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fix(solvers): correct reverse rules of the projected damage solve - #14
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The damage update solves A(H) d_unc = b(H) and projects the result, d = clamp(max(d_unc, d_prev), 0, 1). Three defects affected gradients through this step: - the history pullback evaluated dA/dH at the projected damage instead of the unconstrained solution d_unc; - the history-only route returned no gradient for d_prev, so nodes held at their previous damage did not propagate gradients to earlier steps; - with fixed material values the solve was dispatched to the forward-only path, detaching the damage from H and d_prev. The forward solution is unchanged. Gradients with respect to Gc and l0 were already evaluated at d_unc and are unaffected. Adds three regression tests: the history gradient against a dense solve-and-project reference and central differences with the projection active, the d_prev gradient on the irreversibility branch, and the history gradient with fixed material values on a small mesh. All three fail on the previous implementation.
… damage
The unconstrained-damage history pullback is derived for solve-then-clamp
routes ('post_clamp', 'direct'). The projected-CG route solves a
bound-constrained problem whose exact sensitivity needs a reduced
active-set system, which is not implemented. On an AT1 projected-CG test
case the unconstrained pullback moved the gradient further from central
differences (relative error 0.66 against 0.56 with the projected damage),
so that route keeps the projected damage. The d_prev gradient and the
dispatch correction apply to all routes.
The fixed-material dispatch test meshed a SENT plate with gmsh, which fails to load on the Ubuntu CI runners (missing libGLU). It now uses a structured unit-square T3 mesh from FEMMesh.from_tensors; the test still fails on the previous code at the intended assertion.
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Summary
The damage update solves
A(H) d_unc = b(H)and enforces the boundsd_prev <= d <= 1. Three defects affected reverse-mode gradients through this step:bounds_method='post_clamp'or'direct'),dA/dHwas evaluated at the projected damage instead of the unconstrained solutiond_unc(_AdjointDamageSolve,_AdjointDamageSolveScalar,_AdjointDamageSolveField).d_prevgradient. The history-only route returnedNoneford_prev, so nodes held at their previous damage (irreversibility branch) did not pass gradients to earlier steps.Gc/l0passed withoutrequires_grad), the solve was dispatched to the forward-only path even whenHord_prevrequired gradients.Forward solutions are unchanged. The direct
Gc/l0pullback term was already evaluated atd_uncand is unchanged, but total multi-step gradients with respect toGc,l0or other parameters change wherever the history ord_prevpaths contribute.Projected CG (
bounds_method='projected_cg'). This route solves a bound-constrained problem whose exact sensitivity needs a reduced active-set system, which is not implemented. On an AT1 projected-CG case the unconstrained pullback moved the gradient further from central differences (relative error 0.66 against 0.56), so this route keeps the projected damage in the history pullback; corrections 2 and 3 apply to all routes. Gradients through projected-CG solves remain approximate.Tests
New
tests/test_damage_adjoint_regressions.py:d_prevgradient on the irreversibility branch;All five test cases fail on the current
mainand pass with this change. Full suite locally: 472 passed.