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Hodge heat flow

topic1 events
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