Dynamic Kuramoto-Hodge Operators for PDEs on Complex Geometries and Topologies
Learning PDE operators on complex domains requires capturing interactions among fields on vertices, edges, and faces, alongside global responses shaped by topology. Existing neural operators accommodate irregular geometries but often overlook these distinct field supports or their condition-dependent coupling. We introduce the Dynamic Kuramoto--Hodge Operator (DKHO), which combines topology-constrained interactions with learned coordination. DKHO encodes conditions on their native cochain supports, evolves Kuramoto-inspired relation states through the boundary and coboundary operators that compose the Dirac operator, and decodes non-harmonic and harmonic responses in orthogonal Hodge subs...
| Authors | Xiang Li, Yue Song |
|---|---|
| Primary category | cs.LG |
| Published | 27 September 2026 |
| Last updated at source | 27 September 2026 |
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