A meshfree exterior calculus for generalizable and data-efficient learning of physics from point clouds
We introduce a meshfree exterior calculus (MEEC) for learning structure-preserving descriptions of physics on point clouds, and use it to build MEEC-Net, a data-efficient surrogate that transfers across resolutions, geometries, and physical parameters. MEEC equips an $\varepsilon$-ball graph with virtual node and edge measures via a single sparse Schur complement solve; the resulting complex satisfies discrete conservation exactly, is end-to-end differentiable in the point positions, and exposes a direct geometry-to-physics link without the mesh-generation step required by conventional structure-preserving discretizations. MEEC-Net learns unknown physics as a shared edge-wise flux law in ...
| Authors | Benjamin D. Shaffer, Brooks Kinch, M. Ani Hsieh et al. |
|---|---|
| Primary category | cs.LG |
| Published | 8 May 2026 |
| Last updated at source | 8 May 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.