Topology-Preserving Neural Operator Learning via Hodge Decomposition

Researchers introduced Hodge Spectral Duality, a hybrid Eulerian-Lagrangian neural operator for topology-preserving operator learning.

The model splits topology-driven and dynamics-driven components of a solution operator using Hodge decomposition and spectral duality.

This separation is designed to reduce spectral interference and improve accuracy on geometric meshes and complex domains.

The approach aims to preserve key physical invariants and topological structure while making operator learning more efficient.