Neural-Schwarz Tiling for Geometry-Universal PDE Solving at Scale
Most learned PDE solvers follow a global-surrogate paradigm: a neural operator is trained to map full problem descriptions to full solution fields for a prescribed distribution of geometries, boundary conditions, and coefficients. This has enabled fast inference within fixed problem families, but limits reuse across new domains and makes large-scale deployment dependent on expensive problem-specific data generation. We introduce $\textbf{NEST}$ ($\textbf{Ne}$ural-$\textbf{S}$chwarz $\textbf{T}$iling), a local-to-global framework that shifts learning from full-domain solution operators to reusable local physical solvers. The central premise is that, although global PDE solutions depend on ...
| Authors | Paolo Secchi, Daniel S. Balint, Marco Maurizi |
|---|---|
| Primary category | cs.LG |
| Published | 12 May 2026 |
| Last updated at source | 12 May 2026 |
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