HSD

Topology-Preserving Neural Operator Learning via Hodge Decomposition

arXiv:2605.13834v2 Announce Type: replace Abstract: In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective. We reveal that Hodge orthogonality fundamentally resolves spectral interference by isolating unlearnable topological degrees of freedom from learnable geometric dynamics, enabling an additive approximation confined to structure-preserving subspaces. Building on Hodge theory and operator splitting, we derive a...