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Topological Neural Operators

paperactivetopological-neural-operators-0c263a43·1 events·first seen Jun 9, 2026

Aliases: Topological Neural Operators

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4arXiv · cs.LG·Jun 9, 2026·source ↗

Topological Neural Operators: operator learning on cell complexes via Discrete Exterior Calculus

Researchers introduce Topological Neural Operators (TNOs), a framework that extends neural operators from point/edge functions to general topological domains (cell complexes) using Discrete Exterior Calculus. The design decouples fixed topological information flow from learned transformations, enabling models that respect geometric structure and conservation laws. A hierarchical variant (HTNOs) adds learned coarse complexes for long-range propagation. TNOs subsume existing neural operators as a special case and show accuracy improvements on PDE benchmarks including irregular-geometry flow problems.

Evaluation and Benchmarking Discrete Exterior Calculus Topological Neural Operators