488287014625,
                2.9782362852254964,
                1.7617442087726471,
                -0.6068089839762845,
                -0.35757950426462215,
                3.009573490283202,
                5.5543317461950465,
                4.10195167469297,
                0.4806837282978049,
                -0.9989073694103204,
                0.995891815286728,
                3.557610264921515,
                3.2829887012024503
              ],
              "metrics": {
                "initial_rmse_K": 0.9116905401695126,
                "observation_residual_rms_K": 0.019816681972350057,
                "future_predictive_rmse_K": 0.02669128975759241
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.861520828122065,
                -2.3024627979767573,
                -0.43254359467956366,
                -0.10455538241744648,
                0.0521663811819301,
                -0.5093178908027132,
                0.020353215155107497,
                0.0004768581371160906
              ],
              "initial_K": [
                -0.15334689287310904,
                -0.0927832727864899,
                0.20879559496367572,
                0.5953992330864605,
                0.911399575088785,
                1.163118270598208,
                1.4817750956085138,
                1.9308182283053026,
                2.379286510158531,
                2.5972170551598923,
                2.480623044901902,
                2.157147691707474,
                1.8453839249071888,
                1.6160367777839397,
                1.3214800516194063,
                0.7779808787466669
              ],
              "metrics": {
                "initial_rmse_K": 1.3588820181681753,
                "observation_residual_rms_K": 0.05250397022162442,
                "future_predictive_rmse_K": 0.041847580124372494
              }
            },
            "learned": {
              "coefficients_K": [
                5.932588274262528,
                -2.3586311504844653,
                -0.44949091003421765,
                -0.09905446137246877,
                0.01628934677141023,
                -0.05037440120916869,
                0.003173954342406208,
                -0.0001287381030278525
              ],
              "initial_K": [
                -0.03239751532601953,
                0.010363300905009698,
                0.1708986255874534,
                0.44876651614201624,
                0.8141625930327927,
                1.227996775440138,
                1.6498263931687314,
                2.0331551113835777,
                2.324048756379745,
                2.475109248990421,
                2.4663676671414136,
                2.311430782047905,
                2.0390886458555846,
                1.6670708692729472,
                1.1956618732524718,
                0.6288941069903465
              ],
              "metrics": {
                "initial_rmse_K": 1.4734011368569924,
                "observation_residual_rms_K": 0.05219158638417192,
                "future_predictive_rmse_K": 0.0283229737036428
              }
            }
          }
        },
        {
          "split": "test",
          "index": 28,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.655962654569335,
            2.779093117337611,
            -0.08398405134231095,
            0.16092454576813897,
            -0.18006023287756892,
            5.979219136565524,
            -0.020572540460693223,
            0.06688472410583254
          ],
          "initial_K": [
            2.5254557245982734,
            2.949873160049301,
            1.4734547424503763,
            0.3012413550260944,
            1.124589988858456,
            3.2370012787317783,
            4.347626298637573,
            3.12915116059043,
            0.690360549060594,
            -0.6047643672413527,
            0.3159439561732147,
            2.071271759859661,
            2.3443520449157624,
            0.4766002652574324,
            -1.7260775470433476,
            -1.9549895948668612
          ],
          "observed_K": [
            0.5763722958436469,
            1.1134108314651594,
            1.4977617224798156,
            1.7522510188751077,
            1.9709195361961211,
            2.0687905739138754,
            2.0988789231184732,
            1.8860896257297572,
            1.5837924014670184,
            1.2950206242802798,
            1.1286254931640798,
            0.8554121225476085,
            0.560328603682446,
            0.3296703835221743,
            0.1322814723409709,
            0.006848150285064556
          ],
          "future_observed_K": [
            0.49170492825987183,
            0.9817090597367211,
            1.356911412741829,
            1.6486421089174548,
            1.8564567186923548,
            1.947613796322566,
            1.9314402043676488,
            1.8405302865014115,
            1.5893458577520554,
            1.3115564473105872,
            1.062958904834826,
            0.8213800458625953,
            0.5972798160764485,
            0.3716754151340553,
            0.22005408815964328,
            0.09702454373315646
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.646183806144819,
                2.7493224729903405,
                -0.08602483995463017,
                0.3186200184818231,
                -0.535233452490715,
                5.7419820088904725,
                3.2651787954191436,
                -30.07118934245141
              ],
              "initial_K": [
                -6.822032682404308,
                1.5067268454658609,
                10.659357685823839,
                3.1659934187700216,
                -7.786973726309805,
                -1.0930463144459734,
                12.844111576690912,
                9.01798896801526,
                -7.220650311946539,
                -8.337287449954724,
                7.048779253097549,
                11.633756591603126,
                -2.4154771699182853,
                -10.32075806473811,
                0.6656282003182035,
                9.36405638997369
              ],
              "metrics": {
                "initial_rmse_K": 7.580022896144831,
                "observation_residual_rms_K": 0.01719769931980116,
                "future_predictive_rmse_K": 0.030077683097212607
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.578228620351959,
                2.6900750353508975,
                -0.08122500401904373,
                0.25792940020671734,
                -0.22390429709057488,
                0.43519606936970695,
                0.020445164762596578,
                -0.009806772402900475
              ],
              "initial_K": [
                0.8055502131051724,
                1.4242607567475678,
                1.819386277142041,
                2.0935627899803966,
                2.33187281043451,
                2.4799529952314328,
                2.4053246840098823,
                2.0760396972556614,
                1.6391757726330933,
                1.289610686948184,
                1.0731902577355685,
                0.8572371083556516,
                0.508261474129349,
                0.07465991989411525,
                -0.2321500425191818,
                -0.24082419445991277
              ],
              "metrics": {
                "initial_rmse_K": 1.3867466978162335,
                "observation_residual_rms_K": 0.048528698493310055,
                "future_predictive_rmse_K": 0.043660630359547356
              }
            },
            "learned": {
              "coefficients_K": [
                5.645861317336347,
                2.755699150099048,
                -0.08440744799631161,
                0.2443590872021631,
                -0.06991580892294297,
                0.04304333658598046,
                0.0031882932983769694,
                0.002647548983038422
              ],
              "initial_K": [
                0.734537404897736,
                1.3833242298540953,
                1.8906206294435517,
                2.235200591363228,
                2.4148516902911474,
                2.435541154895698,
                2.314612880838566,
                2.084322940081937,
                1.7831978622245082,
                1.441551786453262,
                1.0765813170808758,
                0.7031342555019655,
                0.35112529977030815,
                0.07181103719544313,
                -0.08103703087868497,
                -0.08952295200064997
              ],
              "metrics": {
                "initial_rmse_K": 1.4845583672208262,
                "observation_residual_rms_K": 0.04795700463547843,
                "future_predictive_rmse_K": 0.030487702285924904
              }
            }
          }
        },
        {
          "split": "test",
          "index": 29,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.608043060768968,
            0.29341304963263093,
            -0.5652863008777103,
            0.29211979222911494,
            0.08191861570761154,
            -6.090647122115375,
            -0.013020152688873845,
            -0.01960056688216214
          ],
          "initial_K": [
            -1.4403681313240746,
            -0.8309051678542696,
            1.5736540617718013,
            3.4918112061852566,
            3.1553315671326896,
            1.2669157214375892,
            0.2026799489824711,
            1.3591478831748136,
            3.5850067919027957,
            4.425700042148513,
            2.8154337423751215,
            0.26446383759025127,
            -0.7689403906534613,
            0.45289364593925496,
            2.170661813545913,
            2.1054322261274843
          ],
          "observed_K": [
            0.2813863272310897,
            0.657870646462826,
            1.0741451674732734,
            1.4320583080784064,
            1.6845521337203924,
            1.8262747341963919,
            1.9752032886756652,
            2.0908293100094304,
            2.1410525218717527,
            2.0869193748661528,
            1.8030932296523152,
            1.5088787603226297,
            1.1892379477487287,
            0.9164796144209234,
            0.6613431827131998,
            0.3747975571875916
          ],
          "future_observed_K": [
            0.37612676729137656,
            0.714545699023032,
            1.0909360692909498,
            1.3667758611503176,
            1.6011263721930082,
            1.8050710243872217,
            1.9192689793948838,
            1.9800950719561676,
            1.9830552648821442,
            1.886063231932761,
            1.7341174743280483,
            1.4673110321037577,
            1.1779168782862668,
            0.9502629839994021,
            0.6118921330898909,
            0.29601800160314284
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.56042315454237,
                0.2373424549113608,
                -0.6002820628810692,
                0.178724748288617,
                0.16745358210743116,
                -7.145332766933274,
                -3.0671309655033814,
                -7.7040005451060045
              ],
              "initial_K": [
                -5.41530097130971,
                -2.195481540635779,
                4.8227606849773625,
                5.667295606812061,
                0.802543883409774,
                -1.304498024242479,
                1.589865501854433,
                3.812411227121176,
                2.8467593856476734,
                2.2772112616396107,
                3.23632095798792,
                2.139110096721664,
                -1.141020453140257,
                -1.4046564330275109,
                2.4554545208544396,
                4.093425848051259
              ],
              "metrics": {
                "initial_rmse_K": 2.084417913779362,
                "observation_residual_rms_K": 0.009831113101517155,
                "future_predictive_rmse_K": 0.03082444018594084
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.481464553538003,
                0.23222776486146698,
                -0.5667887670095035,
                0.1446813271426929,
                0.07005088419377835,
                -0.5415587735547097,
                -0.019205073249328408,
                -0.00251241741978659
              ],
              "initial_K": [
                0.21406327202932662,
                0.6033845745777131,
                1.1357294048642086,
                1.6032225640216282,
                1.853586256993816,
                1.9513134801727179,
                2.0845005460025465,
                2.3268949169174618,
                2.5278875102140566,
                2.4580278089289105,
                2.054756394657202,
                1.5038701302316877,
                1.068411119261865,
                0.8439982154851857,
                0.6940180856234862,
                0.42392520543432
              ],
              "metrics": {
                "initial_rmse_K": 1.388217353236568,
                "observation_residual_rms_K": 0.0521568868674033,
                "future_predictive_rmse_K": 0.04031131517487674
              }
            },
            "learned": {
              "coefficients_K": [
                6.5600484478167616,
                0.23789293824462787,
                -0.5889958880769223,
                0.13706927945186315,
                0.021873917998966253,
                -0.05356320567179447,
                -0.002994908920846283,
                0.0006782810808127519
              ],
              "initial_K": [
                0.3570332775218633,
                0.7258197035366761,
                1.1004663183804035,
                1.459093148245882,
                1.7812793903161601,
                2.058613277777891,
                2.2836831617768834,
                2.430508726613402,
                2.454145876801566,
                2.3189027202414745,
                2.0318500849982013,
                1.6486449078372054,
                1.2441450643482543,
                0.8730410176888732,
                0.551486401015834,
                0.26716294940987106
              ],
              "metrics": {
                "initial_rmse_K": 1.5099769884167653,
                "observation_residual_rms_K": 0.05233534512494548,
                "future_predictive_rmse_K": 0.03162738097746052
              }
            }
          }
        },
        {
          "split": "test",
          "index": 30,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            6.022028047866522,
            -1.3518810968495025,
            -0.3362361886406321,
            -0.01624701096388649,
            -0.04467320659660451,
            6.091724521143678,
            -0.04042773839908142,
            -0.006286635853356148
          ],
          "initial_K": [
            1.9902519933358584,
            1.9699640107960579,
            0.17494949023394157,
            -1.1516496384255384,
            -0.2332528688154898,
            2.255686647354543,
            3.8996974686753854,
            3.183215606235936,
            1.1467888644888082,
            0.21342100682913978,
            1.4777158210723438,
            3.4720198836177976,
            3.79162931950337,
            1.777723489958701,
            -0.7281970487272819,
            -1.4037235516549766
          ],
          "observed_K": [
            0.251017657423949,
            0.48342835220259484,
            0.6662838882737401,
            0.8392708906365407,
            1.1410407405604375,
            1.4143663959809987,
            1.7365083570061812,
            1.9125516228436379,
            1.9208077633199991,
            1.9368473955476613,
            1.9234354783611645,
            1.8043840756962934,
            1.6119438640981862,
            1.2539011079712081,
            0.7505536177766851,
            0.38596547779816975
          ],
          "future_observed_K": [
            0.2413860912344785,
            0.4318419399661913,
            0.6995077458482701,
            0.9289046470353615,
            1.1297369730463875,
            1.4358514630563068,
            1.6154861753840244,
            1.7347702688980482,
            1.840389183506029,
            1.8650661985492096,
            1.8163668587478508,
            1.6920479390646572,
            1.4564836970587467,
            1.10960004356677,
            0.8156678412220124,
            0.36589100879255243
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.02449388580401,
                -1.3618319362497349,
                -0.33602509637496636,
                0.08876886427008814,
                0.09459686567563404,
                6.903122925921113,
                -4.014952827490051,
                -6.7423418572098575
              ],
              "initial_K": [
                -1.3110711646420978,
                1.1297384127162073,
                3.307937817171847,
                0.6143298215514288,
                -2.8085814869885235,
                -0.28631363378097796,
                5.503633414656866,
                6.004056554535891,
                0.5888108533391736,
                -2.3563563921636907,
                1.2419689074092455,
                5.452626392244559,
                4.417274731325869,
                0.5171146499015304,
                -1.230657600056686,
                -0.6481912544757912
              ],
              "metrics": {
                "initial_rmse_K": 1.9662811763494124,
                "observation_residual_rms_K": 0.017874716081260518,
                "future_predictive_rmse_K": 0.023050088460764933
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.951985512826105,
                -1.3324846866960658,
                -0.3172762636693189,
                0.0718602052291373,
                0.03957272217853723,
                0.5232012150308505,
                -0.025139931751133965,
                -0.0021988026912811223
              ],
              "initial_K": [
                0.33177208671634495,
                0.5082884592304108,
                0.5553662569686034,
                0.6661953321835914,
                1.000610579248173,
                1.5057532823617734,
                1.9529039206713585,
                2.1586029350792812,
                2.15441222851515,
                2.1196454095533155,
                2.1537559975316984,
                2.1488924797136946,
                1.9119818470649426,
                1.398774897229495,
                0.7888710603374216,
                0.3089805987233257
              ],
              "metrics": {
                "initial_rmse_K": 1.3925965889389622,
                "observation_residual_rms_K": 0.05270394933075847,
                "future_predictive_rmse_K": 0.030976942336822216
              }
            },
            "learned": {
              "coefficients_K": [
                6.0241497893449525,
                -1.3649905189984315,
                -0.3297073364238089,
                0.0680794595027899,
                0.012356881571040566,
                0.05174753998440967,
                -0.0039204123250907545,
                0.0005936140444619391
              ],
              "initial_K": [
                0.1849246228343089,
                0.37059428362664576,
                0.5736524644773959,
                0.8217152315978897,
                1.1292132017292713,
                1.4766687411885122,
                1.814007224775984,
                2.085832659720992,
                2.2563487863191116,
                2.313729450261511,
                2.2557941221210607,
                2.0779796032849287,
                1.7798055856053456,
                1.3815070886388061,
                0.9265204045624151,
                0.4595370986972179
              ],
              "metrics": {
                "initial_rmse_K": 1.5102417940692185,
                "observation_residual_rms_K": 0.05294322961025249,
                "future_predictive_rmse_K": 0.024371847619385247
              }
            }
          }
        },
        {
          "split": "test",
          "index": 31,
          "scenario": "high-frequency",
          "true_kappa_m2_per_s": 0.01,
          "coefficients_K": [
            5.377356295188499,
            0.7716874304292267,
            -1.1237860672550566,
            -0.24010557718598957,
            0.019814182809407426,
            -6.003852254828625,
            -0.0564822158563766,
            0.04301894278658247
          ],
          "initial_K": [
            -1.6658033602339675,
            -1.2267619098255294,
            1.1380772161237729,
            3.172526923461172,
            3.020797521337213,
            1.2523106690922459,
            0.17870499570818255,
            1.2131964735397305,
            3.2444732351009478,
            3.877172108740222,
            2.1437160489680354,
            -0.3761820691729163,
            -1.2750454130826756,
            0.06723586063791698,
            1.8619081869873013,
            1.9113725355319011
          ],
          "observed_K": [
            0.226804965724429,
            0.5224231282276467,
            0.8541390461674527,
            1.2196325543689854,
            1.4878807105490923,
            1.5970339084181997,
            1.7587753173179694,
            1.8609237319687635,
            1.8102156987756626,
            1.647018737516508,
            1.3957497483731338,
            1.0716283715548538,
            0.7919948063170619,
            0.571413426433202,
            0.4202319635846641,
            0.20812930099384103
          ],
          "future_observed_K": [
            0.271869770955309,
            0.562877459684676,
            0.8675352316485929,
            1.1459570026086225,
            1.372366709278941,
            1.5826132843958571,
            1.6708307261812378,
            1.7234241772923704,
            1.6846309854550074,
            1.5694677589127637,
            1.3181440436285332,
            1.0709589754787274,
            0.8485698995635745,
            0.6327815148678336,
            0.387287586729236,
            0.19911296430470773
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.3678169045221935,
                0.7043095454334901,
                -1.128296683079252,
                -0.18726397629830704,
                0.2305581468063157,
                -5.207028923412952,
                -4.128323973384469,
                -6.420420476991973
              ],
              "initial_K": [
                -4.911816409111722,
                -2.08181420782221,
                4.177697048498441,
                4.899542488820924,
                0.488600553156762,
                -1.2939183641259508,
                1.6982706904063058,
                4.017296103871253,
                2.7953166194114423,
                1.3709193183887223,
                1.8059152677844463,
                1.4924622133534415,
                -0.5846205760871226,
                -1.0448782137499006,
                1.380414882951464,
                2.5832934204772826
              ],
              "metrics": {
                "initial_rmse_K": 1.9209816538547844,
                "observation_residual_rms_K": 0.015316678328805556,
                "future_predictive_rmse_K": 0.018821547983702915
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.303212030226058,
                0.6891317929937959,
                -1.065342320498595,
                -0.1515940062934331,
                0.09644942699105531,
                -0.39465092664084633,
                -0.02584981378282779,
                -0.0020938181603577764
              ],
              "initial_K": [
                0.088215602999444,
                0.35645636148881815,
                0.8073061768571863,
                1.2806257424342782,
                1.6302825407599706,
                1.8536799146411147,
                2.0353631559987284,
                2.1908165544983778,
                2.2079366673566785,
                1.9618341545941238,
                1.4749565475400594,
                0.9397408181212605,
                0.5680981639993855,
                0.41598642585850104,
                0.3578319327400469,
                0.23127767383073772
              ],
              "metrics": {
                "initial_rmse_K": 1.4030223800127746,
                "observation_residual_rms_K": 0.04207538087836514,
                "future_predictive_rmse_K": 0.031862704810327956
              }
            },
            "learned": {
              "coefficients_K": [
                5.3675103149854255,
                0.7059430950079514,
                -1.107083066375375,
                -0.1436182652054938,
                0.03011706249436612,
                -0.039033194150795945,
                -0.0040311139090871955,
                0.0005652712139503774
              ],
              "initial_K": [
                0.18779535573733278,
                0.43777873859302185,
                0.7754541881290099,
                1.1779317480255043,
                1.5894879243232067,
                1.945345553391633,
                2.186057841677884,
                2.2638771527967467,
                2.1536595018514237,
                1.8699000848847784,
                1.4735957225877954,
                1.0534506100943437,
                0.6882135547247922,
                0.4160253042317363,
                0.23092408765661637,
                0.10281243026681747
              ],
              "metrics": {
                "initial_rmse_K": 1.491595916729347,
                "observation_residual_rms_K": 0.04131430611860796,
                "future_predictive_rmse_K": 0.021446556025939104
              }
            }
          }
        }
      ],
      "wrong-diffusivity": [
        {
          "split": "test",
          "index": 0,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            6.064136750230109,
            1.768324303923217,
            0.2456775890493475,
            0.005338822758752014,
            0.08703779952503056,
            0.008671880120626883,
            -0.009365291777447502,
            -0.002943137637902704
          ],
          "initial_K": [
            0.6692855762874994,
            1.2664598933935682,
            1.736654368808024,
            2.0574636298236393,
            2.2394901043514093,
            2.305931789950305,
            2.2695599894446725,
            2.132380473991563,
            1.90631236400416,
            1.6267097319388422,
            1.3403251111018104,
            1.0804804834308834,
            0.8538973310738912,
            0.6469957081128842,
            0.44120325626692913,
            0.2252954098552855
          ],
          "observed_K": [
            0.4903688401088555,
            0.8718493410698824,
            1.2512759688583701,
            1.557562808193551,
            1.7480714161152007,
            1.8633897784299212,
            1.8695028272466425,
            1.8359686249584786,
            1.715295331609875,
            1.5304858385733775,
            1.3313305204864163,
            1.1484811528493966,
            0.8679993800694908,
            0.629168211373262,
            0.4789463000716529,
            0.22233870462631009
          ],
          "future_observed_K": [
            0.39948067138286697,
            0.7500703121501001,
            1.0764573970985523,
            1.3599158521307857,
            1.5290121666128815,
            1.674461955905366,
            1.719530029297715,
            1.6106821446357054,
            1.5795614266970153,
            1.4426446931983359,
            1.2641747561145014,
            1.1197509031894093,
            0.9150081534489547,
            0.651006223504629,
            0.43628591638582515,
            0.23116758644687563
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.762141721806938,
                1.4288298217025543,
                0.12132594682978844,
                0.034104144663739566,
                0.1521778706015371,
                -0.41585566504227117,
                2.8545187814773882,
                -8.239873870514131
              ],
              "initial_K": [
                -1.3885223449050368,
                1.0255044431930147,
                3.6337354161004103,
                2.1090710552154053,
                -0.24847974860256095,
                1.5417908224114498,
                4.597090037735029,
                3.1081066571097598,
                -0.7214391096746058,
                -0.12470010587390234,
                3.860815575895517,
                3.6888127719027306,
                -1.1875212000678972,
                -2.751490963336058,
                1.608172770335073,
                4.1254000560017055
              ],
              "metrics": {
                "initial_rmse_K": 2.1859791144934215,
                "observation_residual_rms_K": 0.01768506392884998,
                "future_predictive_rmse_K": 0.05871236398164732
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.692790913417734,
                1.398038778967352,
                0.1145564528113189,
                0.0276080003371894,
                0.06366059331907829,
                -0.03151851583152078,
                0.01787378592777488,
                -0.0026871756469792935
              ],
              "initial_K": [
                0.5718060614936123,
                1.0884523038303588,
                1.5104813815223073,
                1.8197877813198486,
                2.01448662083064,
                2.1012493583063883,
                2.091757855958655,
                2.0007642144848274,
                1.8415217623187319,
                1.6238965042565232,
                1.3629105416684886,
                1.0891047905079392,
                0.8398901515103918,
                0.6311184340304673,
                0.44108165444658876,
                0.23378967902186276
              ],
              "metrics": {
                "initial_rmse_K": 0.13592313170401965,
                "observation_residual_rms_K": 0.025369828143783524,
                "future_predictive_rmse_K": 0.04530982307785767
              }
            },
            "learned": {
              "coefficients_K": [
                5.761812609917933,
                1.4321437968749102,
                0.11904484278075587,
                0.0261554741586877,
                0.019878501378726845,
                -0.0031173583152797127,
                0.002787303137532249,
                0.0007254608202492249
              ],
              "initial_K": [
                0.5737815372321022,
                1.0965883206653255,
                1.5296966403924839,
                1.851267196762835,
                2.053936082189969,
                2.1410728044685112,
                2.124232523235925,
                2.0202125187195903,
                1.8476317997446707,
                1.6256311566896617,
                1.3748348231346266,
                1.1165569873406342,
                0.8678415784238096,
                0.6360174308009805,
                0.418470200803857,
                0.208213327160295
              ],
              "metrics": {
                "initial_rmse_K": 0.11876892117311297,
                "observation_residual_rms_K": 0.01938485515610915,
                "future_predictive_rmse_K": 0.0587311965736463
              }
            }
          }
        },
        {
          "split": "test",
          "index": 1,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            6.184809778754638,
            -2.9132134703184316,
            0.12478018733153877,
            0.44910633776766584,
            -0.04817235905362789,
            0.06297486629680303,
            0.022310270053648815,
            -0.0271975656568205
          ],
          "initial_K": [
            0.15936968186868739,
            0.28851202182038094,
            0.38171436211981635,
            0.4810999040850209,
            0.6611364175348915,
            0.9671936865354203,
            1.3763207707564038,
            1.8286623041396564,
            2.271857602126564,
            2.6462488760941696,
            2.8525291209434225,
            2.791285766741742,
            2.449223902575053,
            1.9147878565538514,
            1.2970411488360951,
            0.6536436012780684
          ],
          "observed_K": [
            0.1609592899982093,
            0.34957718351822126,
            0.4854400741891118,
            0.7332658334784705,
            0.9115588647955228,
            1.2064972268369747,
            1.441131949667395,
            1.7020039516217766,
            1.9699092246032368,
            2.027434952758538,
            2.0333491723108694,
            1.9501770911300345,
            1.7255217474913438,
            1.4240300995017245,
            0.9782354156232099,
            0.5079766954364239
          ],
          "future_observed_K": [
            0.18531042493330016,
            0.34457932172520067,
            0.5292856279619631,
            0.7742964623048424,
            0.966382637212805,
            1.2377240235084703,
            1.3966741530441453,
            1.5886284244701006,
            1.6982044334064506,
            1.8292151171791775,
            1.8082530447833083,
            1.6881445420428323,
            1.5004547304810936,
            1.238342880191704,
            0.875104552834902,
            0.4468420892580465
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.845437800194972,
                -2.2365665112163176,
                -0.021514008194936162,
                0.2871164261851729,
                0.39819576065789625,
                -0.11128696382172767,
                -3.042236981899944,
                15.85757806139704
              ],
              "initial_K": [
                4.6408329161529505,
                0.8499334637254315,
                -4.0321216695726845,
                -0.46685146823045764,
                5.374505862647542,
                2.807711561947334,
                -3.2889580037570134,
                -0.9024427266343573,
                6.819420141038838,
                6.452058280549577,
                -1.4775325587969639,
                -2.8353104311740167,
                4.8809185792879575,
                7.633036941899648,
                -0.2504974504331984,
                -5.701080904125581
              ],
              "metrics": {
                "initial_rmse_K": 4.050986187300759,
                "observation_residual_rms_K": 0.017625536917471506,
                "future_predictive_rmse_K": 0.05660667088950061
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.775084473879144,
                -2.188368878453498,
                -0.02031361410286906,
                0.23242660002438822,
                0.16657729721424638,
                -0.00843465708396797,
                -0.019049197682243477,
                0.005171450225608907
              ],
              "initial_K": [
                0.18135582853153417,
                0.3325587787654208,
                0.45141173170159776,
                0.5740806245034755,
                0.7597515359187655,
                1.0536706529225501,
                1.4472503416905707,
                1.866009031632425,
                2.2048889714079665,
                2.3888551633948163,
                2.405240342462771,
                2.280514867614641,
                2.035304053658343,
                1.6703490567554051,
                1.1891189038860919,
                0.617885746200226
              ],
              "metrics": {
                "initial_rmse_K": 0.22572825496484356,
                "observation_residual_rms_K": 0.027392754224268706,
                "future_predictive_rmse_K": 0.04227176839071366
              }
            },
            "learned": {
              "coefficients_K": [
                5.8451039307468795,
                -2.2417539210652118,
                -0.02110951358775013,
                0.2201980533353042,
                0.052015019962838305,
                -0.0008342349791402535,
                -0.002970601118405542,
                -0.0013961441362292857
              ],
              "initial_K": [
                0.1502219789238233,
                0.2912528858078254,
                0.42782197331733607,
                0.5850945608143903,
                0.7997821136709224,
                1.0963610929799716,
                1.4638144279573435,
                1.8516501382203745,
                2.188449010509554,
                2.4084019557010325,
                2.469575452706385,
                2.35889873266453,
                2.0877123243603606,
                1.6828608581512796,
                1.1775050254137125,
                0.6054515395748347
              ],
              "metrics": {
                "initial_rmse_K": 0.20238495884848196,
                "observation_residual_rms_K": 0.021574877348343388,
                "future_predictive_rmse_K": 0.05648755805423895
              }
            }
          }
        },
        {
          "split": "test",
          "index": 2,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            5.475793918696814,
            -0.03163023368275662,
            0.3355965009422605,
            0.11297519515169935,
            0.19505591894691615,
            -0.03313017528591373,
            0.11145245560602077,
            0.05838141932070094
          ],
          "initial_K": [
            0.5278243832025117,
            0.8918796777488686,
            1.105806779562422,
            1.2877547244560041,
            1.4755562725067433,
            1.6136283539542802,
            1.6873441083119647,
            1.7533741839079795,
            1.8243029018841872,
            1.8227323945420035,
            1.6926124073808857,
            1.4860629535636722,
            1.2877276387135923,
            1.0977279370986268,
            0.8401054764614775,
            0.46391701582748557
          ],
          "observed_K": [
            0.30947797952772355,
            0.5954702823364088,
            0.8867443630897351,
            1.1353479454721418,
            1.305858819163741,
            1.4462825376976314,
            1.546665771290913,
            1.5577853082482045,
            1.583624515711846,
            1.5134046592720976,
            1.4633782372695334,
            1.3143665412292151,
            1.0858917201548397,
            0.8770828569022514,
            0.6134514562745702,
            0.3139672614742362
          ],
          "future_observed_K": [
            0.2849798468023555,
            0.5620462105898556,
            0.7518082916623415,
            1.0259339680289055,
            1.200132997691147,
            1.3447025997927735,
            1.42731106406133,
            1.492538034237521,
            1.4871741336752982,
            1.4214171352204055,
            1.3466690787670719,
            1.1865233152669423,
            0.9987989518889331,
            0.7527265769583639,
            0.5653055069455439,
            0.263549703763987
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.202820901980999,
                0.017864140125322687,
                0.2235533288065266,
                -0.006071836222147314,
                -0.2701132497900072,
                -0.5825694947599918,
                1.583457570055283,
                -11.523925907789627
              ],
              "initial_K": [
                -3.2971434529181716,
                0.026392364898356946,
                4.458753137339829,
                2.4518072650367504,
                -1.7528267637753907,
                0.040492781114225274,
                4.8043695670620945,
                3.746419748495711,
                -1.3727521634492899,
                -1.116479544911606,
                4.332702896319668,
                5.04053562017517,
                -0.7997542626806298,
                -3.2258928048507007,
                1.7938068863960113,
                4.930603379513176
              ],
              "metrics": {
                "initial_rmse_K": 2.925519161479299,
                "observation_residual_rms_K": 0.010649653995616654,
                "future_predictive_rmse_K": 0.04086034315669076
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.1402018528709945,
                0.01747917090528567,
                0.21107996295439074,
                -0.004915275199575137,
                -0.11299651964510124,
                -0.044154083705189924,
                0.00991493971471945,
                -0.0037581659068616105
              ],
              "initial_K": [
                0.32060896416592055,
                0.6562557184118092,
                0.991982335410583,
                1.2836031531856003,
                1.4880378584074767,
                1.5946897733667116,
                1.63171569357645,
                1.643115949411427,
                1.6539031269702715,
                1.650487981775396,
                1.5941769219000916,
                1.4566318607200162,
                1.2422187853799795,
                0.9758942384922334,
                0.6761803875617097,
                0.3482301447374364
              ],
              "metrics": {
                "initial_rmse_K": 0.1259030694029432,
                "observation_residual_rms_K": 0.01946803817739482,
                "future_predictive_rmse_K": 0.030171297740441434
              }
            },
            "learned": {
              "coefficients_K": [
                5.202523736396069,
                0.0179055735528391,
                0.2193502014719368,
                -0.0046566702367120474,
                -0.03528401723022147,
                -0.004367086976039535,
                0.0015461717336748388,
                0.0010145976592521215
              ],
              "initial_K": [
                0.3584993380976423,
                0.7020215678280328,
                1.0137423718403347,
                1.2752500247126641,
                1.4714178630104038,
                1.5983110580612658,
                1.6665056058573315,
                1.6939001102551372,
                1.69253510584949,
                1.6607182654317985,
                1.5861522171795643,
                1.4552806838610493,
                1.260976271618541,
                1.0054151598287462,
                0.6991901108293819,
                0.3582029375146257
              ],
              "metrics": {
                "initial_rmse_K": 0.10420382416742223,
                "observation_residual_rms_K": 0.013873391971459897,
                "future_predictive_rmse_K": 0.04070691012789284
              }
            }
          }
        },
        {
          "split": "test",
          "index": 3,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            5.6585834541058055,
            1.133465957070806,
            0.1259019836794421,
            -0.2656798847535495,
            -0.13024952652174732,
            -0.005406078317735114,
            0.03481519825014512,
            0.01213347660713752
          ],
          "initial_K": [
            0.43673684386642164,
            0.8735621263519217,
            1.3121912055988982,
            1.725504221351472,
            2.038014362866824,
            2.1708752648936187,
            2.11486860159269,
            1.9421184811672547,
            1.7409655519247713,
            1.5527277437091729,
            1.3720364756844161,
            1.1842514944711797,
            0.984198961186709,
            0.7689227434886668,
            0.5326367185585184,
            0.2736690301047573
          ],
          "observed_K": [
            0.35866786791443517,
            0.7230851172081018,
            1.040474151159479,
            1.3361993188183188,
            1.5058298809150141,
            1.6798854681559487,
            1.6780204259633469,
            1.6695970811165597,
            1.5972814721163027,
            1.5111017402071665,
            1.2933114419380793,
            1.131063370351433,
            0.9154656542463647,
            0.7239049923892859,
            0.486308562850487,
            0.22294384759506633
          ],
          "future_observed_K": [
            0.31033599226313335,
            0.6623819953682953,
            0.9261013355952294,
            1.1874305234039844,
            1.3772175336095862,
            1.5029926640400122,
            1.5288723822863517,
            1.5423980781442825,
            1.494805324304927,
            1.3566372765804997,
            1.2440164636747002,
            1.102652892289286,
            0.9052570038282053,
            0.7004836617728576,
            0.4420199371229221,
            0.2134920607527038
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.328700169161622,
                0.8556670112431756,
                0.048419203251366845,
                -0.1455964142587729,
                -0.15735162423456575,
                -0.7300360152719516,
                -0.7833764983040108,
                15.0481625140321
              ],
              "initial_K": [
                5.030766172012057,
                1.378350356347886,
                -3.5553249542486993,
                0.1728890836900081,
                6.566562415819248,
                4.310831249719234,
                -2.529285963251739,
                -1.5670448235126324,
                5.5071840592178285,
                5.808859680075614,
                -1.5070817405294727,
                -3.6287087130235105,
                2.8541612975416335,
                5.835794587420321,
                -0.4148354895725276,
                -4.944608986274659
              ],
              "metrics": {
                "initial_rmse_K": 3.7706419280488976,
                "observation_residual_rms_K": 0.01508066029178322,
                "future_predictive_rmse_K": 0.03992977315719537
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.264566088079151,
                0.8372275308305276,
                0.045717608783292916,
                -0.11786326540608251,
                -0.06582493051648691,
                -0.0553308602940168,
                -0.004905171380336459,
                0.004907484808013289
              ],
              "initial_K": [
                0.38161016138517845,
                0.782113751782646,
                1.1858546444102367,
                1.538577799755337,
                1.7806202222800729,
                1.889156038106969,
                1.888599679790938,
                1.8203235547763759,
                1.7078320200610786,
                1.5543562895279457,
                1.365000419423323,
                1.1570629724591994,
                0.94625969083012,
                0.7325185017433452,
                0.5053679755906942,
                0.2592329589587049
              ],
              "metrics": {
                "initial_rmse_K": 0.13218337451992176,
                "observation_residual_rms_K": 0.022931287556381436,
                "future_predictive_rmse_K": 0.02811008782944694
              }
            },
            "learned": {
              "coefficients_K": [
                5.32839581382583,
                0.857651613739563,
                0.047508851892291315,
                -0.11166218324167042,
                -0.02055433202559302,
                -0.005472532981918992,
                -0.0007649302522583849,
                -0.0013248809984505508
              ],
              "initial_K": [
                0.4168571657379819,
                0.8263467509618472,
                1.2095264061211117,
                1.5360622364811158,
                1.7752966359848255,
                1.9081914410811436,
                1.9331277375446017,
                1.865260897189467,
                1.730845963696568,
                1.5578481049273933,
                1.3668417874996954,
                1.1673720758685933,
                0.9603638663110894,
                0.7424261537965631,
                0.5094175837315766,
                0.2601931179200142
              ],
              "metrics": {
                "initial_rmse_K": 0.11948966438482295,
                "observation_residual_rms_K": 0.017734734067722566,
                "future_predictive_rmse_K": 0.040091957863123334
              }
            }
          }
        },
        {
          "split": "test",
          "index": 4,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            6.497192439893651,
            -1.1318418722730608,
            0.05168256978725702,
            -0.18610872515166946,
            0.08827460384575889,
            0.1058831793403847,
            0.048580982748094505,
            -0.0148131148411177
          ],
          "initial_K": [
            0.30321572873227864,
            0.5617413082720306,
            0.7902803061899073,
            1.0532463002224979,
            1.388903920832873,
            1.7498622146955727,
            2.036075868432583,
            2.190034646177437,
            2.2415015981346706,
            2.2500976270261432,
            2.22578715102297,
            2.126522155893968,
            1.9160221134049606,
            1.5907736973059834,
            1.1558515488792591,
            0.6148055197359373
          ],
          "observed_K": [
            0.26472941064647826,
            0.5690809948885751,
            0.8434902468642133,
            1.0842593354973546,
            1.342676585460293,
            1.5694490855600074,
            1.7460284244580446,
            1.8585368955383572,
            1.9018852536574962,
            1.9161775648843196,
            1.8654279749221785,
            1.709770312096791,
            1.4989450302487508,
            1.2387154116160723,
            0.8254929888670527,
            0.4242878069596224
          ],
          "future_observed_K": [
            0.2573637608589175,
            0.5136463735163612,
            0.7657371981195362,
            1.0234664388795542,
            1.2380157075167029,
            1.4860074330271824,
            1.6406986312471652,
            1.7025795837085076,
            1.7685079350799682,
            1.7548272930721989,
            1.7030794655303239,
            1.5308966913103033,
            1.3292417609298466,
            1.0575349021418143,
            0.774119423768526,
            0.38923280226955
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.149704611549088,
                -0.8571572544373038,
                0.11113518422625411,
                -0.18053258966175004,
                -0.12491462412727533,
                0.8644356411068287,
                -0.6537556708063879,
                0.8564686617898435
              ],
              "initial_K": [
                0.5677936189351166,
                0.6677106145895922,
                0.6343370465828446,
                0.9793228006112206,
                1.5115495881557552,
                1.7734716016881427,
                1.875713597651513,
                2.1307837823493347,
                2.2777366811006923,
                1.9527902999969242,
                1.6000814283087308,
                1.8854747346019247,
                2.3701777542982527,
                1.933594535653263,
                0.6059816474952066,
                -0.25221742469271446
              ],
              "metrics": {
                "initial_rmse_K": 0.3599501120090127,
                "observation_residual_rms_K": 0.012142230931879012,
                "future_predictive_rmse_K": 0.051070856078063706
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.075689252893174,
                -0.838685659534057,
                0.10493429328314365,
                -0.14614481158809253,
                -0.05225555499454912,
                0.06551727132726905,
                -0.004093540734391137,
                0.00027931031063452554
              ],
              "initial_K": [
                0.2687414038966413,
                0.5412854491004764,
                0.8256325036166892,
                1.1260593823631642,
                1.4282639077598789,
                1.696352685675373,
                1.8920775244560604,
                2.002527287020951,
                2.048497319217217,
                2.060607636066647,
                2.042714775498881,
                1.9589647130724772,
                1.7606584117260204,
                1.4290976828356126,
                0.9928103708181891,
                0.5036934728406947
              ],
              "metrics": {
                "initial_rmse_K": 0.1351894228841767,
                "observation_residual_rms_K": 0.02187742629459882,
                "future_predictive_rmse_K": 0.036685351223913094
              }
            },
            "learned": {
              "coefficients_K": [
                6.149353363523744,
                -0.8591453133487739,
                0.10904568131815691,
                -0.1384557663080564,
                -0.016317191968331483,
                0.006480026269582269,
                -0.0006383616195634339,
                -7.540582145598394e-05
              ],
              "initial_K": [
                0.26609718509886626,
                0.5458716691528038,
                0.8436529581030509,
                1.1496741357445033,
                1.4422751674747825,
                1.696070995680242,
                1.8920014181966953,
                2.0235981711986484,
                2.0952087434773365,
                2.112774048872495,
                2.073464810476505,
                1.9621858130982228,
                1.7582382006940265,
                1.447796928769645,
                1.0339636920668993,
                0.5390615592019758
              ],
              "metrics": {
                "initial_rmse_K": 0.11842110819793662,
                "observation_residual_rms_K": 0.014041351487379831,
                "future_predictive_rmse_K": 0.05112877783942447
              }
            }
          }
        },
        {
          "split": "test",
          "index": 5,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            5.522111901523194,
            -0.9107309638742822,
            0.0861641534473814,
            0.14234900537895906,
            -0.05158663102566782,
            -0.021699515731567264,
            0.04003948010891521,
            0.02107881625588748
          ],
          "initial_K": [
            0.283267362181444,
            0.5344415686118913,
            0.7646303525156298,
            0.9991045959623999,
            1.227647472964337,
            1.4205383823248134,
            1.5822299776933995,
            1.7469385084480342,
            1.9145905840938824,
            2.0248965575937863,
            2.010792694242107,
            1.8569880366735307,
            1.5941585746014602,
            1.2571350769444802,
            0.8673251780698562,
            0.4420954797125666
          ],
          "observed_K": [
            0.22155583968151654,
            0.4799851986932454,
            0.6803906099749562,
            0.9304229247730851,
            1.1222810305522222,
            1.3385892022624801,
            1.4388090970804963,
            1.6080543419046527,
            1.6320103951180895,
            1.661303183021017,
            1.5889319113467193,
            1.4831818569998603,
            1.2700914996167734,
            1.0139818692946168,
            0.7214398716950781,
            0.3670587168239188
          ],
          "future_observed_K": [
            0.23961437370855818,
            0.45939576354719647,
            0.6812108508716717,
            0.8758138107040753,
            1.0737967015640886,
            1.2560492308651767,
            1.3347891075262286,
            1.4697602387768642,
            1.5289893172002167,
            1.5137813349215004,
            1.4388732769058474,
            1.3061286900351894,
            1.114142764157184,
            0.8914644962650456,
            0.6150664288642682,
            0.33185876085993715
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.233606977587082,
                -0.7739788214106685,
                0.022422337460705676,
                -0.04737922657121505,
                -0.07131797514487757,
                -0.19628321387813322,
                0.6632699954229309,
                -1.3009728858213152
              ],
              "initial_K": [
                -0.07824710577926519,
                0.4208389913905922,
                0.9815171896010891,
                0.9833500860595144,
                0.9005935883504446,
                1.393063265026187,
                1.9629472012273925,
                1.79888293254275,
                1.354340020124355,
                1.6352355830515766,
                2.303966011106705,
                2.1023450587130394,
                1.0660996851292728,
                0.5996041363851221,
                1.0823390821855008,
                1.144634716843616
              ],
              "metrics": {
                "initial_rmse_K": 0.37989322780314466,
                "observation_residual_rms_K": 0.014710792776826893,
                "future_predictive_rmse_K": 0.045573769403993006
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.170617399716508,
                -0.7572997077722085,
                0.02117126229264373,
                -0.03835444976119361,
                -0.02983446012282634,
                -0.014876689448130677,
                0.00415311539984681,
                -0.0004242713797682537
              ],
              "initial_K": [
                0.21549925182949764,
                0.44588081845581284,
                0.6942647273485982,
                0.9486103934659237,
                1.1887607361177994,
                1.3980036704127854,
                1.5696166362648998,
                1.703094981413083,
                1.794225192209811,
                1.82947683521525,
                1.7911095373273724,
                1.66796667466655,
                1.460811337630774,
                1.178146442525789,
                0.8302641402406952,
                0.4303162953642233
              ],
              "metrics": {
                "initial_rmse_K": 0.10788804138927148,
                "observation_residual_rms_K": 0.02079928096459514,
                "future_predictive_rmse_K": 0.03333374257781435
              }
            },
            "learned": {
              "coefficients_K": [
                5.233308053617166,
                -0.7757739593334113,
                0.022000764943805012,
                -0.036336525910869805,
                -0.009316035647243025,
                -0.0014713881771230113,
                0.0006476519094109805,
                0.00011454117765652685
              ],
              "initial_K": [
                0.22653714450632467,
                0.4601627869165341,
                0.7030775151193931,
                0.9500235165309533,
                1.1894030916998235,
                1.4072971129206977,
                1.591441169143624,
                1.7323734062612566,
                1.8217403419526699,
                1.8503503581192664,
                1.8083313321823564,
                1.6873916079453393,
                1.4835677032747023,
                1.1992444252625103,
                0.8442991775987265,
                0.4363997689977823
              ],
              "metrics": {
                "initial_rmse_K": 0.09415868006091581,
                "observation_residual_rms_K": 0.014919003247556888,
                "future_predictive_rmse_K": 0.04558848730414967
              }
            }
          }
        },
        {
          "split": "test",
          "index": 6,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            5.822054874763854,
            2.859774744073671,
            0.01098550497731065,
            0.20400532732130353,
            0.19347015101728815,
            -0.04255049655318044,
            -0.0029728544021611013,
            0.015425310860645847
          ],
          "initial_K": [
            0.8145816491780948,
            1.5078681757408505,
            2.011162252461714,
            2.316015379202442,
            2.4498783424008685,
            2.454162718378249,
            2.364985242977714,
            2.1887361951255975,
            1.9013079337848486,
            1.4950204763071726,
            1.0281990941025625,
            0.6075143363283373,
            0.312627063818542,
            0.14817496616012849,
            0.06821903065889945,
            0.027213012889801047
          ],
          "observed_K": [
            0.47982989314717617,
            0.9679360688907843,
            1.4192624668654508,
            1.6578050237784079,
            1.8553167816992713,
            1.966190441300075,
            1.9288600526166726,
            1.8100190509088099,
            1.5940432335461898,
            1.3687936066490523,
            1.110495687447582,
            0.852285104336121,
            0.6875091003099835,
            0.4330159935077594,
            0.2749003292886453,
            0.08911818790139625
          ],
          "future_observed_K": [
            0.4631934695320182,
            0.8511312523185169,
            1.1956186132483189,
            1.4362337942270558,
            1.6472450749317704,
            1.752594419166818,
            1.720550818030092,
            1.6466746153855327,
            1.511520490801696,
            1.3211712541177765,
            1.0810301511280083,
            0.9104334840288879,
            0.707174438934486,
            0.5026331109966252,
            0.31127477458378056,
            0.17261684971439142
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.521460502613541,
                2.2596684479138376,
                0.03757231232298729,
                -0.019623596330300176,
                -0.12851224509676917,
                1.1148101774072654,
                -4.75230627148721,
                -5.09334167846455
              ],
              "initial_K": [
                -2.370011393322245,
                0.2947612236230204,
                4.390515921336092,
                3.8023321183433283,
                0.18790949870997276,
                -0.057007821119914204,
                3.404858261675241,
                4.657794428162845,
                1.6116119442598853,
                -0.9729912449941456,
                0.2561171511257989,
                2.3327927128107637,
                1.7346782963503655,
                -0.2064508870709254,
                -0.70440843471717,
                -0.1263906409385227
              ],
              "metrics": {
                "initial_rmse_K": 1.7783423768353535,
                "observation_residual_rms_K": 0.0188170780781124,
                "future_predictive_rmse_K": 0.04594182363519472
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.455006436081968,
                2.210972972294357,
                0.03547593022025901,
                -0.015885701267266156,
                -0.053760548358891956,
                0.08449364810788315,
                -0.029756926285074876,
                -0.0016610331584190365
              ],
              "initial_K": [
                0.6213334578917254,
                1.192184825681597,
                1.6670412717815242,
                2.0155259071579903,
                2.2262544274856126,
                2.295513051995304,
                2.2177660255351754,
                1.9999615349069995,
                1.6860484670327553,
                1.3509392367265696,
                1.0543283992276893,
                0.8017711636314494,
                0.5626212860426999,
                0.32758468074975067,
                0.13518615752602947,
                0.03002341941693981
              ],
              "metrics": {
                "initial_rmse_K": 0.20659330577404522,
                "observation_residual_rms_K": 0.028249969831042644,
                "future_predictive_rmse_K": 0.03286887159826776
              }
            },
            "learned": {
              "coefficients_K": [
                5.521145137531629,
                2.264909439542371,
                0.03686589827050334,
                -0.015049914659299505,
                -0.01678713752033277,
                0.008356896559641036,
                -0.004640403232580873,
                0.0004484316010091917
              ],
              "initial_K": [
                0.6283788321760342,
                1.2095811555746057,
                1.6991276604700212,
                2.0601317987497008,
                2.269369241535902,
                2.3212018794138416,
                2.227608272914688,
                2.0156297785366983,
                1.7235951920379093,
                1.3949780476075742,
                1.0691475968190622,
                0.7731180691187897,
                0.5205667387116528,
                0.31788710493855643,
                0.16849881966966318,
                0.06862946831514788
              ],
              "metrics": {
                "initial_rmse_K": 0.18372757890091468,
                "observation_residual_rms_K": 0.022745196155147286,
                "future_predictive_rmse_K": 0.046427936554574604
              }
            }
          }
        },
        {
          "split": "test",
          "index": 7,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            6.719353124787714,
            -0.11954545828251328,
            -0.014730721284114578,
            -0.03840727740350079,
            -0.09190249194734669,
            0.021902025373027635,
            -0.030855775710861892,
            -0.05555103725941407
          ],
          "initial_K": [
            0.34956135749198214,
            0.7538996496880537,
            1.1737183638902817,
            1.5311234348259508,
            1.8122026740506352,
            2.0473586914027346,
            2.2234188656702405,
            2.2939911250825205,
            2.265959811023671,
            2.197634059837623,
            2.102094289196215,
            1.921444261010157,
            1.6183074142594482,
            1.2342617886866465,
            0.830394862101637,
            0.42143147071060677
          ],
          "observed_K": [
            0.34898309481007883,
            0.7049148728925242,
            1.005113121293367,
            1.2736598477386223,
            1.5679202287320984,
            1.7467314776267158,
            1.865113272006022,
            1.9428684026370815,
            1.9654196548977034,
            1.8944978416169518,
            1.8174136627739474,
            1.592769026294118,
            1.3648212432685092,
            1.0415115124590988,
            0.700817631395326,
            0.3763698418256462
          ],
          "future_observed_K": [
            0.3227834130555752,
            0.6465660540175068,
            0.9623082416728977,
            1.2298298662338754,
            1.4455708338183106,
            1.6374242543277808,
            1.7336115394635154,
            1.767661296360648,
            1.799131570069793,
            1.731549265599356,
            1.649853932202934,
            1.4549866612183402,
            1.2495524505451685,
            0.9541022076694685,
            0.6716515302783642,
            0.3459545334589067
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.328481121978588,
                -0.11728377166985349,
                -0.017848109102405516,
                0.0920873055692971,
                -0.3143180138655906,
                0.27787488644163744,
                2.8508078409044595,
                3.914303294607326
              ],
              "initial_K": [
                2.679023448775693,
                1.5168203014128818,
                -0.8807533079340278,
                0.027994245343042956,
                3.099341121809986,
                3.6692238156017294,
                1.399369234200282,
                0.4173276005082056,
                2.1635834119824784,
                3.4512929130854886,
                2.311758502895595,
                0.9347180424714943,
                1.249845585831551,
                1.7585670641100566,
                0.8626003950282617,
                -0.1788426913597374
              ],
              "metrics": {
                "initial_rmse_K": 1.2336060953982089,
                "observation_residual_rms_K": 0.012872038273365354,
                "future_predictive_rmse_K": 0.04625298340007932
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.252314081514438,
                -0.11475632608411601,
                -0.016852257258947567,
                0.0745465511091122,
                -0.13148870577872093,
                0.021060682211946128,
                0.017850549591821644,
                0.0012765268805629568
              ],
              "initial_K": [
                0.3708203265101253,
                0.7341503848441805,
                1.0861965496683708,
                1.4168054984642824,
                1.6995198925209365,
                1.9040795423236851,
                2.0237128280540424,
                2.082717962973587,
                2.1086408041884837,
                2.097244977394072,
                2.0104075050142263,
                1.811107209355244,
                1.500007517006384,
                1.1193533349773774,
                0.7245745486003284,
                0.35100143459613337
              ],
              "metrics": {
                "initial_rmse_K": 0.12198384277583978,
                "observation_residual_rms_K": 0.022747956995134325,
                "future_predictive_rmse_K": 0.032054869466410646
              }
            },
            "learned": {
              "coefficients_K": [
                6.328119662910564,
                -0.117555795322727,
                -0.01751253872356322,
                0.07062446998478171,
                -0.04105834210511496,
                0.0020830198087314566,
                0.002783679578854255,
                -0.0003446258672686323
              ],
              "initial_K": [
                0.38762684963657473,
                0.7631699706837627,
                1.1141430204877631,
                1.4276975291677834,
                1.6920249191202004,
                1.8992377753586656,
                2.0473674593209363,
                2.1379730843300244,
                2.16938104733501,
                2.131577677764559,
                2.0097987455754,
                1.7962679253860334,
                1.5003828273998396,
                1.1477041773725112,
                0.7681603516875875,
                0.38307539140143543
              ],
              "metrics": {
                "initial_rmse_K": 0.10371852602826279,
                "observation_residual_rms_K": 0.015474275067963388,
                "future_predictive_rmse_K": 0.046385787663300045
              }
            }
          }
        },
        {
          "split": "test",
          "index": 8,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            5.741946397165456,
            -0.7547739471050924,
            -0.10218431985307472,
            -0.1775817626729975,
            0.05262716988903501,
            0.026150007209080988,
            -0.07053828811899616,
            0.002862834288456887
          ],
          "initial_K": [
            0.20902450387344565,
            0.4569837803302624,
            0.7417696146874112,
            1.033055127711684,
            1.3144900875986631,
            1.5889335395774755,
            1.8388635753487748,
            2.008740479929308,
            2.051753622396379,
            1.9860908173922844,
            1.8774396818036143,
            1.7586924334003362,
            1.5889648418847242,
            1.307658581090374,
            0.9124277363699712,
            0.4601208711818634
          ],
          "observed_K": [
            0.25497896918523516,
            0.4775511579044396,
            0.7638272018495087,
            0.9791551278255789,
            1.177491072844406,
            1.405862365918894,
            1.57145236963524,
            1.6407353698739795,
            1.732415519540282,
            1.7334883805730914,
            1.5968688654345575,
            1.4792493383196355,
            1.2556812423518984,
            0.956828050344686,
            0.7101353815028743,
            0.3649128875704092
          ],
          "future_observed_K": [
            0.22911536627482665,
            0.46421045471400313,
            0.7245185652365512,
            0.9823926976859043,
            1.1171434208138555,
            1.3192383650478543,
            1.4505174447646425,
            1.5090587119673544,
            1.5856836661476499,
            1.529384393405253,
            1.470387054093556,
            1.3306148587122748,
            1.1110286269129936,
            0.9202700683929042,
            0.60423070997217,
            0.3139973277842595
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.41362628405645,
                -0.6054042645923088,
                -0.14731035979753862,
                0.017060563214931584,
                0.1641368636283489,
                -0.6934426727887891,
                1.8091836175551834,
                -8.788546568793548
              ],
              "initial_K": [
                -2.3291904289593406,
                0.12859074308231055,
                3.2913415584629395,
                1.7375316924792883,
                -1.2194706026994349,
                0.40728482612115924,
                4.10871859344654,
                3.3180649228538135,
                -0.41261190755275945,
                0.0003322869124491312,
                4.095606309161053,
                4.262508795827751,
                -0.486512245893165,
                -2.2323865101706364,
                1.884146864506847,
                4.241952255622232
              ],
              "metrics": {
                "initial_rmse_K": 2.2572454059844764,
                "observation_residual_rms_K": 0.017939026519779692,
                "future_predictive_rmse_K": 0.04563437149944199
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.348470066586911,
                -0.5923579043470254,
                -0.1390910412958907,
                0.013810873711524584,
                0.06866340081386178,
                -0.0525573791529902,
                0.011328340487387624,
                -0.0028661079869820743
              ],
              "initial_K": [
                0.24718636926392196,
                0.49796382205630485,
                0.7502924332070955,
                0.9982074200937624,
                1.2373497338990176,
                1.4652302565993218,
                1.6739855511529764,
                1.8426799108221956,
                1.9384252060427989,
                1.9307156506567045,
                1.8126796615343512,
                1.6106496530559453,
                1.3656993051928699,
                1.097969214682778,
                0.7914221309836775,
                0.42182773394352124
              ],
              "metrics": {
                "initial_rmse_K": 0.12051525319690239,
                "observation_residual_rms_K": 0.02447042083908818,
                "future_predictive_rmse_K": 0.033742537787624205
              }
            },
            "learned": {
              "coefficients_K": [
                5.413317078060011,
                -0.6068084169074576,
                -0.144540711037492,
                0.013084248987931415,
                0.021440665827683607,
                -0.005198220113144752,
                0.0017665825869863708,
                0.0007737674511512469
              ],
              "initial_K": [
                0.24803504839303073,
                0.49662507718746335,
                0.7476772340174209,
                1.0021068196273468,
                1.2554877590523787,
                1.4959402329761609,
                1.705269417628554,
                1.861632848872694,
                1.943598967675992,
                1.9364148895917745,
                1.837770399410266,
                1.657711759167432,
                1.4117108782052816,
                1.112996812805437,
                0.7708731588902342,
                0.3950247509532312
              ],
              "metrics": {
                "initial_rmse_K": 0.10465009773618889,
                "observation_residual_rms_K": 0.01959692820251227,
                "future_predictive_rmse_K": 0.045584260156269304
              }
            }
          }
        },
        {
          "split": "test",
          "index": 9,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            5.532372949943475,
            1.3849097516507591,
            -0.09422401342588824,
            -0.03524605733377563,
            -0.025646583943571666,
            -0.0831566784603012,
            -0.01762022259597104,
            0.07964854294653081
          ],
          "initial_K": [
            0.4839574394355701,
            0.9351547677474741,
            1.3622024364767942,
            1.7509843342159965,
            2.0172033574167254,
            2.099278519113066,
            2.0538080357090918,
            1.975758667266523,
            1.8592949267868726,
            1.6324365906416383,
            1.309718035529355,
            1.003360580909578,
            0.7743099223400631,
            0.5731268825445451,
            0.35467535559633,
            0.15371155854292184
          ],
          "observed_K": [
            0.40402674744853506,
            0.7452796590835689,
            1.0524830980830255,
            1.319491100223883,
            1.57614365270366,
            1.6595182417755634,
            1.6834671162539088,
            1.6663017109594014,
            1.5788280986768115,
            1.4102939030409096,
            1.2428754602586927,
            1.0061158192076147,
            0.8120108325116365,
            0.6059264252242106,
            0.41123743768772414,
            0.1595455825434572
          ],
          "future_observed_K": [
            0.33777980156082815,
            0.6614880749013519,
            0.9687548231742484,
            1.2174344796569774,
            1.3538812122792394,
            1.515545006095594,
            1.5432363424991538,
            1.5550733375752384,
            1.484106647551202,
            1.3561222324035718,
            1.1826401331412895,
            1.0267847675333086,
            0.8220172994316852,
            0.6097018877846342,
            0.44962104682172593,
            0.18620260823056023
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.185026219756538,
                1.1499246047194895,
                -0.1014990688909102,
                -0.04994744696621106,
                -0.05691538167515161,
                -0.0023931499653089086,
                0.778125955521095,
                27.471434188673406
              ],
              "initial_K": [
                10.062223527567447,
                2.712419891918142,
                -8.008661695570424,
                -2.07175078719415,
                10.298860485273185,
                7.168616226759414,
                -5.470423543081508,
                -4.6958639631086685,
                7.84363525265234,
                9.124100745718984,
                -3.4140005877511754,
                -7.348585818714415,
                3.9551783417144213,
                9.438080589440299,
                -1.246397077817971,
                -8.963044000903004
              ],
              "metrics": {
                "initial_rmse_K": 6.8516730172009,
                "observation_residual_rms_K": 0.012793754066373366,
                "future_predictive_rmse_K": 0.03226250697581869
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.122621340248198,
                1.1251439225777995,
                -0.09583583396309059,
                -0.04043347652553914,
                -0.02380942085797165,
                -0.00018138152587418772,
                0.004872294708332961,
                0.00895894404446648
              ],
              "initial_K": [
                0.4337135677455406,
                0.8450164000375935,
                1.2196085973292827,
                1.5409608584426748,
                1.779998561039188,
                1.908953880291086,
                1.9242807931739865,
                1.8463417050251603,
                1.69870212444512,
                1.4981572206453762,
                1.2631416982288857,
                1.0174337563047853,
                0.7796081608454453,
                0.5567066696621084,
                0.3516183863273806,
                0.16757014829632016
              ],
              "metrics": {
                "initial_rmse_K": 0.12444762519889793,
                "observation_residual_rms_K": 0.023197049756125136,
                "future_predictive_rmse_K": 0.024658006829311636
              }
            },
            "learned": {
              "coefficients_K": [
                5.184730070537009,
                1.1525916974216703,
                -0.0995907389493775,
                -0.03830616985993952,
                -0.007434671602566361,
                -1.7939652074497418e-05,
                0.0007598033445401621,
                -0.002418659495657317
              ],
              "initial_K": [
                0.4401321610735596,
                0.8626153079350759,
                1.245273038703432,
                1.563455127271029,
                1.7958217101918534,
                1.927848934687146,
                1.953633823728743,
                1.879070971532815,
                1.7231815361747196,
                1.5125642366739256,
                1.2724827690558536,
                1.0229771650631165,
                0.7803739424592104,
                0.5568650825289185,
                0.35642385748014427,
                0.1738750890815013
              ],
              "metrics": {
                "initial_rmse_K": 0.1087376402937149,
                "observation_residual_rms_K": 0.017935015361711656,
                "future_predictive_rmse_K": 0.03236033096037065
              }
            }
          }
        },
        {
          "split": "test",
          "index": 10,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            6.857473922033986,
            0.046136057016025515,
            -0.07095537977773908,
            0.12194996194946563,
            0.006794916496936428,
            0.027784206927363494,
            -0.02724361969343163,
            -0.030469329332704697
          ],
          "initial_K": [
            0.444276913309555,
            0.883206469405026,
            1.2769678216603402,
            1.5903639493515624,
            1.8416072662703498,
            2.0694430306306715,
            2.26446962898741,
            2.374867444941711,
            2.375157191549243,
            2.28703670998618,
            2.1287681326633145,
            1.8867571251653548,
            1.55425957052406,
            1.16527537367356,
            0.7672151460065686,
            0.3802355866274073
          ],
          "observed_K": [
            0.3742123514788799,
            0.7667270540004154,
            1.0840308095494953,
            1.3334817766993368,
            1.5579056150055024,
            1.8073211574683785,
            1.948610031360842,
            2.0127647652690093,
            2.0160635912185456,
            1.9675741019134187,
            1.8141108539458728,
            1.6137553348819536,
            1.318288848277475,
            1.0281135177585596,
            0.6690090699937368,
            0.38247219169424657
          ],
          "future_observed_K": [
            0.37172588861078504,
            0.6966647014740448,
            0.9827178439013844,
            1.2568705059096474,
            1.4864696663824226,
            1.679269123019385,
            1.768930504890881,
            1.8623080150638662,
            1.8311443556640397,
            1.7919024831891377,
            1.6915053009389918,
            1.469876395482406,
            1.2732761107500343,
            0.970684976035595,
            0.6577375011748298,
            0.3197374350429997
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.4763906863674405,
                0.02967956986907046,
                -0.1085538554191371,
                0.32152981420010174,
                0.3234594689420768,
                0.72166702707557,
                3.253515998483774,
                -16.284728802223565
              ],
              "initial_K": [
                -3.7117739540073247,
                0.7511571790028491,
                5.844628987187978,
                2.219541347023187,
                -3.3612292112225735,
                0.0828057392080801,
                7.19570923541438,
                5.311833868694838,
                -2.3988544919776755,
                -2.0253479671461303,
                5.9807652993420835,
                7.068897947472563,
                -1.4006144827596407,
                -5.003423586931095,
                2.17545644336706,
                6.812693908615943
              ],
              "metrics": {
                "initial_rmse_K": 4.151301192867626,
                "observation_residual_rms_K": 0.013901081314101608,
                "future_predictive_rmse_K": 0.042965484950925795
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.398443466179484,
                0.029039980122047938,
                -0.10249699211707193,
                0.2602849391584624,
                0.13531285216523853,
                0.054696558277391276,
                0.020372137274708053,
                -0.005310752002113719
              ],
              "initial_K": [
                0.50724038905873,
                0.9198897424913102,
                1.2108512296176344,
                1.428717992318321,
                1.6420495197760243,
                1.8746166111668823,
                2.09106615387774,
                2.235753319215117,
                2.2743870282983667,
                2.2001451805335646,
                2.018820441487622,
                1.7454246063281285,
                1.410845613482732,
                1.0539197748480071,
                0.6994031591342705,
                0.3497926594767754
              ],
              "metrics": {
                "initial_rmse_K": 0.125318101057896,
                "observation_residual_rms_K": 0.025479981480422517,
                "future_predictive_rmse_K": 0.02849782468021935
              }
            },
            "learned": {
              "coefficients_K": [
                6.476020779260737,
                0.029748407568408998,
                -0.10651288524247665,
                0.24659069533856112,
                0.04225246071528603,
                0.005409796948392033,
                0.003176905126506707,
                0.0014337516447518327
              ],
              "initial_K": [
                0.46435349166595,
                0.8768841865977547,
                1.213280606765294,
                1.4824310883793166,
                1.7096519651684032,
                1.914142811158813,
                2.09524477965776,
                2.230990474800501,
                2.2870572033255416,
                2.2330170421247315,
                2.058701366384928,
                1.7806946412275568,
                1.434952586441034,
                1.0616482539650718,
                0.691555463126484,
                0.33871793027736946
              ],
              "metrics": {
                "initial_rmse_K": 0.10194231529728305,
                "observation_residual_rms_K": 0.019124141307050462,
                "future_predictive_rmse_K": 0.0428886680825062
              }
            }
          }
        },
        {
          "split": "test",
          "index": 11,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            6.064394954021725,
            -2.411669180940734,
            -0.2575990270640851,
            0.06749840108382132,
            -0.006010335171964219,
            0.02343749436883363,
            -0.008668201445281585,
            -0.00471828157506624
          ],
          "initial_K": [
            0.05355825429045091,
            0.1406599895020456,
            0.28637507542741825,
            0.5080112293201009,
            0.814850180579118,
            1.196333949462685,
            1.611846148847614,
            2.0016692178773012,
            2.311745072083807,
            2.505627852630594,
            2.556998580112885,
            2.4441909835927373,
            2.1611320324986574,
            1.730215694816407,
            1.1968745093761335,
            0.6088293651942323
          ],
          "observed_K": [
            0.17478054946686378,
            0.3091047922530774,
            0.49422112907225535,
            0.7144946629485149,
            0.9881420751211518,
            1.245134515387299,
            1.4819409908774455,
            1.7384395171605298,
            1.8691632390388675,
            1.9475904893066591,
            1.9287207931711816,
            1.832362399952661,
            1.6068075302611604,
            1.3093262300317225,
            0.9440141368896717,
            0.4715882681784504
          ],
          "future_observed_K": [
            0.19743101446541714,
            0.367118465146288,
            0.5616745356541639,
            0.7599660010549625,
            1.0224443759448956,
            1.2489516953339184,
            1.4245686900452654,
            1.5654025365648672,
            1.7031768510232315,
            1.7376622886991204,
            1.7198242668177033,
            1.5946148304410201,
            1.4098095221750564,
            1.1261333409586671,
            0.7857412206567551,
            0.41279228904837656
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.704201784424312,
                -1.9240168520140342,
                -0.19539768492882587,
                -0.13413255215933806,
                0.2567749854876599,
                0.29934025140862464,
                1.163765768466248,
                7.2564192604611994
              ],
              "initial_K": [
                3.0792758968098832,
                0.9905000590348261,
                -2.3141052064652667,
                -0.8024967847720365,
                3.071089011494521,
                2.966812205618983,
                -0.10283363563079595,
                0.045563390179133245,
                3.500312255392029,
                4.277568185994376,
                1.2368989856516612,
                -0.025529825424339014,
                2.5243632741683544,
                3.766386112458929,
                0.8927595306590745,
                -1.5223902540140697
              ],
              "metrics": {
                "initial_rmse_K": 1.8482418374611578,
                "observation_residual_rms_K": 0.010898745528106674,
                "future_predictive_rmse_K": 0.05597383449323814
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.6355483176989365,
                -1.8825546119251326,
                -0.1844952894074112,
                -0.10858303533940693,
                0.10741672137365972,
                0.022687584289792263,
                0.00728700765628608,
                0.002366452864134213
              ],
              "initial_K": [
                0.10310173371464554,
                0.21263936818887602,
                0.35624712760482635,
                0.5725277365778677,
                0.8774909906317792,
                1.243397347694709,
                1.6100092637893628,
                1.9149381544776716,
                2.1182288595704284,
                2.208975217640445,
                2.1958535580684058,
                2.089432982336658,
                1.8876834384414583,
                1.5761439095704517,
                1.14411593465002,
                0.6042505307807885
              ],
              "metrics": {
                "initial_rmse_K": 0.17912836092859813,
                "observation_residual_rms_K": 0.02103132471493987,
                "future_predictive_rmse_K": 0.04296020591072221
              }
            },
            "learned": {
              "coefficients_K": [
                5.703875981846871,
                -1.9284793457147682,
                -0.19172392460047621,
                -0.10287020936703084,
                0.03354168305064625,
                0.0022439295656384584,
                0.0011363624576047643,
                -0.0006388748118589818
              ],
              "initial_K": [
                0.07217925245348417,
                0.17895764064287523,
                0.3481266395744579,
                0.5933577095711704,
                0.9077600214761564,
                1.2622714140677198,
                1.6125970114585324,
                1.9130609638143843,
                2.12955011747614,
                2.2439750395843037,
                2.2497892563694197,
                2.144463980341569,
                1.924929404881029,
                1.5885374576204576,
                1.1393265416354055,
                0.5966752756499661
              ],
              "metrics": {
                "initial_rmse_K": 0.1579037758974331,
                "observation_residual_rms_K": 0.012848217992268393,
                "future_predictive_rmse_K": 0.05634207229638864
              }
            }
          }
        },
        {
          "split": "test",
          "index": 12,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            5.219832099640153,
            2.6671383183638744,
            -0.18560462213307943,
            -0.05593799433153152,
            -0.014870897683554967,
            -0.1263067944977912,
            0.05443173497232211,
            0.048045278628120774
          ],
          "initial_K": [
            0.6045295703027185,
            1.1603591519624197,
            1.6604200402432898,
            2.08445452884174,
            2.3482091776596183,
            2.377935949832441,
            2.2132139243525604,
            1.9656371449834946,
            1.6833966684907709,
            1.3282592178162518,
            0.8948914898501101,
            0.48033556531978916,
            0.1982367009796796,
            0.06899379915315695,
            0.02903553827756067,
            0.014182441698113724
          ],
          "observed_K": [
            0.46787582828371,
            0.8646400537901345,
            1.2585923761674513,
            1.4733763456108266,
            1.679672686046439,
            1.763516186884564,
            1.7926907703854744,
            1.6120101600691052,
            1.4208819269015358,
            1.2259202774292406,
            0.9908632957252282,
            0.7374400916352972,
            0.5343185383225842,
            0.3583727978479453,
            0.2117528763270873,
            0.09602322796406888
          ],
          "future_observed_K": [
            0.376039266050527,
            0.7209284566963694,
            1.047096909895536,
            1.277724664408773,
            1.4633088437763675,
            1.5681705769256866,
            1.5343463479263901,
            1.4766404114873122,
            1.3864870733620844,
            1.1519399797090262,
            0.96725596449234,
            0.8275437319933012,
            0.5710254678237797,
            0.41578569711184715,
            0.2761104225080879,
            0.14443503904718527
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                4.92683309544891,
                2.12337215893087,
                -0.09259111143406197,
                -0.03995584340446072,
                0.07963800090719061,
                1.1326395086589431,
                3.4302003296659476,
                -8.678673827234451
              ],
              "initial_K": [
                -0.915203915853599,
                1.4677342030201141,
                3.5079806623445338,
                1.4698980807577398,
                -0.6926098645277938,
                1.8393536393469967,
                5.234827910082705,
                3.147495560204316,
                -1.5499501163332758,
                -1.0812025843019923,
                3.5040275222448645,
                3.744769701430303,
                -1.3788095095748367,
                -3.3575388012828227,
                0.9876171337801674,
                3.809666074108543
              ],
              "metrics": {
                "initial_rmse_K": 2.365583367250743,
                "observation_residual_rms_K": 0.01612694506229071,
                "future_predictive_rmse_K": 0.05527171386663677
              }
            },
            "tikhonov": {
              "coefficients_K": [
                4.867535724008882,
                2.0776138454527304,
                -0.0874249042756239,
                -0.03234506975792548,
                0.033314977850963844,
                0.0858449680646867,
                0.021478459619768183,
                -0.0028302764487784403
              ],
              "initial_K": [
                0.5825414329319419,
                1.0834955821809442,
                1.4727887559506927,
                1.7677966011705228,
                1.9820202808928813,
                2.0891439897863706,
                2.0459483583858753,
                1.846725775610169,
                1.544515615573005,
                1.215611034980189,
                0.9101922031356213,
                0.6409268519924286,
                0.4086619158036868,
                0.22363423093223,
                0.09877951330317986,
                0.031854663236047964
              ],
              "metrics": {
                "initial_rmse_K": 0.18249181710299275,
                "observation_residual_rms_K": 0.02487088913267502,
                "future_predictive_rmse_K": 0.04375460449657825
              }
            },
            "learned": {
              "coefficients_K": [
                4.92655169325071,
                2.1282970299753328,
                -0.0908502640331925,
                -0.030643314469783044,
                0.010402853611861804,
                0.008490549696307201,
                0.003349429053780352,
                0.0007640939573008465
              ],
              "initial_K": [
                0.5575401101797128,
                1.0702701049449668,
                1.50334233584657,
                1.8326910242564045,
                2.039823869738474,
                2.1109586976780994,
                2.0437452092047397,
                1.854124534258713,
                1.5755435176434036,
                1.2509557160430675,
                0.9232551216476982,
                0.6279472048862128,
                0.3885735060448552,
                0.214753813226775,
                0.10286178174655658,
                0.03855345118715675
              ],
              "metrics": {
                "initial_rmse_K": 0.16000694105267882,
                "observation_residual_rms_K": 0.019737408137356145,
                "future_predictive_rmse_K": 0.055712108273528106
              }
            }
          }
        },
        {
          "split": "test",
          "index": 13,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            6.026781424113795,
            0.3370523805996143,
            -0.11418621892443814,
            -0.04510213638445195,
            0.024253871011956536,
            -0.0023616910011002618,
            0.02941545941533061,
            -0.012254116718890413
          ],
          "initial_K": [
            0.40199636783922166,
            0.7860627753051285,
            1.140768053437169,
            1.4625466139078,
            1.7451804799377721,
            1.9667235841282846,
            2.097070559001417,
            2.1246530488048445,
            2.066180086039314,
            1.942559683631435,
            1.7574610824364496,
            1.5129367780173046,
            1.2334071407771263,
            0.9500994114422118,
            0.6639388909469914,
            0.3491361760616862
          ],
          "observed_K": [
            0.35359190949643066,
            0.6920672972938552,
            0.9691407659781738,
            1.239197491096533,
            1.4659548070643982,
            1.6323961130567883,
            1.6973169914458768,
            1.7516329765794767,
            1.7493576360717022,
            1.6741112836572163,
            1.5313742126418293,
            1.3550897414550447,
            1.1235397150579978,
            0.8822890806607616,
            0.5747448060741792,
            0.3296326368915044
          ],
          "future_observed_K": [
            0.2631686842216582,
            0.6516381259791777,
            0.8668623155348184,
            1.1307464524167354,
            1.309330281915078,
            1.5455515505298767,
            1.6225711743314526,
            1.6478073356114997,
            1.601228859380635,
            1.553886083791584,
            1.443629422131273,
            1.2322729046845096,
            1.0614631509524122,
            0.8290216306307898,
            0.52921887146245,
            0.30403103944185583
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.664148770293763,
                0.2445836741348036,
                0.018168797836483386,
                0.07720233833876787,
                0.006867278771036629,
                -0.3116553026418274,
                2.350067026094499,
                9.96430948173936
              ],
              "initial_K": [
                4.493046836072686,
                1.7595841604189575,
                -2.6846314881208135,
                -0.4523916612357012,
                4.8965889366721544,
                4.341072361085714,
                -0.6573476167636034,
                -1.0655753062933777,
                3.640293620560313,
                4.969430717253063,
                0.7369425361509607,
                -1.4997937571653173,
                1.6344302071605126,
                3.6581481529902513,
                0.5084136773826614,
                -2.2181632559198636
              ],
              "metrics": {
                "initial_rmse_K": 2.564002472918259,
                "observation_residual_rms_K": 0.01090666918021773,
                "future_predictive_rmse_K": 0.04152653876542557
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.595977365454833,
                0.23931293702655662,
                0.017155052866914697,
                0.06249686669769134,
                0.0028727898433827006,
                -0.02362096615732132,
                0.014715122987768772,
                0.0032495460730425207
              ],
              "initial_K": [
                0.39937896481909685,
                0.7726244196295317,
                1.1042523528195527,
                1.3858156011629612,
                1.6079110520796092,
                1.7640072796258697,
                1.8592383063687046,
                1.9047344792078469,
                1.900088155030249,
                1.8291068767730077,
                1.6789147951853327,
                1.459668240874446,
                1.1996907805371306,
                0.9222494264823133,
                0.6318573424652006,
                0.32347730401670144
              ],
              "metrics": {
                "initial_rmse_K": 0.11867465551619519,
                "observation_residual_rms_K": 0.02011779624580568,
                "future_predictive_rmse_K": 0.03250030873129946
              }
            },
            "learned": {
              "coefficients_K": [
                5.663825255394026,
                0.24515095248477567,
                0.017827198043580055,
                0.05920874970826765,
                0.0008970503397014571,
                -0.002336246276921009,
                0.0022947297589172187,
                -0.0008772848035583736
              ],
              "initial_K": [
                0.40422748594866614,
                0.7841349169860606,
                1.1202705513815485,
                1.4011239420637165,
                1.6227917012956734,
                1.7855862381370096,
                1.8902655355036204,
                1.9360503887755123,
                1.9202595881660625,
                1.839208585387309,
                1.6913440549459255,
                1.4818804457275816,
                1.2244469678773688,
                0.9364427169161479,
                0.6317839849843379,
                0.31814716617775207
              ],
              "metrics": {
                "initial_rmse_K": 0.1030478845365035,
                "observation_residual_rms_K": 0.012911455015645895,
                "future_predictive_rmse_K": 0.04136901226905055
              }
            }
          }
        },
        {
          "split": "test",
          "index": 14,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            6.311080076657534,
            -1.3591251807694569,
            -0.38326473334367095,
            0.12561504020200748,
            -0.022651107013994504,
            0.06272293803486029,
            0.055553774881321766,
            -0.037699810452175825
          ],
          "initial_K": [
            0.2076896065927406,
            0.41048823598105294,
            0.6185803775329761,
            0.868171932920262,
            1.1940722721089614,
            1.5736145388505403,
            1.9238285735512444,
            2.1785411243018915,
            2.3409148960691306,
            2.428303810789674,
            2.3986004765973767,
            2.1883338822926,
            1.812755597470356,
            1.3674534184810734,
            0.9232215771184211,
            0.4736757196955397
          ],
          "observed_K": [
            0.23137013860557024,
            0.4640487124238206,
            0.7330171681255198,
            0.9740970507691845,
            1.2272933462467632,
            1.4572518331953757,
            1.7003910219651952,
            1.819313101594547,
            1.9065627436089445,
            1.9133752537886326,
            1.8326599308621327,
            1.6726874105324938,
            1.5076229923661406,
            1.1812267391631202,
            0.8125544481573788,
            0.3972233750901738
          ],
          "future_observed_K": [
            0.2421367058935977,
            0.49948484977702784,
            0.7122141921315296,
            0.9634408402349408,
            1.1824125409124047,
            1.410580691414604,
            1.5182623056632836,
            1.676654017909575,
            1.742954629149706,
            1.7587548818614969,
            1.6413996854765893,
            1.5189997719114876,
            1.3249662759107599,
            1.0241744268051085,
            0.7261686213391624,
            0.37214527608236436
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.944161584766761,
                -1.0604605933349647,
                -0.17921054480125231,
                -0.16096757587974614,
                0.03976365757305495,
                0.9028376732619509,
                -4.046303630765201,
                5.139771693109827
              ],
              "initial_K": [
                0.8822902120860578,
                0.23502147441483867,
                -0.17016340043490885,
                1.2526687410256172,
                2.384914928869188,
                1.2480069752001297,
                0.26300514109246587,
                2.137462041436267,
                4.2805563379686395,
                2.7441151845090586,
                -0.357522054405949,
                0.2875164181363259,
                3.8667096417744435,
                4.074221123301334,
                -0.30705261755490404,
                -2.8457513619446435
              ],
              "metrics": {
                "initial_rmse_K": 1.6712407655096166,
                "observation_residual_rms_K": 0.011571937982309658,
                "future_predictive_rmse_K": 0.0489784505877395
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.872620058889407,
                -1.0376078456162285,
                -0.16921132581489048,
                -0.13030653408790993,
                0.01663433732927901,
                0.06842783660313408,
                -0.025336237184484033,
                0.0016761748470667406
              ],
              "initial_K": [
                0.1986733062264134,
                0.4111702052249904,
                0.6513939605911745,
                0.9301060125967623,
                1.245116609701332,
                1.5690461705101084,
                1.8499728501169135,
                2.0362833337626802,
                2.110847083527259,
                2.09884212832584,
                2.033529777411087,
                1.9132746639536977,
                1.700852558743709,
                1.3696307782222528,
                0.9420392502743277,
                0.47285908346918104
              ],
              "metrics": {
                "initial_rmse_K": 0.1613623352354467,
                "observation_residual_rms_K": 0.02280023895482882,
                "future_predictive_rmse_K": 0.03487947349458563
              }
            },
            "learned": {
              "coefficients_K": [
                5.943822076586962,
                -1.062920186509879,
                -0.17584112622215,
                -0.12345078033244683,
                0.005194197545048387,
                0.006767897529554741,
                -0.003951024907813982,
                -0.00045251942529364814
              ],
              "initial_K": [
                0.1846763136370501,
                0.3975249819244091,
                0.6543202347245785,
                0.9526366244318026,
                1.2730453918981084,
                1.5840585866226515,
                1.8497715383075208,
                2.040335857718567,
                2.141072622155953,
                2.1529444189683558,
                2.082971204103131,
                1.9331914743537704,
                1.698597878014679,
                1.3751708636448758,
                0.969432366312301,
                0.5012843296631282
              ],
              "metrics": {
                "initial_rmse_K": 0.1450234210439559,
                "observation_residual_rms_K": 0.015791660311255642,
                "future_predictive_rmse_K": 0.048907802073435806
              }
            }
          }
        },
        {
          "split": "test",
          "index": 15,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            4.884268549802298,
            0.6877274449795013,
            -0.25992970679231264,
            0.35035125405665124,
            0.11789004813219005,
            -0.0268493879993177,
            0.07154517271454933,
            0.03169186925118979
          ],
          "initial_K": [
            0.48552172691417017,
            0.8504093211119879,
            1.089519706863466,
            1.2761288391525716,
            1.4485071252796695,
            1.5882908810024505,
            1.686458893772129,
            1.758272026330791,
            1.782746205267835,
            1.6889320722971826,
            1.438177462773347,
            1.089392217927572,
            0.7523401919885704,
            0.4929336092275198,
            0.3039648935369203,
            0.1480207347089167
          ],
          "observed_K": [
            0.28473776929141265,
            0.5981748894242936,
            0.8369122915123846,
            1.0815817427834677,
            1.23910603610026,
            1.3693180390205584,
            1.4176201541126738,
            1.4794839864876335,
            1.4276476550771566,
            1.3772864341994755,
            1.2278910299283927,
            1.0281196935953378,
            0.8447560748210702,
            0.6212366013744998,
            0.39248691034775424,
            0.1987104389720015
          ],
          "future_observed_K": [
            0.29304758447411616,
            0.4895824758847549,
            0.7513255363394725,
            0.9825438258632921,
            1.1844460947501065,
            1.2654051510291084,
            1.3320062092300005,
            1.304437962048266,
            1.3170130533521156,
            1.2267732226848074,
            1.1160921142219502,
            0.9954416267386369,
            0.7797140280437448,
            0.6222419916957207,
            0.40593809594754526,
            0.19174668148251373
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                4.629702517778071,
                0.48107341446236035,
                -0.17243151751907257,
                0.2936064367888999,
                -0.16202608331912954,
                -0.597261066761488,
                -1.2012087498020434,
                5.065047468190875
              ],
              "initial_K": [
                1.4939786945640416,
                0.6175381974635272,
                -0.3706965810001617,
                1.1729497967265017,
                3.024366543489746,
                1.9349329915470999,
                -0.18550915521433442,
                0.6328173737558465,
                3.201443414494129,
                3.0018137128076177,
                0.1841691167635986,
                -0.5733730438690219,
                1.6684256015671648,
                2.4398248734580115,
                -0.11683687949323202,
                -1.8539342455774883
              ],
              "metrics": {
                "initial_rmse_K": 1.3104550573411555,
                "observation_residual_rms_K": 0.011003879857775442,
                "future_predictive_rmse_K": 0.040191832854795335
              }
            },
            "tikhonov": {
              "coefficients_K": [
                4.573981289854375,
                0.4707063631603167,
                -0.162810540663408,
                0.23768039591056864,
                -0.06778039774436176,
                -0.04526758673916211,
                -0.007521459724787553,
                0.0016518058918379298
              ],
              "initial_K": [
                0.3377560944288869,
                0.6706886625469208,
                0.9755244844092081,
                1.2173913722692358,
                1.3778200333404902,
                1.4728614738731893,
                1.5374934313789232,
                1.5887908307467316,
                1.6054681235401531,
                1.545286635378905,
                1.382624603606596,
                1.1311432889134043,
                0.8364484966815364,
                0.5517437591045636,
                0.3153720464176798,
                0.13793563210090917
              ],
              "metrics": {
                "initial_rmse_K": 0.11387215162015499,
                "observation_residual_rms_K": 0.01797673229657438,
                "future_predictive_rmse_K": 0.03116895327129164
              }
            },
            "learned": {
              "coefficients_K": [
                4.629438086562263,
                0.4821891983908544,
                -0.16918955450068043,
                0.22517543383580016,
                -0.021164941445937772,
                -0.004477218682767011,
                -0.0011729237652524965,
                -0.0004459405020778238
              ],
              "initial_K": [
                0.3652942896746062,
                0.7015417162110886,
                0.9858923273298269,
                1.208030372294458,
                1.3726649339707615,
                1.4936312582032527,
                1.5814058239771869,
                1.6325338821252533,
                1.6289648181713905,
                1.548362252666889,
                1.3795067253387558,
                1.1340353279372064,
                0.8472141301548592,
                0.5656634795668606,
                0.32739436713589937,
                0.1447919332418442
              ],
              "metrics": {
                "initial_rmse_K": 0.09913528051027765,
                "observation_residual_rms_K": 0.013096033576614746,
                "future_predictive_rmse_K": 0.040038136069043176
              }
            }
          }
        },
        {
          "split": "test",
          "index": 16,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            6.125696078420558,
            1.6783579303051732,
            -0.14240359145815265,
            0.04012788816479341,
            -0.09569853536567843,
            -0.09255828759098637,
            0.010008089659754228,
            -0.0006444199244397005
          ],
          "initial_K": [
            0.5260599646423819,
            1.061673338072496,
            1.575629230443767,
            1.997088577571985,
            2.2600222504585807,
            2.3499042414306848,
            2.308299070603891,
            2.191233992246892,
            2.0227468683382743,
            1.7897069748576695,
            1.4807580851749338,
            1.1247411720003302,
            0.7843675062524665,
            0.5109286166665549,
            0.3093587001222755,
            0.14887945877780975
          ],
          "observed_K": [
            0.39330885721719056,
            0.8572688950519638,
            1.2263982155273938,
            1.5258148668673124,
            1.7368736870377925,
            1.8422995551379304,
            1.9202791718915422,
            1.8617459372048526,
            1.7682567867180463,
            1.557507433554215,
            1.3409855504511787,
            1.1338884812298344,
            0.8983190946046599,
            0.6541073378103204,
            0.4086911801752863,
            0.24288773335750657
          ],
          "future_observed_K": [
            0.3876223263322332,
            0.7321712833597309,
            1.065888593535437,
            1.386773215318804,
            1.5428900745815881,
            1.6927742169954123,
            1.7009890037888376,
            1.7080160673375053,
            1.6005716301807635,
            1.453608391365172,
            1.3495398333546467,
            1.089790832867342,
            0.8984531414077315,
            0.6501041241785112,
            0.41404190867142876,
            0.19700865551948127
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.7912082643835046,
                1.365132732638613,
                -0.08933932872982245,
                -0.06341961152183774,
                0.056255778454300374,
                -0.3685285768813276,
                -4.399136553057557,
                -17.797631307699955
              ],
              "initial_K": [
                -7.124186481312549,
                -1.0144311811095663,
                8.335195853336653,
                5.443334352292777,
                -3.6399711986402936,
                -2.5964035669493892,
                6.401282876399971,
                7.368715012182565,
                -0.9111911771299841,
                -3.621972906276108,
                3.133004272019916,
                6.195201232637034,
                -0.13473410989636658,
                -4.25783679476773,
                0.8431478026709883,
                4.9501272942298
              ],
              "metrics": {
                "initial_rmse_K": 4.585957359844416,
                "observation_residual_rms_K": 0.01385652428754068,
                "future_predictive_rmse_K": 0.04731981832068134
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.721507622838143,
                1.335714351477018,
                -0.08435455781104213,
                -0.051339468370860744,
                0.023533488935487904,
                -0.027931503069992446,
                -0.02754552729749594,
                -0.005804137560297809
              ],
              "initial_K": [
                0.4858038078586151,
                0.9689183872932831,
                1.4133119988015606,
                1.7661102961307331,
                2.0004512265790155,
                2.1252305137541474,
                2.154102962183951,
                2.083526769154139,
                1.9098405454966956,
                1.6561124692629317,
                1.36915693066266,
                1.0912530252983945,
                0.840330228971208,
                0.6138352309878735,
                0.4027067887277036,
                0.199644103674121
              ],
              "metrics": {
                "initial_rmse_K": 0.13971817416821147,
                "observation_residual_rms_K": 0.024752533415368212,
                "future_predictive_rmse_K": 0.034544797253568356
              }
            },
            "learned": {
              "coefficients_K": [
                5.790877492322778,
                1.368298971132672,
                -0.08765961956761534,
                -0.048638370106290574,
                0.007348509774415694,
                -0.002762582598081063,
                -0.0042955496374152205,
                0.0015669516803139703
              ],
              "initial_K": [
                0.507726095172483,
                0.9911632916828894,
                1.4240570947044087,
                1.7791014981274587,
                2.032731872979983,
                2.170896043970995,
                2.191245497890546,
                2.1015362741090655,
                1.9187294007305538,
                1.6699895303113919,
                1.3898676719331235,
                1.1101149952723752,
                0.8491566994824885,
                0.611128253178274,
                0.3933401420561037,
                0.19175267934910994
              ],
              "metrics": {
                "initial_rmse_K": 0.12196511828035285,
                "observation_residual_rms_K": 0.01847956827020177,
                "future_predictive_rmse_K": 0.04733709068533181
              }
            }
          }
        },
        {
          "split": "test",
          "index": 17,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            6.66936998021999,
            -2.9652521436342125,
            -0.4790226749520172,
            -0.25661258666649445,
            0.0812490107136822,
            0.09913406257747438,
            -0.00947824150363086,
            -0.03526847257965021
          ],
          "initial_K": [
            -0.05535493681063591,
            -0.04354579180999474,
            0.07760919615818473,
            0.3410095204026522,
            0.7721763212333901,
            1.3348625380314174,
            1.9017663949074373,
            2.3343474797138497,
            2.5924301562287875,
            2.728003983997841,
            2.7770015711807496,
            2.703472418379978,
            2.455494178895258,
            2.0282065597748615,
            1.4523096283676225,
            0.7612721100198756
          ],
          "observed_K": [
            0.12593628372104615,
            0.25759367314280357,
            0.47606669398618756,
            0.7840664622678061,
            1.00940441422509,
            1.316310250460687,
            1.6040810524726055,
            1.8688249417349625,
            2.0872380666458445,
            2.2016351031093992,
            2.1872217971108268,
            2.047289531979072,
            1.8113941739960548,
            1.4620222383530828,
            1.0662733175626045,
            0.5156453853697515
          ],
          "future_observed_K": [
            0.14540814246809827,
            0.41442375310014024,
            0.5908799005858953,
            0.811091667708604,
            1.0461757291925486,
            1.3222409506446748,
            1.5609907980282882,
            1.7673739890240654,
            1.872636773437907,
            1.9550753388619908,
            1.9083012192734226,
            1.8009790882356655,
            1.6011315198644678,
            1.2958462990676374,
            0.9189561886068436,
            0.44960602506065456
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.261693391985727,
                -2.361435404690613,
                -0.32070584929626855,
                -0.07571322165826472,
                -0.17893473707188248,
                -1.8000901751839877,
                -2.03077909041693,
                3.6536634879391348
              ],
              "initial_K": [
                0.002864468825555133,
                -0.5823042553588296,
                -0.36947823667065793,
                1.344845895580865,
                2.3797180472608632,
                1.1058551879157794,
                -0.14104844577175268,
                1.4365482006586932,
                4.054058655147083,
                3.894970146659237,
                1.4752664452436004,
                0.8349225275729505,
                2.6851120039791425,
                3.3058820636915898,
                1.0856381989266841,
                -0.7672646285383002
              ],
              "metrics": {
                "initial_rmse_K": 1.1714629761391269,
                "observation_residual_rms_K": 0.014413998484316333,
                "future_predictive_rmse_K": 0.05873858268235757
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.186330181640499,
                -2.3105468682408294,
                -0.30281176822600037,
                -0.061291396388355124,
                -0.07485379761434417,
                -0.1364323621248117,
                -0.012715877353564758,
                0.0011915274070129504
              ],
              "initial_K": [
                -0.031397991183059415,
                0.054437823149214526,
                0.2892784905581278,
                0.6159144919666522,
                0.9612532786984965,
                1.3025735596470347,
                1.659264081049194,
                2.0302989146373944,
                2.3561777664253816,
                2.549877912674451,
                2.5603869644388837,
                2.3998499287602266,
                2.1121772438478663,
                1.7252738671049266,
                1.2386641803897813,
                0.6524700035941196
              ],
              "metrics": {
                "initial_rmse_K": 0.22532844593508858,
                "observation_residual_rms_K": 0.027240904108410745,
                "future_predictive_rmse_K": 0.045484929614613374
              }
            },
            "learned": {
              "coefficients_K": [
                6.261335747581944,
                -2.366912430844044,
                -0.3146761134442626,
                -0.058066702216967206,
                -0.023373664012549367,
                -0.01349392721460874,
                -0.0019829601287206784,
                -0.00032167843252551924
              ],
              "initial_K": [
                0.019810041661728284,
                0.10064170872250267,
                0.2789955036355489,
                0.5579902179329957,
                0.9153576496026251,
                1.3165881115735585,
                1.722558773584724,
                2.0912945327165535,
                2.379981414133264,
                2.5507043878006743,
                2.577466812575224,
                2.4500546161223165,
                2.1730886524982442,
                1.7623364664524148,
                1.2416047062480495,
                0.6416956379883696
              ],
              "metrics": {
                "initial_rmse_K": 0.19618884926792074,
                "observation_residual_rms_K": 0.020080913119143257,
                "future_predictive_rmse_K": 0.05891881944902618
              }
            }
          }
        },
        {
          "split": "test",
          "index": 18,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            5.807302046901371,
            0.0017489550590784845,
            -0.3149889416754652,
            -0.1285277374178691,
            -0.061114877660351924,
            -0.01244514269873259,
            -0.0513899601285698,
            0.014605475623798663
          ],
          "initial_K": [
            0.24713484261318136,
            0.5474196623815,
            0.9066397535289007,
            1.2773150368230044,
            1.5993111149124961,
            1.8434639566601954,
            2.0099466877089305,
            2.093022108589769,
            2.072195474775573,
            1.94688559906659,
            1.7555125824595095,
            1.5370215606080795,
            1.28772943549715,
            0.9839944512351427,
            0.639376439887629,
            0.3037664502787767
          ],
          "observed_K": [
            0.2810558835903203,
            0.5946250833421634,
            0.8954210886055911,
            1.1352549273913002,
            1.3686816027702875,
            1.510142455672093,
            1.6767604024756448,
            1.6820585211033658,
            1.7286100273527227,
            1.6498835226317132,
            1.5319904840352188,
            1.4014428431723749,
            1.1083575693026133,
            0.8453739090094796,
            0.5855760077786577,
            0.30642371559462744
          ],
          "future_observed_K": [
            0.25858626550068603,
            0.561859286346218,
            0.8267882611895103,
            1.0238730061462753,
            1.2338173838294377,
            1.4487188190048887,
            1.5048042174849543,
            1.5657814049729841,
            1.590489176572175,
            1.52997647089352,
            1.4115782442858693,
            1.2720804796094765,
            1.0288894456968214,
            0.8115530751017531,
            0.5316580895270051,
            0.28736425754132267
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.486252600962323,
                0.012809607606816664,
                -0.15872834456500007,
                0.11283698716481584,
                -0.3708858910772468,
                -0.4086586384216572,
                1.0067123429770375,
                -21.33841790609264
              ],
              "initial_K": [
                -6.83789488136902,
                -0.7247673494215982,
                7.7580239867771725,
                3.7724007165772484,
                -4.801296961897143,
                -1.813296026689284,
                7.616771790138796,
                6.380502459036915,
                -3.3071511024310998,
                -3.720825142865512,
                6.061343617302191,
                8.145568394683355,
                -1.808075918249098,
                -6.442361321163647,
                2.1056831758767864,
                7.933321500860198
              ],
              "metrics": {
                "initial_rmse_K": 5.347370852976297,
                "observation_residual_rms_K": 0.016042553580670443,
                "future_predictive_rmse_K": 0.040915119860138474
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.420222282502055,
                0.012533562713819758,
                -0.14987194898622253,
                0.09134384135444508,
                -0.15515275503805145,
                -0.03097303907948798,
                0.006303605716655112,
                -0.006958853720747703
              ],
              "initial_K": [
                0.2849362254471208,
                0.60070503125999,
                0.9399324312582769,
                1.2586567088816696,
                1.5110897453460288,
                1.6798692526105052,
                1.7793278439796893,
                1.8367575975329706,
                1.8657828548986428,
                1.8482409225708947,
                1.7434657070673214,
                1.525766006264985,
                1.2164207406856784,
                0.8737353293440682,
                0.5503514781717861,
                0.26338880227804884
              ],
              "metrics": {
                "initial_rmse_K": 0.12209989694976262,
                "observation_residual_rms_K": 0.0246588351600753,
                "future_predictive_rmse_K": 0.028907738310941157
              }
            },
            "learned": {
              "coefficients_K": [
                5.4859392468234915,
                0.012839317738094597,
                -0.15574402110456648,
                0.08653801263842933,
                -0.04844762032735998,
                -0.0030634075995216873,
                0.000983007185092002,
                0.0018786921256609991
              ],
              "initial_K": [
                0.32598460734661205,
                0.6479120618930126,
                0.9583477135203081,
                1.2441004922369518,
                1.4888041562500742,
                1.6806658894416522,
                1.8170747741031767,
                1.898970405482287,
                1.920771484272087,
                1.8687000950421713,
                1.7308162667715197,
                1.509014693447541,
                1.2228664513897995,
                0.9039428495031261,
                0.5843072113876496,
                0.2834071292931013
              ],
              "metrics": {
                "initial_rmse_K": 0.10552329188336086,
                "observation_residual_rms_K": 0.020280549507896355,
                "future_predictive_rmse_K": 0.041013998656626256
              }
            }
          }
        },
        {
          "split": "test",
          "index": 19,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            5.955620357912321,
            1.1049016266397764,
            -0.15437426852275474,
            0.15907621310153364,
            0.022577552990945143,
            -0.042911330097955495,
            -0.0173039345769594,
            0.012378956026638271
          ],
          "initial_K": [
            0.5126667764136865,
            0.9935359090594259,
            1.4108569090159437,
            1.7351905707091064,
            1.951733008455496,
            2.0740766796598398,
            2.132350650925062,
            2.13596203164056,
            2.0573260669733506,
            1.8671111665585993,
            1.5803375545764957,
            1.2527251865378928,
            0.9351703115512102,
            0.6480370510183397,
            0.39617500004345957,
            0.18323928868240497
          ],
          "observed_K": [
            0.3843434548001997,
            0.7629183783676343,
            1.0506717621191253,
            1.383855181239357,
            1.5642833486560483,
            1.677961656261102,
            1.771956775013544,
            1.7740432950165288,
            1.7126682146765666,
            1.571171291294537,
            1.3937798576261249,
            1.1739768791871823,
            0.9520539035397934,
            0.698601373316787,
            0.47396022204418475,
            0.2560883574730668
          ],
          "future_observed_K": [
            0.35365286259906614,
            0.6282334196549889,
            1.0085462051712246,
            1.1983220944871296,
            1.437420408884693,
            1.580826744553727,
            1.6434341283018818,
            1.625675326483922,
            1.579274042212397,
            1.4851360597871084,
            1.3375495547286964,
            1.131870150252734,
            0.9313457041183084,
            0.7122210922179693,
            0.4789163931706516,
            0.2597083347516076
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.557991699992754,
                0.868041754739602,
                -0.10910841535748796,
                0.08938207345248761,
                0.17159367609555143,
                -0.750483843936117,
                -0.6640535239916756,
                -3.1142149897816913
              ],
              "initial_K": [
                -1.0073400218486184,
                0.4212809902147943,
                2.506698709203785,
                2.3629108952292026,
                0.8948094380644138,
                0.9997507957545665,
                2.512742254818606,
                2.79642987336107,
                1.5409450080637561,
                1.0619545380749085,
                1.894141067863823,
                1.9198784491609544,
                0.49180537325545515,
                -0.22465665123324063,
                0.7624519098305467,
                1.3243181934764872
              ],
              "metrics": {
                "initial_rmse_K": 0.826810771116095,
                "observation_residual_rms_K": 0.013159172289965116,
                "future_predictive_rmse_K": 0.032471018774758845
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.491097958737443,
                0.8493356006825156,
                -0.10302060986800417,
                0.07235661056289876,
                0.07178281038408885,
                -0.056880641301343494,
                -0.004158021523427749,
                -0.0010156032496984177
              ],
              "initial_K": [
                0.44989939854974315,
                0.8770129066901462,
                1.2506726787740448,
                1.5425042346645712,
                1.7454329631420586,
                1.8758401890024878,
                1.951341920399813,
                1.9670903047296882,
                1.898033180057929,
                1.727351689042961,
                1.4730876337905305,
                1.1855017288437086,
                0.9154477052033339,
                0.6816647280117518,
                0.46633327377691425,
                0.24160887350575225
              ],
              "metrics": {
                "initial_rmse_K": 0.1356053716071243,
                "observation_residual_rms_K": 0.021134273141982265,
                "future_predictive_rmse_K": 0.02361078078126274
              }
            },
            "learned": {
              "coefficients_K": [
                5.557674248386081,
                0.8700550587594938,
                -0.10705701864838446,
                0.06854974770624021,
                0.02241472504092046,
                -0.005625815031615662,
                -0.0006484169881528615,
                0.00027418392519380774
              ],
              "initial_K": [
                0.4588767662363717,
                0.8859679386925416,
                1.2560513036464407,
                1.5543876266670749,
                1.7763130886142744,
                1.922653273899523,
                1.993624076796836,
                1.9857757748575469,
                1.895250009369089,
                1.7255092743542786,
                1.4928791360676321,
                1.22423170258017,
                0.9477960698836574,
                0.6837157616150923,
                0.4400918450740432,
                0.2148556848601253
              ],
              "metrics": {
                "initial_rmse_K": 0.11878608597110078,
                "observation_residual_rms_K": 0.01471842961659003,
                "future_predictive_rmse_K": 0.032432048686007735
              }
            }
          }
        },
        {
          "split": "test",
          "index": 20,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            7.180732206431159,
            -1.189659729794893,
            -0.5444413310804779,
            0.16352564588851226,
            -0.16319068955682428,
            0.015665053162013543,
            -0.03842669357752824,
            -0.026288524616383802
          ],
          "initial_K": [
            0.18313104007782438,
            0.445366634597879,
            0.786475107762756,
            1.1536208379361117,
            1.517656278888774,
            1.8812758253917239,
            2.22723573575444,
            2.506152153706002,
            2.678826962698064,
            2.732182707694785,
            2.646044524281446,
            2.385038769647284,
            1.949448107895559,
            1.4121272634382276,
            0.8782085004779696,
            0.41070400282354635
          ],
          "observed_K": [
            0.2907647897218052,
            0.5488221563692287,
            0.8785257718103434,
            1.1872726446009394,
            1.4594291825877586,
            1.7089202295060695,
            1.9478396649521819,
            2.1135840388914655,
            2.150849584283791,
            2.1742979397003994,
            2.077899949895917,
            1.8774904370076986,
            1.5946262849888704,
            1.2535730779703953,
            0.9056447165128574,
            0.41106235774278926
          ],
          "future_observed_K": [
            0.29765605797611666,
            0.5763101286702718,
            0.8736904056516219,
            1.121499012178798,
            1.4203926807486866,
            1.621488778880248,
            1.799996293841164,
            1.9351654113661108,
            1.960020105292242,
            1.9407580660282635,
            1.8615879059849851,
            1.6875147206990293,
            1.4735934047848271,
            1.1559313550457826,
            0.7994194778476115,
            0.42533919216637117
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.782082945948784,
                -0.9405888925994127,
                -0.2956993044444451,
                -0.03217049187790436,
                -0.13876160797452392,
                -0.34103839050015256,
                -0.6959417273028967,
                -7.618870835824529
              ],
              "initial_K": [
                -2.724316095474068,
                -0.2237648545751877,
                3.5046191553311634,
                2.4582270724462303,
                -0.7417085761954105,
                0.23057530634413936,
                4.019769157856156,
                4.2054118919445385,
                0.9180892269017071,
                0.4018019429263895,
                3.5601720876424143,
                4.388242406515294,
                0.991718492396365,
                -0.9701478080906916,
                1.3799679787392707,
                2.937269382817628
              ],
              "metrics": {
                "initial_rmse_K": 1.9125995625680703,
                "observation_residual_rms_K": 0.016661395397878122,
                "future_predictive_rmse_K": 0.051677480510863814
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.700456537302124,
                -0.9203193599032268,
                -0.2792004867965551,
                -0.02604266898847198,
                -0.05804816599581408,
                -0.02584796796995131,
                -0.004357691927877194,
                -0.0024846550431761654
              ],
              "initial_K": [
                0.22572507460931931,
                0.4957672237212207,
                0.8210712406038261,
                1.1765834952151257,
                1.5252854858858975,
                1.839852535415582,
                2.104492885893584,
                2.305042800545513,
                2.422782644730953,
                2.4371508712082717,
                2.3337873682063965,
                2.11269391299054,
                1.790836525892582,
                1.3955772659135424,
                0.9533463010380188,
                0.48339466025612754
              ],
              "metrics": {
                "initial_rmse_K": 0.1627888599837249,
                "observation_residual_rms_K": 0.025608691955392324,
                "future_predictive_rmse_K": 0.03559164117217296
              }
            },
            "learned": {
              "coefficients_K": [
                6.781695578848581,
                -0.9427704597742591,
                -0.29013972796233745,
                -0.024672498820339443,
                -0.018125978531125977,
                -0.00255650926950146,
                -0.0006795543166988768,
                0.0006707860305615684
              ],
              "initial_K": [
                0.24677468439861527,
                0.5181631918253068,
                0.827073389517191,
                1.1683673649568092,
                1.5206963038224899,
                1.8543750607807485,
                2.1394101315172627,
                2.3495401723032314,
                2.463496603526742,
                2.4668350103729315,
                2.3545930928973067,
                2.1322394280375905,
                1.813933127543892,
                1.4196339348963183,
                0.9720338433136682,
                0.4929165163610235
              ],
              "metrics": {
                "initial_rmse_K": 0.1465861170736035,
                "observation_residual_rms_K": 0.017446369278345,
                "future_predictive_rmse_K": 0.05159967868588562
              }
            }
          }
        },
        {
          "split": "test",
          "index": 21,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            5.656457177825757,
            -0.8046586944460525,
            -0.3496565046537763,
            -0.0662370360402944,
            0.12229509305188335,
            0.037066554291200905,
            -0.037136746228791595,
            0.03332413208248
          ],
          "initial_K": [
            0.2223438377553089,
            0.43083134764895104,
            0.6471501904404015,
            0.9053325292007383,
            1.2090065152252487,
            1.5300568342004048,
            1.8285707024347484,
            2.0514251889573205,
            2.138454112126707,
            2.0714058735480916,
            1.9056319729226379,
            1.7126725442442343,
            1.4960332097720548,
            1.2041928154370631,
            0.8234578044141322,
            0.4068332720868984
          ],
          "observed_K": [
            0.2533458367970054,
            0.47873471785169747,
            0.6988430610417581,
            0.9664486447696404,
            1.173194077827786,
            1.36383356805989,
            1.5287422172420506,
            1.6685356664161788,
            1.6969394915923857,
            1.6673401959566525,
            1.5758952833087767,
            1.4617111026935101,
            1.2558995287403079,
            0.9908986377670981,
            0.6525496912882272,
            0.35873610736424605
          ],
          "future_observed_K": [
            0.23943670035597656,
            0.5146260530813629,
            0.7091705804012011,
            0.9209327888925348,
            1.1010075832069115,
            1.3140518894324487,
            1.4205280287614073,
            1.5541866909386197,
            1.5738046771986007,
            1.5316282942298414,
            1.4825312579296004,
            1.3351047587689062,
            1.1262427380240985,
            0.8647552835250795,
            0.5568601625584565,
            0.31250165728444046
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.325544762511252,
                -0.6259726179248812,
                -0.15643125015153658,
                -0.06679623179919929,
                0.05185345165148199,
                0.7644623767545284,
                -2.734050753656812,
                1.5994208653384423
              ],
              "initial_K": [
                0.10759979603909775,
                0.2778549833711094,
                0.7600604522263728,
                1.3495062252803134,
                1.368273768005666,
                0.9334691206571373,
                1.1883496739806434,
                2.3720125552422613,
                2.8974690401223473,
                1.7267884659918842,
                0.465036757486272,
                1.1283026289055231,
                2.686257490015037,
                2.332692769982443,
                -0.007327024615406491,
                -1.2683600743216124
              ],
              "metrics": {
                "initial_rmse_K": 0.8077298009307438,
                "observation_residual_rms_K": 0.012211136650885884,
                "future_predictive_rmse_K": 0.037231708975447905
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.261448658627637,
                -0.6124830131190234,
                -0.14770302309151467,
                -0.054072911319660875,
                0.021691862849223895,
                0.05794010169824286,
                -0.017119466231447014,
                0.000521600799496199
              ],
              "initial_K": [
                0.23480891011157506,
                0.4665280702634413,
                0.6995497891311668,
                0.9449325315367149,
                1.2078377595773004,
                1.471381574471169,
                1.6948020968858744,
                1.8354767281023014,
                1.878598289052464,
                1.8434913558236834,
                1.7564522280164536,
                1.6188877804936799,
                1.40847457520568,
                1.1129104824282015,
                0.7547392220165574,
                0.375642067227611
              ],
              "metrics": {
                "initial_rmse_K": 0.12397827678759987,
                "observation_residual_rms_K": 0.020539493869614758,
                "future_predictive_rmse_K": 0.028968829526348387
              }
            },
            "learned": {
              "coefficients_K": [
                5.325240587400436,
                -0.6274244757198884,
                -0.15349011540303542,
                -0.05122799976212922,
                0.006773448110893196,
                0.0057306016178762,
                -0.0026696717826098526,
                -0.00014081734637277319
              ],
              "initial_K": [
                0.22101759786568453,
                0.4535294415470845,
                0.7036045787793967,
                0.9687288205079088,
                1.2370055676790563,
                1.4880983562088366,
                1.6968132878139832,
                1.8400690130556498,
                1.904327211403029,
                1.887945352281988,
                1.7964028275408026,
                1.6352195330968515,
                1.4075059504189111,
                1.1175649403280672,
                0.7753673650439987,
                0.3967517423735731
              ],
              "metrics": {
                "initial_rmse_K": 0.1108089560750543,
                "observation_residual_rms_K": 0.014499417200842668,
                "future_predictive_rmse_K": 0.03736250329880901
              }
            }
          }
        },
        {
          "split": "test",
          "index": 22,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            5.616317898180286,
            2.8494047653427668,
            -0.14949376274781773,
            -0.15241351632198927,
            -0.08747961663688894,
            -0.08000786612325637,
            -0.005665201640811569,
            0.02009165091951631
          ],
          "initial_K": [
            0.6012971730607417,
            1.2058465558071387,
            1.785094592131872,
            2.261878766696778,
            2.5404883688195863,
            2.5760557775222077,
            2.409645766953102,
            2.1215539423852983,
            1.762792284251721,
            1.3526977584588793,
            0.9281985642881142,
            0.5560767258955849,
            0.28694258161169606,
            0.12194886777863767,
            0.03436551000394805,
            0.0010320653522276069
          ],
          "observed_K": [
            0.5138680405700309,
            0.945781945950242,
            1.3311567721337862,
            1.6304195682207692,
            1.7973422297531476,
            1.8819978627428737,
            1.8689229212367107,
            1.7438390639039245,
            1.5404899155281728,
            1.3470061931791877,
            1.0507887630982018,
            0.7936583151883422,
            0.6128826676883602,
            0.4211538393806137,
            0.23080791302214448,
            0.11000071533038085
          ],
          "future_observed_K": [
            0.3884416113119388,
            0.7924451638125719,
            1.1290996326705947,
            1.413383461834771,
            1.570311999694393,
            1.6778915389397895,
            1.681416772228922,
            1.5540917150153566,
            1.4516500370184,
            1.2763011727620621,
            1.0570185540534092,
            0.8389587695568099,
            0.6201152863312946,
            0.4817216996249391,
            0.30909883510899566,
            0.12491631736708089
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.311395444935424,
                2.2377827713052736,
                -0.0097854246070934,
                0.047699569309763004,
                0.2296339229944794,
                0.4433190241603213,
                -1.3849107795121192,
                13.905077306450407
              ],
              "initial_K": [
                5.112421905560949,
                2.011902062082594,
                -2.6109514325248613,
                0.506539010512399,
                6.183490583897703,
                4.2678430244738905,
                -1.6678529055438496,
                -0.7311189867629659,
                5.264781742657153,
                4.862622107553082,
                -2.0571179246874816,
                -3.6096952946126017,
                2.710287146835295,
                5.219312797040233,
                -1.0503136070135906,
                -5.234512355445528
              ],
              "metrics": {
                "initial_rmse_K": 3.4963927829475008,
                "observation_residual_rms_K": 0.012276661270111832,
                "future_predictive_rmse_K": 0.053072879338131415
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.247469636518219,
                2.189558928341766,
                -0.009239437742149857,
                0.03861377373841246,
                0.09606279629377625,
                0.033600017640714644,
                -0.00867172392162575,
                0.004534703527558551
              ],
              "initial_K": [
                0.6445746424843999,
                1.2061003168422029,
                1.6374933260155067,
                1.9339465681133987,
                2.1108239899605454,
                2.1781620551672543,
                2.132008964465273,
                1.965338893174894,
                1.688873149285238,
                1.344537865640922,
                0.9950338123375732,
                0.6928260067890306,
                0.4567548679142599,
                0.2790244598001258,
                0.1488513214720828,
                0.060404699969957176
              ],
              "metrics": {
                "initial_rmse_K": 0.20531285522882756,
                "observation_residual_rms_K": 0.02213745146309031,
                "future_predictive_rmse_K": 0.03956302983868545
              }
            },
            "learned": {
              "coefficients_K": [
                5.311092077980473,
                2.2429730021029446,
                -0.009601444409320379,
                0.036582206202887886,
                0.029996334137179777,
                0.003323230539969652,
                -0.0013523001445933703,
                -0.00122424067975897
              ],
              "initial_K": [
                0.6277360677487442,
                1.196396964959469,
                1.6586325680515528,
                1.9870476699525077,
                2.1744353052692533,
                2.2259848867179435,
                2.151329156217629,
                1.964381151404458,
                1.6889513973713082,
                1.360849577019746,
                1.0218580591836355,
                0.710004661575566,
                0.45222264913848553,
                0.2608592874206428,
                0.13315078297619276,
                0.05379451704639515
              ],
              "metrics": {
                "initial_rmse_K": 0.18327390152463463,
                "observation_residual_rms_K": 0.015053886846276884,
                "future_predictive_rmse_K": 0.0533250424589054
              }
            }
          }
        },
        {
          "split": "test",
          "index": 23,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            6.3073933628624665,
            -0.12895218170690614,
            -0.5797098359900882,
            -0.004750410625855255,
            0.04804790973107032,
            0.020260473845860535,
            0.01728589544363994,
            -0.008473803232893842
          ],
          "initial_K": [
            0.29795725439702275,
            0.5960873620178911,
            0.9034863110307689,
            1.2348503172798584,
            1.590327977921797,
            1.9352009913882426,
            2.2073713024985793,
            2.353536438451543,
            2.3573809740751153,
            2.23254447914464,
            2.000699011401208,
            1.6882629835973466,
            1.3348003324484605,
            0.9822361975301281,
            0.6489044805611504,
            0.32545496363917653
          ],
          "observed_K": [
            0.3129000452301684,
            0.5903081752767327,
            0.8839642564970629,
            1.1824765210300032,
            1.4577322508213633,
            1.6285295265444881,
            1.7575800329280042,
            1.8749196579654919,
            1.891391595018005,
            1.813814701373587,
            1.704279780704459,
            1.5149228995927297,
            1.2566446508786369,
            0.9838523131637664,
            0.6573813676704153,
            0.3037037429128521
          ],
          "future_observed_K": [
            0.2856085427816581,
            0.5420540547417639,
            0.8330196469334443,
            1.125892829715404,
            1.347031087003698,
            1.5513155445981468,
            1.620961600758237,
            1.7096937609114398,
            1.6876659043171423,
            1.6871277188152884,
            1.523132495583153,
            1.3649747145509203,
            1.1823642485817718,
            0.8675219032803435,
            0.5875421011868985,
            0.2810471112504614
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.955563241829857,
                -0.17979976854039134,
                -0.2662534710298744,
                0.008856045822308343,
                -0.38320496345664035,
                -0.10903508824276029,
                -1.83603733213522,
                16.065967149613584
              ],
              "initial_K": [
                5.050036175148017,
                1.1424280754644498,
                -3.9849149903231345,
                -0.07929500664797184,
                6.509462682964919,
                4.142149235901168,
                -2.6953225871865465,
                -1.2378093100337355,
                6.25133424484217,
                6.2446026567679525,
                -1.5284532198798657,
                -3.2848368540629034,
                3.9517651594478487,
                6.707340544296751,
                -0.7459701377562078,
                -5.816692794552793
              ],
              "metrics": {
                "initial_rmse_K": 4.048533416984039,
                "observation_residual_rms_K": 0.010894088173594349,
                "future_predictive_rmse_K": 0.05235881071982331
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.883884490217269,
                -0.1759251137194905,
                -0.25139761103759983,
                0.007169149628561421,
                -0.16030619458686943,
                -0.008263983020698725,
                -0.011496487058670903,
                0.005239409771076656
              ],
              "initial_K": [
                0.2568809454007182,
                0.5567564770752359,
                0.9060939807133787,
                1.265730830235914,
                1.5775846003549474,
                1.8049429959995749,
                1.9494543253498766,
                2.031731244441622,
                2.0610891572765415,
                2.0259015808178304,
                1.9061366585437907,
                1.689213591900332,
                1.3808417114568778,
                1.0126162072716178,
                0.6370270602172774,
                0.2986595176111703
              ],
              "metrics": {
                "initial_rmse_K": 0.14464153313019282,
                "observation_residual_rms_K": 0.02176231239007855,
                "future_predictive_rmse_K": 0.04014921689287452
              }
            },
            "learned": {
              "coefficients_K": [
                5.955223082430237,
                -0.18021678948990386,
                -0.26124751899154175,
                0.00679196267601514,
                -0.05005682077359055,
                -0.0008173543552815987,
                -0.001792803974419174,
                -0.0014144912761545148
              ],
              "initial_K": [
                0.29237198250630764,
                0.6011935534290401,
                0.9273341503919439,
                1.253511054273795,
                1.5537369799626872,
                1.803976612717279,
                1.9871215643877709,
                2.0931984521896023,
                2.117239558154708,
                2.0561579145523194,
                1.907828392261006,
                1.6755889127960206,
                1.3748654226149448,
                1.033246647389966,
                0.6804673692045426,
                0.33536065515826685
              ],
              "metrics": {
                "initial_rmse_K": 0.12213877450625542,
                "observation_residual_rms_K": 0.015340894263972624,
                "future_predictive_rmse_K": 0.052947880823372276
              }
            }
          }
        },
        {
          "split": "test",
          "index": 24,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            5.714850767936276,
            -0.7122801141751662,
            -0.36390482425410486,
            0.10663356330007517,
            -0.19171585434582544,
            0.022988197840341743,
            0.049432722517613964,
            0.007037053860749392
          ],
          "initial_K": [
            0.20415243457210236,
            0.4206072874313576,
            0.679157150021953,
            0.9953922896417096,
            1.3303696423986238,
            1.6127747784409132,
            1.808052441550762,
            1.9438950748134727,
            2.0550540912832247,
            2.1189088346155622,
            2.0648216365696386,
            1.8451482694748593,
            1.485398391600072,
            1.065717759773858,
            0.6634789830914641,
            0.31245822419369396
          ],
          "observed_K": [
            0.25632459659570234,
            0.5179591850105718,
            0.7608307122044385,
            0.9690718485647044,
            1.1687166377167875,
            1.3797700649775797,
            1.5909433004958147,
            1.6487569074093655,
            1.747218439660831,
            1.6999089259230764,
            1.5859921732858098,
            1.4405307099743567,
            1.24518793154413,
            0.9680168467631567,
            0.6524509621697684,
            0.35604190776045835
          ],
          "future_observed_K": [
            0.24506195369261805,
            0.49269516994180307,
            0.6964971716744704,
            0.9370108511120524,
            1.1515681478410864,
            1.3287256418813056,
            1.4521955481083055,
            1.5620153732801978,
            1.5864590553051303,
            1.5231250281555104,
            1.4795067886438171,
            1.3276143074071822,
            1.1381985629809885,
            0.900277970804165,
            0.6057651377789381,
            0.2960578178087271
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.383722305567434,
                -0.5540757910624564,
                -0.18942955941379505,
                0.09546935829326046,
                0.4925880216846543,
                0.6628992337722557,
                -1.3137979442542969,
                -4.476687652183676
              ],
              "initial_K": [
                -1.365486162584806,
                0.338062193065538,
                2.5631388991248123,
                1.659411597063586,
                -0.5286150259722933,
                0.19306549531238604,
                3.010532673748615,
                3.5194707734854527,
                1.3046709703865,
                0.36574919581935905,
                2.0117685069544633,
                2.9268353463068806,
                1.3538677477855237,
                -0.019069644158946186,
                0.7303141225357419,
                1.3785089004830442
              ],
              "metrics": {
                "initial_rmse_K": 1.1990929890711974,
                "observation_residual_rms_K": 0.014812763947169835,
                "future_predictive_rmse_K": 0.031110614734422934
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.318926000294156,
                -0.5421355508029017,
                -0.17886016100496138,
                0.07728439173417992,
                0.20606442709679604,
                0.050242432052067944,
                -0.008226445508198186,
                -0.0014599308468941756
              ],
              "initial_K": [
                0.322235067640009,
                0.5854009676946077,
                0.7787697000803588,
                0.9487541339107666,
                1.1579605013928376,
                1.4260348138327403,
                1.703969692064898,
                1.9067871723474779,
                1.9754570630081068,
                1.9120911719655207,
                1.7618883913367007,
                1.5676910971570657,
                1.3421163213651979,
                1.0747442850414717,
                0.7558387201917537,
                0.3910089595492418
              ],
              "metrics": {
                "initial_rmse_K": 0.154753275276282,
                "observation_residual_rms_K": 0.022535832925690214,
                "future_predictive_rmse_K": 0.019586759308570748
              }
            },
            "learned": {
              "coefficients_K": [
                5.383414807573908,
                -0.5553608940098433,
                -0.1858680085149467,
                0.07321826594410379,
                0.0643451746925931,
                0.0049692588373959875,
                -0.0012828618104968768,
                0.00039413970980481855
              ],
              "initial_K": [
                0.2726881472544122,
                0.5290198703949546,
                0.7659245311803071,
                0.9951281859647584,
                1.2309854003621663,
                1.4738430101063578,
                1.7016831311875766,
                1.8767774700836404,
                1.9633131436245608,
                1.9440233983239692,
                1.8248033229853067,
                1.6259121692261584,
                1.3686246245307756,
                1.0677630294062268,
                0.7328975997506252,
                0.37315332964708847
              ],
              "metrics": {
                "initial_rmse_K": 0.12139688497128666,
                "observation_residual_rms_K": 0.018341484732475762,
                "future_predictive_rmse_K": 0.030854594071059734
              }
            }
          }
        },
        {
          "split": "test",
          "index": 25,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            4.986804801747439,
            1.409274362677173,
            -0.12718695672699243,
            0.03689907187329964,
            0.12627846114006258,
            -0.1106416293018512,
            0.08567935609441617,
            0.01678757000823148
          ],
          "initial_K": [
            0.509065992664648,
            0.944993307678865,
            1.2970869050704315,
            1.5864694936775365,
            1.8004718716335195,
            1.9021318480005827,
            1.8938817977872537,
            1.820834389282905,
            1.7000520672301658,
            1.4923760093169012,
            1.1763471629653488,
            0.8225061549732091,
            0.5503460976345522,
            0.40861419871791843,
            0.3269436556282219,
            0.19925654600422413
          ],
          "observed_K": [
            0.3575312965766424,
            0.7017382007526838,
            0.9594613176941941,
            1.215311815287132,
            1.4411487374125758,
            1.4909819344263169,
            1.5197945739374372,
            1.5340421397636586,
            1.426809482276736,
            1.2832180563593463,
            1.1200340709109777,
            0.9127705371946694,
            0.7153873817038761,
            0.5183350404438942,
            0.34445335034658364,
            0.1633851370734911
          ],
          "future_observed_K": [
            0.3430677007449951,
            0.6442097687950445,
            0.8328210484986751,
            1.0407723511732792,
            1.2520758736971886,
            1.403124520515603,
            1.3848437378696963,
            1.384543276712661,
            1.3237194172191862,
            1.1908263195669258,
            1.040297548657626,
            0.8673551264432463,
            0.6738958202140701,
            0.5285660640317458,
            0.3798120689789465,
            0.18581866792888094
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                4.699003053423757,
                1.095423142403036,
                -0.11896294348078892,
                0.0748533850214,
                0.008103392389151287,
                -0.39443040712301586,
                0.4350129536647732,
                11.644500294914579
              ],
              "initial_K": [
                4.429319702106067,
                1.5315537842954854,
                -2.751548643646431,
                -0.015610137402444435,
                5.310430264901309,
                3.9258282648416314,
                -1.5150869132344693,
                -1.1746833620968764,
                4.229749260795541,
                4.779322554591284,
                -0.731884941829396,
                -2.718211581134318,
                1.8520786542274326,
                4.168203667142645,
                -0.27770478945704025,
                -3.5885054347800214
              ],
              "metrics": {
                "initial_rmse_K": 2.9112183788720456,
                "observation_residual_rms_K": 0.014414491075732146,
                "future_predictive_rmse_K": 0.046234459894841914
              }
            },
            "tikhonov": {
              "coefficients_K": [
                4.642447752268116,
                1.0718169576226324,
                -0.11232529543141878,
                0.06059534110256671,
                0.0033898934539662545,
                -0.029894653545422496,
                0.0027238666145993967,
                0.003797487450106472
              ],
              "initial_K": [
                0.41306100277311764,
                0.8027667334115021,
                1.145996461182496,
                1.4198358346552817,
                1.6065448093001469,
                1.703002623833953,
                1.7217442088187838,
                1.676673919203972,
                1.5691371518847514,
                1.3943886660502927,
                1.1622702130476086,
                0.9050874926774195,
                0.6612902017856841,
                0.4533836959383903,
                0.2819209992368089,
                0.13521377657332082
              ],
              "metrics": {
                "initial_rmse_K": 0.12794375950626516,
                "observation_residual_rms_K": 0.020588327099369263,
                "future_predictive_rmse_K": 0.03667731959947725
              }
            },
            "learned": {
              "coefficients_K": [
                4.698734664021687,
                1.0979638264243299,
                -0.11672626732742193,
                0.05740726814647667,
                0.001058519850115983,
                -0.0029567492108568748,
                0.0004247696594202977,
                -0.0010252133549726262
              ],
              "initial_K": [
                0.423544133578037,
                0.819227921173505,
                1.1619479202555552,
                1.4332043861764134,
                1.6235537168200138,
                1.7309912928001896,
                1.7571189411258383,
                1.7052845751775463,
                1.5817050405652502,
                1.3973227336170522,
                1.1689077947432682,
                0.9191041069337258,
                0.6737792280864702,
                0.45523773096392994,
                0.2743371927555286,
                0.1274431174915119
              ],
              "metrics": {
                "initial_rmse_K": 0.11599848415622627,
                "observation_residual_rms_K": 0.015655607209650688,
                "future_predictive_rmse_K": 0.04625707977071159
              }
            }
          }
        },
        {
          "split": "test",
          "index": 26,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            6.5287372691079035,
            -0.056908109949892954,
            -0.585948894231754,
            -0.03780142717700538,
            -0.08439024445458593,
            -0.012358905128850904,
            0.020233371164114115,
            -0.04275300105504225
          ],
          "initial_K": [
            0.2550691555772773,
            0.5727083445459744,
            0.9506698802624346,
            1.3448294949131172,
            1.7223065127618422,
            2.0555572743139305,
            2.295252085346513,
            2.4003877910879545,
            2.382898366623391,
            2.2776277672809275,
            2.0802711646359175,
            1.766745616460929,
            1.3697174154078802,
            0.9765430935526446,
            0.6369842178073036,
            0.323434047999801
          ],
          "observed_K": [
            0.3193945659729517,
            0.6313787984207151,
            0.9498376620097778,
            1.2110668433069989,
            1.4694948241302006,
            1.6882553512223544,
            1.8894598057332326,
            1.9735928550428627,
            1.9640667873761541,
            1.8541834979955245,
            1.7264789884601333,
            1.5343663774947576,
            1.2492311270138208,
            0.9390708309426571,
            0.6816980914504653,
            0.3276768090486633
          ],
          "future_observed_K": [
            0.30429278088926304,
            0.5970587574166916,
            0.8863263477822441,
            1.1224488452239578,
            1.3743094012294275,
            1.6031042526419508,
            1.7345189079757914,
            1.764804028390547,
            1.7796495707594766,
            1.728806415514744,
            1.5862878280204276,
            1.3847990307439109,
            1.1765929625846694,
            0.9155003557146397,
            0.6126066555632347,
            0.3396665288761696
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.140732218190548,
                -0.07016080654248545,
                -0.4097980406081316,
                -0.030296492139468698,
                0.35470504473117115,
                0.6850581674833662,
                0.037305138443694756,
                -24.08424676174837
              ],
              "initial_K": [
                -7.608519918578404,
                -0.5981732026380865,
                8.876634879010119,
                3.9635843203226058,
                -6.059508361865923,
                -2.431047027404381,
                8.97040875916342,
                8.019473160656943,
                -3.357153789253379,
                -4.6753666910675555,
                6.115139169383454,
                9.08202469632199,
                -1.5009769255591368,
                -6.868296608507788,
                2.115767755078047,
                8.453368246987784
              ],
              "metrics": {
                "initial_rmse_K": 6.014849945850878,
                "observation_residual_rms_K": 0.010240496667983389,
                "future_predictive_rmse_K": 0.04324982248386781
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.066824847633962,
                -0.06864885294257264,
                -0.3869329778811192,
                -0.02452562799768492,
                0.14838381895868427,
                0.05192190106426059,
                0.0002335889547741926,
                -0.00785431942175736
              ],
              "initial_K": [
                0.35227724081923156,
                0.671377843449962,
                0.953163219769463,
                1.2279731159553293,
                1.5293622679345926,
                1.8472430581959907,
                2.115276027818687,
                2.2550755436061305,
                2.2352707055130274,
                2.0852406084690105,
                1.8586113575515915,
                1.5946192664069616,
                1.3102684886298006,
                1.0101075724254243,
                0.6924228430304689,
                0.3541046400063792
              ],
              "metrics": {
                "initial_rmse_K": 0.1399147525892099,
                "observation_residual_rms_K": 0.0234236097286572,
                "future_predictive_rmse_K": 0.028985067937312172
              }
            },
            "learned": {
              "coefficients_K": [
                6.1403814826346075,
                -0.07032353492862538,
                -0.4020932421363895,
                -0.023235273163008826,
                0.04633396888035266,
                0.005135367759478463,
                3.642671055622515e-05,
                0.002120442337519971
              ],
              "initial_K": [
                0.315310013176758,
                0.6300109704113546,
                0.948165335122754,
                1.273016258998137,
                1.595547044994665,
                1.8894170908127168,
                2.117181569564574,
                2.2429014435372805,
                2.245133310244359,
                2.1259622253156043,
                1.9105455333075296,
                1.6346272623451976,
                1.327894666044039,
                1.0061156073522095,
                0.6753037964914385,
                0.338873166670639
              ],
              "metrics": {
                "initial_rmse_K": 0.11314583404502768,
                "observation_residual_rms_K": 0.017040147291761606,
                "future_predictive_rmse_K": 0.04325407051527382
              }
            }
          }
        },
        {
          "split": "test",
          "index": 27,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            5.957312760882661,
            -2.3510480167926078,
            -0.35876480690229295,
            -0.33014295349320666,
            0.04855441761960698,
            0.06140967563426924,
            0.013760287624349882,
            -0.005853890030697762
          ],
          "initial_K": [
            -0.022225986887687954,
            0.00690321083042833,
            0.1418194080734232,
            0.4220935683995457,
            0.8384588286430119,
            1.3171593639604615,
            1.7524311555804308,
            2.069295586817411,
            2.2589529774167096,
            2.353579124262073,
            2.3732715262205692,
            2.3024475966668776,
            2.1087020296321395,
            1.7701540366202622,
            1.286073495746904,
            0.679250973902292
          ],
          "observed_K": [
            0.12879581072069357,
            0.3260819400845975,
            0.4891540555337721,
            0.6774249314400138,
            0.9941825349988072,
            1.2045615758058492,
            1.4623967467948955,
            1.6899243413907934,
            1.8406891276641324,
            1.966278834084288,
            1.8944818888616641,
            1.7813061495819658,
            1.5723774720337218,
            1.2218256706867896,
            0.8790397145224065,
            0.4848512382943329
          ],
          "future_observed_K": [
            0.16012363061191975,
            0.3309285335739922,
            0.5471841073841271,
            0.7450125019959538,
            0.9717337989822885,
            1.207868771863062,
            1.3699222419570183,
            1.5652875890270388,
            1.6843824596446997,
            1.7563000077859827,
            1.7311261408021827,
            1.6191413930185978,
            1.429398407163353,
            1.1171386923233697,
            0.8013731422389856,
            0.4276681539891963
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.5903913888454415,
                -1.8573218953206883,
                -0.30988601638076113,
                0.07298403459867656,
                0.08719498632484607,
                -0.774071476129438,
                3.2374896455213853,
                1.4679449313330912
              ],
              "initial_K": [
                1.4387259680666906,
                0.6872578021434628,
                -0.8194964389383079,
                -0.35905127993386043,
                1.669726364999071,
                2.4582485550427724,
                1.2985829869589818,
                0.547077131654562,
                1.7572336450505683,
                3.3464828376572404,
                3.1848717539923035,
                1.6623875784287663,
                0.7534594820194662,
                1.1520757729765452,
                1.7344865904903195,
                1.3378919777093907
              ],
              "metrics": {
                "initial_rmse_K": 0.928955497733041,
                "observation_residual_rms_K": 0.01981668197235018,
                "future_predictive_rmse_K": 0.029338320695336723
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.5231076980328355,
                -1.81729692034942,
                -0.29259563794885046,
                0.05908206382762756,
                0.036476292787819775,
                -0.0586683941714113,
                0.020271787049685384,
                0.0004787240596850115
              ],
              "initial_K": [
                0.08256700156539351,
                0.1944128181943191,
                0.35891383362466,
                0.585707408625652,
                0.8678409085283054,
                1.1886418137936823,
                1.5280663665265795,
                1.8559475031084627,
                2.121069072925551,
                2.2609633737695467,
                2.236842775722236,
                2.0608346642535373,
                1.7810062564773594,
                1.4354510275984502,
                1.0259788705876751,
                0.5413059254480651
              ],
              "metrics": {
                "initial_rmse_K": 0.20061559450862942,
                "observation_residual_rms_K": 0.027252259568146524,
                "future_predictive_rmse_K": 0.018132882252567355
              }
            },
            "learned": {
              "coefficients_K": [
                5.590072086690255,
                -1.8616296991995513,
                -0.3040597091053979,
                0.05597360818645837,
                0.011389998092528268,
                -0.0058026338356786875,
                0.0031612561477068033,
                -0.00012924184892882946
              ],
              "initial_K": [
                0.08201892340069247,
                0.19095060986238982,
                0.3503413525405974,
                0.5751242928814496,
                0.8657722895327605,
                1.2052093662827779,
                1.560277407794274,
                1.8868583853855596,
                2.13742548939306,
                2.270831725950117,
                2.262747579908844,
                2.111699888717085,
                1.835827804187598,
                1.4620666112262595,
                1.0162644559583869,
                0.521132155847472
              ],
              "metrics": {
                "initial_rmse_K": 0.18243465422469118,
                "observation_residual_rms_K": 0.021652519070436006,
                "future_predictive_rmse_K": 0.02944717508403575
              }
            }
          }
        },
        {
          "split": "test",
          "index": 28,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            5.655962654569335,
            2.779093117337611,
            -0.08398405134231095,
            0.16092454576813897,
            -0.18006023287756892,
            -0.020780863434476177,
            -0.020572540460693223,
            0.06688472410583254
          ],
          "initial_K": [
            0.6832248693314179,
            1.3075672552743929,
            1.8516081303642962,
            2.280662198521159,
            2.511044185283134,
            2.4935720629843487,
            2.298422269685895,
            2.0457627073067015,
            1.7737490023443212,
            1.4444396617103263,
            1.0593731719206438,
            0.6848175634349857,
            0.36493120142069635,
            0.09844687734351176,
            -0.08377164226844147,
            -0.11275873960000488
          ],
          "observed_K": [
            0.45739397529313425,
            0.94010959471797,
            1.3348706040441811,
            1.606252900124079,
            1.8009388905261507,
            1.852101661179675,
            1.8755903868377835,
            1.7310510807922892,
            1.5353098061922765,
            1.3188291575712194,
            1.1572347440103412,
            0.8595931044648482,
            0.5736153217323535,
            0.39875778795953515,
            0.24917013336287966,
            0.10039970729629374
          ],
          "future_observed_K": [
            0.4003713312685604,
            0.8173399662451657,
            1.1442676343897737,
            1.4073059081109682,
            1.6002454696558321,
            1.692997582943474,
            1.7027123804596624,
            1.6633393205438796,
            1.477729514950712,
            1.261608053569449,
            1.0596314247769343,
            0.8509519648504583,
            0.6522536848492151,
            0.44390891007651573,
            0.29179660625982634,
            0.1426839979553486
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.320975193046827,
                2.1631935719639954,
                -0.051328179143997274,
                0.22008850286221898,
                -0.3961436567772759,
                -0.2397021429036244,
                3.2846212501405203,
                -30.1365626572799
              ],
              "initial_K": [
                -8.74610553869928,
                -0.28402277955081323,
                10.816859755567663,
                4.844343903014982,
                -6.73139341880723,
                -2.1014765056614513,
                10.639345836703143,
                7.843149152089535,
                -6.216074842252353,
                -6.3407812672649895,
                7.802132752419195,
                10.31618673280763,
                -4.287297682181004,
                -10.5465199259506,
                2.495888040878746,
                11.348637251530754
              ],
              "metrics": {
                "initial_rmse_K": 7.5983685498740074,
                "observation_residual_rms_K": 0.01719769931980117,
                "future_predictive_rmse_K": 0.033025663545944134
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.256934086654015,
                2.116577113721619,
                -0.048464275661078714,
                0.1781661296930878,
                -0.16571884026464995,
                -0.018167495169722846,
                0.02056690516796903,
                -0.00982809185297095
              ],
              "initial_K": [
                0.5784845475745253,
                1.1298689139362748,
                1.6104040306281573,
                1.9664156888714786,
                2.1580816345059475,
                2.1789946546927714,
                2.0615441987755547,
                1.865212140340536,
                1.6445852586855882,
                1.4136229011116992,
                1.1459121703128843,
                0.8235294631905807,
                0.4837689942675445,
                0.20435370296503264,
                0.04117462682212969,
                -0.010494104528860626
              ],
              "metrics": {
                "initial_rmse_K": 0.19485571506490243,
                "observation_residual_rms_K": 0.028740028711215018,
                "future_predictive_rmse_K": 0.022199018664518375
              }
            },
            "learned": {
              "coefficients_K": [
                5.320671278932651,
                2.1682108033246528,
                -0.05036313481230866,
                0.16879236251180688,
                -0.05174696029253963,
                -0.0017968673537127934,
                0.003207277939640452,
                0.0026533046267950087
              ],
              "initial_K": [
                0.6211487167014963,
                1.1856458296517056,
                1.6475355939527572,
                1.9754714652868683,
                2.154049098342781,
                2.1879266580648573,
                2.102418378477132,
                1.931839896419493,
                1.7022379975444384,
                1.4257449236178477,
                1.1118289912560844,
                0.7819446868164147,
                0.47263148860607995,
                0.22520858687386536,
                0.06895672745605885,
                0.005128365211791164
              ],
              "metrics": {
                "initial_rmse_K": 0.17823888811068203,
                "observation_residual_rms_K": 0.02423441999548438,
                "future_predictive_rmse_K": 0.03251853602719576
              }
            }
          }
        },
        {
          "split": "test",
          "index": 29,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            6.608043060768968,
            0.29341304963263093,
            -0.5652863008777103,
            0.29211979222911494,
            0.08191861570761154,
            -0.09064712211537529,
            -0.013020152688873845,
            -0.01960056688216214
          ],
          "initial_K": [
            0.40186272394278105,
            0.8114007369206384,
            1.1955006738578815,
            1.512390362690192,
            1.7688773707080119,
            2.010344937185019,
            2.25188397793415,
            2.442536336458542,
            2.501618338619069,
            2.3764960131968342,
            2.072004526627692,
            1.6509180340149265,
            1.2104804528416047,
            0.8310470338531757,
            0.5283559087710069,
            0.2632013708606279
          ],
          "observed_K": [
            0.31538375215068837,
            0.6683922903622714,
            1.010230540610524,
            1.3057384270862669,
            1.5567489552670275,
            1.7381274973459675,
            1.9023575414797915,
            1.9732608135589542,
            1.9567426184181727,
            1.8875796981217614,
            1.6702857005445553,
            1.475716294071772,
            1.2109358813170845,
            0.9203257599624319,
            0.6210040572552523,
            0.3292285696634907
          ],
          "future_observed_K": [
            0.35818292791664685,
            0.6689182374578575,
            1.0088502801177377,
            1.2500293580688362,
            1.4602533366011405,
            1.6488113541372347,
            1.7480715934366307,
            1.7918651709551103,
            1.785151059365909,
            1.699507035502406,
            1.58343011476074,
            1.3646009891556976,
            1.116399004779363,
            0.9130538239002751,
            0.5867137404276255,
            0.28157189377530295
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                6.180471473399578,
                0.17545972516219763,
                -0.36674311436680523,
                -0.00013551030915230487,
                0.10417451519849007,
                -1.0654381593679243,
                -3.0548260326437924,
                -7.684842896678095
              ],
              "initial_K": [
                -3.586033166657964,
                -0.5995126729867742,
                4.365765790239661,
                3.6105097159666975,
                -0.6372847413993445,
                -0.6181959580341123,
                3.523079498399497,
                4.694451510308573,
                1.5055012718912328,
                -0.019554961345872757,
                2.3249110886966537,
                3.4735879411232764,
                0.883313462644661,
                -0.9467182192326473,
                0.8714325181079982,
                2.2740801900966856
              ],
              "metrics": {
                "initial_rmse_K": 2.08087720212301,
                "observation_residual_rms_K": 0.009831113101517259,
                "future_predictive_rmse_K": 0.041143590653073756
              }
            },
            "tikhonov": {
              "coefficients_K": [
                6.106085817232088,
                0.17167859754733686,
                -0.34628034128411106,
                -0.00010969835771155353,
                0.0435793418586331,
                -0.08075164610329601,
                -0.01912802497863036,
                -0.0025061697554269345
              ],
              "initial_K": [
                0.3235281801029746,
                0.6785476888700025,
                1.0526951349365252,
                1.399767096684872,
                1.6868956892408087,
                1.9165944032951279,
                2.098951785512697,
                2.2151231907469358,
                2.221459295793177,
                2.0906731192438883,
                1.8434551948340174,
                1.537800837355003,
                1.22861121594075,
                0.9354988934249102,
                0.6438033235734107,
                0.33233485804907253
              ],
              "metrics": {
                "initial_rmse_K": 0.15851643872789759,
                "observation_residual_rms_K": 0.022023529395963793,
                "future_predictive_rmse_K": 0.03150936998142867
              }
            },
            "learned": {
              "coefficients_K": [
                6.180118468086665,
                0.1758666799752229,
                -0.35984781105373415,
                -0.0001039268518303385,
                0.01360797884617311,
                -0.007986791535434055,
                -0.00298289373349169,
                0.0006765943895404144
              ],
              "initial_K": [
                0.34681585654342206,
                0.6976699000452345,
                1.0496361550712288,
                1.390646180293306,
                1.7022761148016965,
                1.963355200849877,
                2.151356966494226,
                2.2439287937734336,
                2.224931801022491,
                2.093608417393644,
                1.8687458667382641,
                1.5820939385111388,
                1.2654283034686529,
                0.9411370511306594,
                0.6207508231448237,
                0.30772475511072395
              ],
              "metrics": {
                "initial_rmse_K": 0.14503173453015006,
                "observation_residual_rms_K": 0.014383562866514144,
                "future_predictive_rmse_K": 0.040859874223949884
              }
            }
          }
        },
        {
          "split": "test",
          "index": 30,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            6.022028047866522,
            -1.3518810968495025,
            -0.3362361886406321,
            -0.01624701096388649,
            -0.04467320659660451,
            0.09172452114367745,
            -0.04042773839908142,
            -0.006286635853356148
          ],
          "initial_K": [
            0.14802113806900288,
            0.32765810602114964,
            0.5531028781478615,
            0.8277712050695261,
            1.1532013276091881,
            1.5122574316071133,
            1.8504934397237065,
            2.099827152952207,
            2.2301773177725353,
            2.262625035780819,
            2.2211450368197734,
            2.0855656871931223,
            1.812208476008304,
            1.3995701020447804,
            0.9141088560476243,
            0.43850730361187956
          ],
          "observed_K": [
            0.21328054929274085,
            0.4605544235406871,
            0.6999684482395552,
            0.904990888063684,
            1.1645248619426967,
            1.3442057879450422,
            1.5946142923345659,
            1.7677799365160003,
            1.8152182099191692,
            1.8457852812789866,
            1.7926026828146226,
            1.621361312192012,
            1.4312793930320873,
            1.1465428098472363,
            0.7328168978679074,
            0.40659684771570104
          ],
          "future_observed_K": [
            0.24157582335724867,
            0.4364602794859018,
            0.7074283342713316,
            0.926260223752123,
            1.0950094648842672,
            1.3541955084772235,
            1.4885902001892344,
            1.5768209129906188,
            1.6651940249609505,
            1.6782793264547118,
            1.6203712444279834,
            1.4965628921018794,
            1.2814873476846895,
            0.9758571297032849,
            0.7323075552516312,
            0.3282516427138529
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.678237110593214,
                -1.0767113777943962,
                -0.19711451986594045,
                0.09871664822634384,
                0.12910524701051107,
                0.822278719840672,
                -3.9767458556862794,
                -6.736197281892428
              ],
              "initial_K": [
                -3.1130897141850546,
                -0.4469955158282351,
                3.759793179743609,
                2.657714180362004,
                -1.3962361583501415,
                -1.0738837639921197,
                3.3341435976635228,
                4.757439864656845,
                1.5075314099268387,
                -0.4657090382986724,
                1.8095507610131452,
                3.866395735680051,
                2.2539878581093054,
                0.025995235127814986,
                0.3821388447218583,
                1.2044462739939863
              ],
              "metrics": {
                "initial_rmse_K": 1.961770375146174,
                "observation_residual_rms_K": 0.0178747160812606,
                "future_predictive_rmse_K": 0.04294216471778404
              }
            },
            "tikhonov": {
              "coefficients_K": [
                5.609896144185722,
                -1.0535084283993157,
                -0.18611633194280808,
                0.07991313913281611,
                0.054008618945758056,
                0.06232211564699121,
                -0.02490069589835191,
                -0.00219679883134182
              ],
              "initial_K": [
                0.232845277147617,
                0.4520430829892723,
                0.6570331310695463,
                0.8682002989745952,
                1.1153904997477997,
                1.405797409917481,
                1.7011733322081681,
                1.936230418215581,
                2.06530799232022,
                2.086926255957398,
                2.02060166021343,
                1.8695129275918765,
                1.6183212396407765,
                1.2666274119335932,
                0.8504969507363979,
                0.42021294455216196
              ],
              "metrics": {
                "initial_rmse_K": 0.1372775748957864,
                "observation_residual_rms_K": 0.026067262562403756,
                "future_predictive_rmse_K": 0.03173017468312027
              }
            },
            "learned": {
              "coefficients_K": [
                5.677912791020404,
                -1.0792086624392194,
                -0.19340848054674917,
                0.07570870834540035,
                0.016864599435874823,
                0.006164007419526957,
                -0.003883105016736265,
                0.0005930730594031973
              ],
              "initial_K": [
                0.21213637250828865,
                0.4272025134933184,
                0.6509422637048659,
                0.891313580464401,
                1.1532288627064118,
                1.4307999696272138,
                1.7022672827701424,
                1.9328249241721538,
                2.0856698347740332,
                2.1346065563186625,
                2.069808343772168,
                1.8951233953101418,
                1.6231573495309692,
                1.273382103679063,
                0.8707969569332317,
                0.44039561943845934
              ],
              "metrics": {
                "initial_rmse_K": 0.12096267985889939,
                "observation_residual_rms_K": 0.020795465917888438,
                "future_predictive_rmse_K": 0.04285252262523909
              }
            }
          }
        },
        {
          "split": "test",
          "index": 31,
          "scenario": "wrong-diffusivity",
          "true_kappa_m2_per_s": 0.016,
          "coefficients_K": [
            5.377356295188499,
            0.7716874304292267,
            -1.1237860672550566,
            -0.24010557718598957,
            0.019814182809407426,
            -0.003852254828625139,
            -0.0564822158563766,
            0.04301894278658247
          ],
          "initial_K": [
            0.17642749503288802,
            0.41554399494937866,
            0.7599238282098529,
            1.1931060799661073,
            1.6343433249125352,
            1.9957398848396755,
            2.227909024659861,
            2.296584926823459,
            2.1610847818172205,
            1.8279680797885427,
            1.400286833220606,
            1.010272127251759,
            0.7043754304123903,
            0.4453892485518376,
            0.21960228221239542,
            0.06914168026504514
          ],
          "observed_K": [
            0.2895944149450045,
            0.5780643232629721,
            0.832340584135926,
            1.1150297887066227,
            1.353936512045205,
            1.4807018912650722,
            1.6518264849277073,
            1.7221203048236875,
            1.6306263313107472,
            1.4808111866323364,
            1.316874820001951,
            1.1004877017386088,
            0.8718967836190558,
            0.6219886659960425,
            0.4117495219994788,
            0.1785694392019118
          ],
          "future_observed_K": [
            0.2734457917000385,
            0.5483028433800821,
            0.8156827700313378,
            1.0474969214833645,
            1.2329396691169692,
            1.4144620270234831,
            1.484717432388622,
            1.5299173063988343,
            1.5009299787746626,
            1.4200436431286991,
            1.2239085661489224,
            1.0353556974081757,
            0.8543447380457909,
            0.6536431774401825,
            0.40413062062858507,
            0.20657692346833748
          ],
          "x_m": [
            0.058823529411764705,
            0.11764705882352941,
            0.17647058823529413,
            0.23529411764705882,
            0.29411764705882354,
            0.35294117647058826,
            0.4117647058823529,
            0.47058823529411764,
            0.5294117647058824,
            0.5882352941176471,
            0.6470588235294118,
            0.7058823529411765,
            0.7647058823529411,
            0.8235294117647058,
            0.8823529411764706,
            0.9411764705882353
          ],
          "estimators": {
            "least_squares": {
              "coefficients_K": [
                5.058627701959266,
                0.5415556230436421,
                -0.6640225336894152,
                -0.04025118644745678,
                0.21525243162897395,
                0.796366378948478,
                -4.074944424735587,
                -6.46246731097351
              ],
              "initial_K": [
                -2.991333037068339,
                -0.3197985485616063,
                3.891974917280372,
                2.9198989114480396,
                -1.0102996378341575,
                -0.7531356930644861,
                3.4819813570693414,
                4.804465722801947,
                1.451997701580617,
                -0.8200628105774743,
                1.0602797725904551,
                2.9543363723727705,
                1.4790390323277283,
                -0.5821449390408824,
                -0.16394270566551566,
                0.8183407927508661
              ],
              "metrics": {
                "initial_rmse_K": 1.929277856190697,
                "observation_residual_rms_K": 0.015316678328805625,
                "future_predictive_rmse_K": 0.025691322582141345
              }
            },
            "tikhonov": {
              "coefficients_K": [
                4.997744103913905,
                0.5298851903025641,
                -0.6269727789799318,
                -0.03258415597196243,
                0.09004658467560663,
                0.06035816854876094,
                -0.025515573688958956,
                -0.0021075304125212574
              ],
              "initial_K": [
                0.2939445645349459,
                0.5795427930621132,
                0.8560045475385218,
                1.1340876626964265,
                1.4240238068918463,
                1.7073797133395319,
                1.9230394557343684,
                1.99719109085844,
                1.8995526806284506,
                1.6692906403758796,
                1.3816063512796783,
                1.0918235752061909,
                0.8155497824771379,
                0.5546696344480812,
                0.32413627010746515,
                0.14206769375695322
              ],
              "metrics": {
                "initial_rmse_K": 0.177572735628375,
                "observation_residual_rms_K": 0.02347794219500638,
                "future_predictive_rmse_K": 0.01586501256380692
              }
            },
            "learned": {
              "coefficients_K": [
                5.058338772148244,
                0.5428116871752527,
                -0.6515379454391145,
                -0.030869821758125766,
                0.028117726591895455,
                0.005969762016280057,
                -0.00397899129409705,
                0.0005689731311336346
              ],
              "initial_K": [
                0.26969452697330537,
                0.5518206422868593,
                0.8528891482490759,
                1.1680694848067747,
                1.477418636130328,
                1.7459155101523949,
                1.929971252933771,
                1.9912440612600284,
                1.9132792872812032,
                1.711223224675351,
                1.4267082694636548,
                1.1105292513323415,
                0.8052632494650876,
                0.537588139864296,
                0.3187058713004184,
                0.14539249537547927
              ],
              "metrics": {
                "initial_rmse_K": 0.16311004435893642,
                "observation_residual_rms_K": 0.018922888052873562,
                "future_predictive_rmse_K": 0.025614343592607523
              }
            }
          }
        }
      ]
    }
  },
  "metrics": {
    "smooth": {
      "least_squares": {
        "initial_rmse_K": 3.254382127718899,
        "observation_residual_rms_K": 0.014445050343379147,
        "future_predictive_rmse_K": 0.0222684484954585
      },
      "tikhonov": {
        "initial_rmse_K": 0.05289324372597765,
        "observation_residual_rms_K": 0.024607679504609622,
        "future_predictive_rmse_K": 0.028315966279206226
      },
      "learned": {
        "initial_rmse_K": 0.04331003310337809,
        "observation_residual_rms_K": 0.01782575143945636,
        "future_predictive_rmse_K": 0.022201657291904067
      }
    },
    "high-frequency": {
      "least_squares": {
        "initial_rmse_K": 3.254382127718902,
        "observation_residual_rms_K": 0.014445050343379147,
        "future_predictive_rmse_K": 0.022268448495458466
      },
      "tikhonov": {
        "initial_rmse_K": 1.3820029324094485,
        "observation_residual_rms_K": 0.04826468141843445,
        "future_predictive_rmse_K": 0.029209058638945747
      },
      "learned": {
        "initial_rmse_K": 1.488879914713517,
        "observation_residual_rms_K": 0.048019780173973584,
        "future_predictive_rmse_K": 0.02349474254128526
      }
    },
    "wrong-diffusivity": {
      "least_squares": {
        "initial_rmse_K": 3.2571620736398725,
        "observation_residual_rms_K": 0.014445050343379163,
        "future_predictive_rmse_K": 0.04503604072367534
      },
      "tikhonov": {
        "initial_rmse_K": 0.1557817559349342,
        "observation_residual_rms_K": 0.023608790520425364,
        "future_predictive_rmse_K": 0.033189200412532156
      },
      "learned": {
        "initial_rmse_K": 0.13715733720481477,
        "observation_residual_rms_K": 0.017689253211618756,
        "future_predictive_rmse_K": 0.04508826112890616
      }
    }
  }
}
