Hodge Spectral Duality provides a topology-preserving neural operator by isolating unlearnable topological components via Hodge orthogonality and operator splitting.
Similar to the continuous case, the combination of dk and δk uniformly describes discrete versions of first-order differential operators such as gradient, curl, and divergence
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Topology-Preserving Neural Operator Learning via Hodge Decomposition
Hodge Spectral Duality provides a topology-preserving neural operator by isolating unlearnable topological components via Hodge orthogonality and operator splitting.