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Where to Compute and How to Interact: Operator-Readable Adaptation with Gauge-Aware Transport

arXiv · AI, language, vision and robotics · article · Sep 14, 2026 · UTC

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. Becau

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