Piola-Conditioned Fixed-Reference Neural Operator / report_bench_2026-09-02T171534.md
Mechanism confirmed, baseline not beaten
Стенд-проверка (stage-2) · промт оператора:
(универсальный)
Ответ агента:
{ "worked": false, "confidence": 9, "verdict": "On the registered spherical_incompressible_field geometry-PDE track, the Piola-style tangent-frame system achieved MSE 717.96 versus the tuned raw-Cartesian baseline MSE 663.23. The paired delta was +54.72 with permutation p=0.7248, so there was no significant win; the benchmark verdict is no significant win. The mechanism signature did confirm reduced predicted normal leakage, but this did not translate into improved physical-field task error.", "metrics": { "baseline": "Best lr=0.01; full 8-seed MSE 663.2344 +/- 227.7878.", "idea": "Best lr=0.01; full 8-seed MSE 717.9575 +/- 296.0030.", "comparison": "Paired delta=+54.7232; idea wins 3/8; permutation p=0.7248; verdict=no significant win.", "math_check": "Registered target tangency max absolute error 7.11e-15.", "mechanism_signature": "Predicted normal leakage baseline=2.23888, idea=1.03e-7; target=9.91e-16; physical RMSE baseline=26.2316, idea=26.0998; confirmed=true." }, "bench_report": { "bench_version": 1, "track": "spherical_incompressible_field", "model": "mlp_tiny", "metric_direction": "lower is better", "n_seeds": 8, "baseline": { "best_cfg": { "lr": 0.01 }, "sweep": [ { "cfg": { "lr": 0.001 }, "mean": 741.4911766052246 }, { "cfg": { "lr": 0.003 }, "mean": 741.5560569763184 }, { "cfg": { "lr": 0.01 }, "mean": 728.7486572265625 } ], "full": { "mean": 663.2343521118164, "std": 227.7878314808697, "per_seed": [ 793.9498901367188, 280.86212158203125, 481.156982421875, 789.7786865234375, 987.4510498046875, 526.4219360351562, 912.3746337890625, 533.8795166015625 ], "n": 8 }, "parity_grid": [ { "lr": 0.001 }, { "lr": 0.003 }, { "lr": 0.01 } ], "idea_grid": [ { "cfg": { "lr": 0.001 }, "mean": 740.4760437011719 }, { "cfg": { "lr": 0.003 }, "mean": 738.7110366821289 }, { "cfg": { "lr": 0.01 }, "mean": 717.9575424194336 } ] }, "idea": { "mean": 717.9575424194336, "std": 296.00301643635, "per_seed": [ 681.2006225585938, 882.7847290039062, 621.8972778320312, 257.99969482421875, 429.0736083984375, 1037.055419921875, 1222.8154296875, 610.8335571289062 ], "n": 8 }, "comparison": { "delta_mean": 54.72319030761719, "idea_wins": 3, "n_pairs": 8, "per_seed_diffs": [ -112.749267578125, 601.922607421875, 140.74029541015625, -531.7789916992188, -558.37744140625, 510.63348388671875, 310.4407958984375, 76.95404052734375 ], "p_value": 0.7248, "mde": 364.2640562876808, "mde_rel_pct": 54.92237474247542, "verdict": "no significant win", "system_worked": false }, "protocol_notes": { "seeds": [ 11, 29, 47, 71, 89, 107, 131, 149 ], "epochs": 16, "batch": 64, "same_architecture": true, "same_lr_union": true }, "registered_track": true, "mechanism_signature": { "predicted_effect": "tangent-frame pullback should reduce normal leakage and preserve tangent coefficients", "baseline": { "predicted": "tangent-frame output should suppress normal component while preserving physical tangent field", "observed_prediction_normal_abs": 2.2388789768045623, "observed_target_normal_abs": 9.906461976316845e-16, "observed_physical_rmse": 26.23157866813025, "confirmed": false }, "idea": { "predicted": "tangent-frame output should suppress normal component while preserving physical tangent field", "observed_prediction_normal_abs": 1.0321635254573538e-07, "observed_target_normal_abs": 9.906461976316845e-16, "observed_physical_rmse": 26.099807644674723, "confirmed": true }, "confirmed": true } }, "how_to_run": "/home/maxwelhelp/main/bin/python3 registered_bench.py", "files": [ "registered_bench.py", "registered_bench_report.json", "registered_stdout.txt" ], "limitations": "The registered track tests tangent vector-field regression on the sphere rather than deformed surfaces, remeshing, Maxwell EFIE, or a full neural operator. The implementation uses a deterministic tangent-frame coefficient representation as a proxy for Piola pullback because the registered track provides sphere coordinates and tangent vector targets but no deformation coefficients or surface Jacobians. Throughput, memory, larger meshes, stronger shape changes, and graph/Fourier operator architectures were not tested.", "system_verdict": "partial", "practical_verdict": "inconclusive", "mechanism_ok": 1, "system_judged": true }