Adjoint-Weak Fractional Residuals / results.json

Mechanism confirmed, baseline not beaten

Raw ⬇ ZIP
  1{
  2  "identity": {
  3    "absolute_error": 1.1102230246251565e-15,
  4    "relative_error": 4.844199237277392e-16
  5  },
  6  "noise_sweep": [
  7    {
  8      "sigma": 0.01,
  9      "weak_var": 1.0987736314266595e-06,
 10      "strong_var": 1.201534342010772,
 11      "weak_over_sigma2": 0.010987736314266595,
 12      "strong_over_sigma2": 12015.34342010772
 13    },
 14    {
 15      "sigma": 0.03,
 16      "weak_var": 9.760296489794363e-06,
 17      "strong_var": 10.571606361267328,
 18      "weak_over_sigma2": 0.010844773877549292,
 19      "strong_over_sigma2": 11746.229290297031
 20    },
 21    {
 22      "sigma": 0.1,
 23      "weak_var": 0.00011386842570602395,
 24      "strong_var": 117.54051836897834,
 25      "weak_over_sigma2": 0.011386842570602393,
 26      "strong_over_sigma2": 11754.051836897832
 27    },
 28    {
 29      "sigma": 0.3,
 30      "weak_var": 0.0009508139823884562,
 31      "strong_var": 1069.144552599165,
 32      "weak_over_sigma2": 0.01056459980431618,
 33      "strong_over_sigma2": 11879.383917768502
 34    }
 35  ],
 36  "resolution_sweep": [
 37    {
 38      "n": 65,
 39      "weak_norm2": 0.0426451257271337,
 40      "strong_norm2": 1278.9461337839193
 41    },
 42    {
 43      "n": 129,
 44      "weak_norm2": 0.0214493667474359,
 45      "strong_norm2": 3877.0424606504353,
 46      "weak_ratio_prev": 0.5029734672300044,
 47      "strong_ratio_prev": 3.031435303048869
 48    },
 49    {
 50      "n": 257,
 51      "weak_norm2": 0.010815577523155226,
 52      "strong_norm2": 11752.9963674464,
 53      "weak_ratio_prev": 0.5042376145882321,
 54      "strong_ratio_prev": 3.031433492599575
 55    },
 56    {
 57      "n": 513,
 58      "weak_norm2": 0.005476211334172537,
 59      "strong_norm2": 35628.42329918625,
 60      "weak_ratio_prev": 0.5063262985678237,
 61      "strong_ratio_prev": 3.0314331924640356
 62    }
 63  ],
 64  "coefficient_fit": [
 65    {
 66      "sigma": 0.01,
 67      "weak_rmse": 0.007329275429032863,
 68      "strong_rmse": 0.1474187070497865,
 69      "weak_noiseless": -0.8849544248348283,
 70      "strong_noiseless": -1.1217589725862713
 71    },
 72    {
 73      "sigma": 0.03,
 74      "weak_rmse": 0.020556991326393284,
 75      "strong_rmse": 0.4889786655378507,
 76      "weak_noiseless": -0.8849544248348283,
 77      "strong_noiseless": -1.1217589725862713
 78    },
 79    {
 80      "sigma": 0.1,
 81      "weak_rmse": 0.0664286302349654,
 82      "strong_rmse": 1.730385220597502,
 83      "weak_noiseless": -0.8849544248348283,
 84      "strong_noiseless": -1.1217589725862713
 85    },
 86    {
 87      "sigma": 0.3,
 88      "weak_rmse": 0.218730328650216,
 89      "strong_rmse": 10.361216350665623,
 90      "weak_noiseless": -0.8849544248348283,
 91      "strong_noiseless": -1.1217589725862713
 92    }
 93  ],
 94  "predictions": {
 95    "noise_linearity": "weak variance / sigma^2 should be constant",
 96    "weak_resolution_ratio_predicted": 0.5,
 97    "strong_resolution_ratio_predicted": 3.0314331330207964,
 98    "observed_weak_ratios": [
 99      0.5029734672300044,
100      0.5042376145882321,
101      0.5063262985678237
102    ],
103    "observed_strong_ratios": [
104      3.031435303048869,
105      3.031433492599575,
106      3.0314331924640356
107    ],
108    "identity_tolerance": "machine precision"
109  }
110}