Эксперимент: Hodge-dual electrostatic loss (#519)

{ "worked": true, "confidence": 8, "verdict": "Built a periodic-grid Hodge-dual electrostatic loss with p=p0+curl(A), anisotropic positive dielectric energy, and exact discrete divergence preservation. The mechanism checks passed: div(curl A) was <=7.45e-9 even at amplitude 1e4, lambda_maxepsilon had 0% spread across epsilon={0.5,1,2,4}, and the gradient-descent transition occurred near the predicted etalambda_max=2 boundary. The toy primal and dual quadratic problems had identical nonzero condition numbers, so no universal speedup was observed.", "metrics": { "baseline": "Primal/dual constant-coefficient condition number: 29.8564; no measured conditioning or speed advantage.", "idea": "Maximum discrete Gauss residual 7.45e-9; epsilon*lambda_max=[2,2,2,2], relative spread 0%; GD final/initial energy ratios at eta/critical=[0.9,0.99,1.01,1.1] were [2.39e-6,0.310,3.154,39130.2]." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "hodge_dual.py", "run_experiment.py", "results.json" ], "limitations": "Only a small 2-D periodic finite-difference toy was tested, with constant dielectric scaling and a hand-constructed flux/potential rather than trained neural networks. Boundary conditions, nonconstant anisotropic dielectric fields, manufactured nonzero charge solves, wall-clock comparisons, alternating theta/psi optimization, and CUDA behavior were not tested." }