Enriched Holomorphic Neural Networks for 2D and 3D Laplace Problems
Boundary-value problems for the Laplace equation develop singular behaviour near corners, edges and junctions that smooth approximators resolve poorly. We combine holomorphic neural networks with singular functions derived from the local geometry and boundary conditions. The representation is harmonic by construction, so no interior residual is needed: the network fits the smooth remainder from boundary data alone, and the enrichment terms capture the singular behaviour. Singular exponents are trainable, so the construction also applies when the local expansion is not known in advance. We extend the approach to three dimensions using independent networks evaluated along complex null direc...
| Authors | Kalp Shah, Andrei Vlad Nicula, Mihnea Andrei Bârsan et al. |
|---|---|
| Primary category | cs.LG |
| Published | 8 October 2026 |
| Last updated at source | 8 October 2026 |
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