Hypernetwork-Parameterized Spatially Adaptive Neural Operators for PDE Learning
Spatially heterogeneous partial differential equations (PDEs) exhibit location-dependent dynamics arising from variations in geometry and physical coefficients. Existing neural operators improve localized modeling through multiscale features, attention mechanisms, or domain decomposition, yet their update rules often remain spatially shared. Hypernetwork-based methods adapt parameters across PDE instances but typically generate only one global parameterization per instance. Consequently, shared operators may underfit boundaries and high-gradient regions, with these localized errors accumulating during autoregressive rollout. We propose a spatially adaptive neural operator (SANO), which re...
| Authors | Jiaquan Zhang, Chaoning Zhang, Shuxu Chen et al. |
|---|---|
| Primary category | cs.LG |
| Published | 31 July 2026 |
| Last updated at source | 31 July 2026 |
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