Эксперимент: Exact Elasticity-Complex Message Passing (#1178)

{ "worked": true, "confidence": 8, "verdict": "Built a reproducible simplicial-complex MVP with deterministic incidence operators D0, D1, and D2, plus a toy defect-regression comparison. The algebraic guarantee was observed exactly: relative residuals for D1D0 and D2D1 were both 0.0, and compatible-field leakage was 9.4e-17 versus 8.36 for an unconstrained cross-order map. The exact operator did not improve the toy regression MSE (0.00226 versus 0.000282), so this demonstrates the claimed structural cancellation but not an end-to-end accuracy win.", "metrics": { "baseline": "Unconstrained random edge-to-face map: compatible leakage 8.3618; toy MSE 0.0002822; accuracy 1.0", "idea": "Incidence complex: relative ||D1D0||/||D0|| = 0.0, relative ||D2D1||/||D1|| = 0.0; compatible leakage 9.399e-17; toy MSE 0.0022564; accuracy 1.0" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 complex_mvp.py", "files": [ "complex_mvp.py", "result.txt" ], "limitations": "This is an algebraic simplicial incidence prototype, not a full 3D elasticity complex with symmetric-tensor geometry-aware finite-element operators, physical elasticity data, remeshing, rollout evaluation, sparse GPU execution, or matched-parameter MeshGraphNet. The learned toy task is small and synthetic, and the unconstrained baseline is a random linear cross-order map rather than a full standard MeshGraphNet." }