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neural PDE operators

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papersTODAY 04:00 UTC

Paper distinguishes mesh flexibility from topology generalization in neural PDE operators

A new arXiv paper argues that neural operators designed to work on arbitrary meshes are not automatically general across domain topologies, since changing the topology alters the invariant and decaying subspaces of a PDE operator. The authors apply Hodge heat flow as a controlled way to probe this difference. The work points to topology, not just geometry, as a source of failure when such models are applied to unseen domains.

neural-operators/pde/research/geometry

papersTODAY 04:00 UTC

Gauge-Aware Transport Method Extends Adaptive Meshes for Neural PDE Operators

A new arXiv preprint argues that existing adaptive-mesh methods for neural operators, which solve partial differential equations, focus mostly on deciding where to place sample points. The authors propose an approach that also addresses how the operator should interact with those points, using a gauge-aware transport formulation. The work aims to let operators adapt to local physical features in a more complete way.

neural-operators/pdes/adaptive-meshes/research