Localized Operator Learning with Adaptive Partition-of-Unity Mixture-of-Expert Networks
Operator learning methods such as DeepONets and FNOs often struggle with PDE families featuring sharp interfaces, heterogeneous coefficients, and localized multiscale structures. We introduce a partition-of-unity (POU) mixture-of-experts framework for localized operator learning, in which geometry-aware gating networks produce smooth spatial partitions which blend the contributions of local expert networks. Our main contribution is HiRefPOU, a residual-style hierarchical POU architecture for DeepONets that organizes localized representations through nested parent-child partitions while preserving global continuity. We also show that the same POU principle can be incorporated into Fourier ...
| Authors | Madison Cooley, Ramansh Sharma, Shandian Zhe et al. |
|---|---|
| Primary category | cs.LG |
| Published | 3 October 2026 |
| Last updated at source | 13 October 2026 |
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