Эксперимент: Energy-Derived Nitsche Neural Fields (#1275)

{ "worked": false, "confidence": 9, "verdict": "Built a two-patch 1D Poisson MVP with AD-computed bulk energy, symmetric Nitsche boundary/interface terms, and a p=1 derivative-jump ghost penalty, alongside a strong-residual point-penalty baseline. The math check passed the F/P identity, showed nonnegative ghost energy, and showed Nitsche coercivity becoming positive as gamma increased (negative at gamma <=1, positive from gamma=2 onward). However, at equal 900 Adam steps the proposed objective had worse boundary RMS (0.01745 vs 0.000129) and max solution error (0.2523 vs 0.2501), while only slightly improving the derivative jump (0.00164 vs 0.00186); therefore the claimed training/accuracy win was not observed.", "metrics": { "baseline": "max_error=0.25013, boundary_rms=1.2868e-4, interface_value_jump=2.1046e-4, interface_derivative_jump=1.8617e-3, final_loss=0.002065, 900 steps in 24.52s", "idea": "max_error=0.25232, boundary_rms=1.7446e-2, interface_value_jump=1.4547e-3, interface_derivative_jump=1.6387e-3, final_energy=-0.167142, 900 steps in 25.65s" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "article.md", "idea_context.json" ], "limitations": "Only a small 1D two-patch Poisson test was run; no curved or moving cut-cell geometry, 2D/3D fields, finite-strain hyperelasticity, sliver-cell study, translation robustness, parameter sweeps, or equal-FLOP normalization was tested. The max error is also limited by the simple tiny-network setup and was not compared across multiple random seeds." }