Harmonic-coordinate neural PDE ansatz / results.json
Mechanism confirmed, baseline not beaten
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}