{"id": "mesh_deformation", "title": "Differentiable mesh deformation", "description": "Surface displacements are propagated to all high-order geometry nodes by inverse-distance weighting. The study deforms a NACA 0012 O-mesh with a thickness bump of increasing amplitude and checks that elements stay valid, that wall nodes follow the prescription exactly while far-field nodes stay fixed, and that the derivative of a geometric quantity through deformation and metric evaluation matches finite differences.", "passed": true, "checks": [{"name": "scale 0.0: mesh valid (min J > 0)", "value": 4.332782712312594e-05, "expected": "> 0", "passed": true}, {"name": "scale 0.0: surface/far-field prescription defect", "value": 0.0, "expected": "< 1e-13", "passed": true}, {"name": "scale 0.5: mesh valid (min J > 0)", "value": 4.33271829409628e-05, "expected": "> 0", "passed": true}, {"name": "scale 0.5: surface/far-field prescription defect", "value": 0.0, "expected": "< 1e-13", "passed": true}, {"name": "scale 1.0: mesh valid (min J > 0)", "value": 4.332653875879968e-05, "expected": "> 0", "passed": true}, {"name": "scale 1.0: surface/far-field prescription defect", "value": 0.0, "expected": "< 1e-13", "passed": true}, {"name": "scale 2.0: mesh valid (min J > 0)", "value": 4.3325250394473455e-05, "expected": "> 0", "passed": true}, {"name": "scale 2.0: surface/far-field prescription defect", "value": 0.0, "expected": "< 1e-13", "passed": true}, {"name": "d(weighted area)/d(surface displacement): AD vs FD", "value": 1.0828212506172907e-08, "expected": "< 1e-7", "passed": true}], "charts": [], "tables": [{"id": "validity", "title": "Mesh validity under deformation", "columns": ["bump scale", "min J", "min scaled Jacobian", "surface defect", "far-field motion"], "rows": [[0.0, 4.332782712312594e-05, 0.12571211623331344, 0.0, 0.0], [0.5, 4.33271829409628e-05, 0.1256267358542962, 0.0, 0.0], [1.0, 4.332653875879968e-05, 0.12554146883908607, 0.0, 0.0], [2.0, 4.3325250394473455e-05, 0.12537127399816933, 0.0, 0.0]]}], "provenance": {"version": "0.4.0", "commit": "39979fcf902ad6116eb550b881b4278d4599c8e2", "dirty": false, "describe": "39979fcf90", "device": {"platform": "cpu", "device": "cpu:0", "device_kind": "cpu", "jax": "0.11.2", "x64": true}, "timestamp": "2026-11-12T10:22:42-0500"}, "wall_time": 2.45, "level": "quick"}