Harmonic-coordinate neural PDE ansatz / results.json

Mechanism confirmed, baseline not beaten

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 1{
 2  "device": "cuda",
 3  "verification": {
 4    "exact_identity_max_abs": 0.0,
 5    "sweep": [
 6      {
 7        "eps": 0.001,
 8        "harmonic": 0.0020000000000000005,
 9        "null_gradient": 0.002064516129032131
10      },
11      {
12        "eps": 0.002,
13        "harmonic": 0.004000000000000001,
14        "null_gradient": 0.0041290322580645345
15      },
16      {
17        "eps": 0.005,
18        "harmonic": 0.010000000000000002,
19        "null_gradient": 0.010322580645161243
20      },
21      {
22        "eps": 0.01,
23        "harmonic": 0.020000000000000004,
24        "null_gradient": 0.02064516129032261
25      },
26      {
27        "eps": 0.02,
28        "harmonic": 0.04000000000000001,
29        "null_gradient": 0.04129032258064519
30      },
31      {
32        "eps": 0.05,
33        "harmonic": 0.10000000000000002,
34        "null_gradient": 0.10322580645161296
35      },
36      {
37        "eps": 0.1,
38        "harmonic": 0.20000000000000004,
39        "null_gradient": 0.20645161290322583
40      }
41    ],
42    "predicted_null_rms_linear_coefficient": 2.3851391759997758,
43    "observed_small_eps_coefficient": 2.0645161290322687,
44    "observed_loglog_scaling_exponent": 1.000000000000008,
45    "predictions": {
46      "harmonic stays zero": true,
47      "null residual O(eps)": true
48    }
49  },
50  "comparison": {
51    "baseline": {
52      "test_mse": 6.722121775072217e-05,
53      "mean_abs_laplacian": 0.04380471542922677,
54      "coordinate_constraint_rms": null
55    },
56    "ansatz": {
57      "test_mse": 0.0002556193802863314,
58      "mean_abs_laplacian": 0.08745113206507407,
59      "coordinate_constraint_rms": 0.09147510471012323
60    }
61  }
62}