Fourier Neural Operators with Least-Squares Readout Refit for Learning Random Obstacle-to-Solution Maps
We study operator learning for random obstacle-to-solution maps arising from elliptic variational inequalities with finite-band self-affine random obstacle fields. Instead of introducing an explicit truncated stochastic parametrization of the random input, we learn the map directly from sampled obstacle realizations on a fixed grid. This problem is challenging because the solution is governed not only by the obstacle field itself, but also by the induced contact set and free-boundary geometry. We introduce a post-training least-squares readout refit for the Fourier neural operator (FNO). After the FNO is trained end to end, its nonlinear backbone is frozen and the final affine readout is ...
| Authors | Chenhui Zhu, Fei Wang |
|---|---|
| Primary category | math.NA |
| Published | 28 June 2026 |
| Last updated at source | 28 June 2026 |
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