Topological Neural Operators
We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains. TNOs represent data as features defined on cells of varying dimension and model their interactions through Discrete Exterior Calculus, enabling explicit cross-dimensional coupling via gradient-, curl-, and divergence-type operators. The key design principle is to decouple where information flows, as governed by fixed topological operators, from how it is transformed (which is learned), yielding models that respect the geometric support of physical quantities and expose conservation a...
| Authors | Lennart Bastian, Samuel Leventhal, Mustafa Hajij et al. |
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| Primary category | cs.LG |
| Published | 8 June 2026 |
| Last updated at source | 8 June 2026 |
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