TNOs lift neural operators to topological cell complexes via Discrete Exterior Calculus for cross-dimensional coupling, subsuming prior NOs and showing accuracy gains on PDE benchmarks with irregular geometries.
and Desbrun, Mathieu , title =
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A convergent GMRF approximation to Whittle-Matern fields on boundaryless Riemannian manifolds using DEC on well-centered simplicial complexes that is agnostic to alpha and kappa.
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Topological Neural Operators
TNOs lift neural operators to topological cell complexes via Discrete Exterior Calculus for cross-dimensional coupling, subsuming prior NOs and showing accuracy gains on PDE benchmarks with irregular geometries.