1{
  2  "seed": 2112,
  3  "prediction_1_invariant_rate_sweep": {
  4    "predicted": "cy=beta*r and cv=r-alpha-beta for every alpha,beta",
  5    "observed_max_relative_error": 1.4083093304007887e-05,
  6    "observed_median_relative_error": 1.6870765728287866e-06,
  7    "n_cases": 16
  8  },
  9  "prediction_2_sampling_transition": {
 10    "predicted": "error small for dt/tau << 1 and degrades around dt/tau >= 1",
 11    "tau": 1.0,
 12    "low_ratio_mean_error": 0.0009303153894811214,
 13    "high_ratio_mean_error": 0.10820631719160569,
 14    "sweep": [
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 18        "coefficient_relative_error": 0.00013315723463044744,
 19        "accel_rmse": 1.1846516644818186e-11,
 20        "cy_hat": 0.07999066816862406,
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 23      {
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 25        "dt": 0.1,
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 27        "accel_rmse": 2.7464752330039324e-12,
 28        "cy_hat": 0.07996269068665479,
 29        "cv_hat": -0.7995736062231972
 30      },
 31      {
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 33        "dt": 0.2,
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 35        "accel_rmse": 6.374175943378787e-13,
 36        "cy_hat": 0.07985105024170594,
 37        "cv_hat": -0.7982976911113664
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 39      {
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 41        "dt": 0.5,
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 43        "accel_rmse": 1.0067963272324585e-13,
 44        "cy_hat": 0.07908144949942851,
 45        "cv_hat": -0.7895012808996074
 46      },
 47      {
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 49        "dt": 1.0,
 50        "coefficient_relative_error": 0.05006925447611736,
 51        "accel_rmse": 3.136028771182511e-14,
 52        "cy_hat": 0.07649240096067265,
 53        "cv_hat": -0.7598979245104208
 54      },
 55      {
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 57        "dt": 1.5,
 58        "coefficient_relative_error": 0.10479490743231888,
 59        "accel_rmse": 2.5002513533779513e-14,
 60        "cy_hat": 0.07266203408466589,
 61        "cv_hat": -0.7160660893307482
 62      },
 63      {
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 65        "dt": 2.0,
 66        "coefficient_relative_error": 0.16975478966638083,
 67        "accel_rmse": 8.169194722800014e-15,
 68        "cy_hat": 0.0681211245747312,
 69        "cv_hat": -0.6640367702678235
 70      }
 71    ]
 72  },
 73  "prediction_3_rollout": {
 74    "predicted": "second-order reduced dynamics has lower long-horizon error than first-order y_dot=k*y",
 75    "reduced_rmse": 0.059759421047770135,
 76    "first_order_rmse": 0.9970232315267102,
 77    "reduced_tail_rmse": 0.08260127529890765,
 78    "first_order_tail_rmse": 1.4071777995230332,
 79    "reduced_coefficients": [
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 84    "fit_accel_rmse": 0.36248977089418594
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100      "cy_hat": 0.024000004621973325,
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248}