Where to Compute and How to Interact: Operator-Readable Adaptation with Gauge-Aware Transport
Adaptive meshes enable neural operators for partial differential equations (PDEs) to allocate spatial samples and computation according to local physical structures. Existing approaches, however, mainly address where to compute, with less attention to how information should interact after node relocation. Mesh adaptation changes local sampling scales, neighborhood structures, and geometric contexts, so representations formed at different nodes may not be directly comparable. Direct aggregation can therefore entangle physical variation with discretization-induced representation variation. Because allocation and interaction are jointly optimized through the same output objective, their indi...
| Authors | Zixuan Shen, Quanxu Wan, Bingchuan Wang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 14 September 2026 |
| Last updated at source | 14 September 2026 |
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