Certified neural approximations for parabolic obstacle problems
Residual-trained neural surrogates carry no error guarantee, a limitation for free-boundary problems such as phase change and contact. We derive guaranteed error bounds for neural approximations of parabolic obstacle problems in first-order state--flux--multiplier form. The main result bounds the flux error of the network and the energy error of its feasible projection $\max\{v,g\}$ by the constitutive residual, the initial mismatch, the complementarity defect, and the PDE residual weighted by $c_F^2/α$, without the coercivity and norm-equivalence constants of the first-order formulation. It extends the Apushkinskaya--Repin majorant for the heat operator to general coefficients, free mult...
| Authors | Davood Damircheli |
|---|---|
| Primary category | math.NA |
| Published | 16 October 2026 |
| Last updated at source | 16 October 2026 |
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