Эксперимент: Diffeomorphic gauge-fixing layer (#1354)

{ "worked": false, "confidence": 9, "verdict": "Built a self-contained PyTorch MVP with differentiable grid-sampled gauge transforms, a learned bounded translation gauge, canonical-space dynamics, and explicit group-action checks. Composition and inverse-cycle errors were small but nonzero due to bilinear interpolation and zero padding. The gauge model improved equivariance error (0.0272 vs 0.0333) but worsened one-step MSE (1.45e-5 vs 8.59e-6) and 20-step rollout MSE (0.0296 vs 0.0294), with higher runtime and parameter count; the claimed overall win was not observed.", "metrics": { "baseline": "one-step MSE 8.5903e-06; 20-step MSE 0.0294243; equivariance error 0.0332526; 17.88 s; 2,881 parameters", "idea": "one-step MSE 1.4466e-05; 20-step MSE 0.0295656; equivariance error 0.0271641; 20.74 s; 3,107 parameters", "math_sanity": "translation composition absolute error 0.001642; inverse-cycle absolute error 0.002603" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py" ], "limitations": "This tests a small translation-only proxy rather than a full 2D stationary-velocity diffeomorphism with scaling-and-squaring, Jacobian/Laplacian regularization, or a U-Net. Only one seed and one toy advection law were tested; no warp-amplitude sweep, sample-efficiency study, FLOP accounting, or repeated-seed analysis was performed. CUDA grid sampling failed in the shared environment, so the run used CPU fallback." }