Learning Discrete Riemannian Metrics for Physical Fields with Cochain-Frame Equivarianc
Physical fields on meshes require a separation between topology and geometry: conservation laws are topological and should be exact, while geometry, material response, and anisotropic coupling must be learned from data. Existing neural surrogates often mix these roles inside unconstrained message passing. We introduce Riemannian Hodge Message Passing (RHMP), which turns this separation into an architectural principle. RHMP fixes the cellular coboundaries ($d_k$) determined by oriented incidence and learns symmetric positive-definite cochain metrics ($H_k$) for geometry-dependent propagation. Treating $H_k$ as the learned metric motivates cochain-frame equivariance: physical propagation sh...
| Authors | Dongzhe Zheng, Christine Allen-Blanchette |
|---|---|
| Primary category | cs.LG |
| Published | 14 May 2026 |
| Last updated at source | 14 May 2026 |
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