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arXiv AI By Vignesh Gopakumar, Zhuoyuan Wang, Ander Gray, Valentin Duruisseaux, Josh Williams, William Michael Edward Ellis, Nuno Nobre, Matthew Field, James Panayis, Alexander I. Blair, Andrew Davis, Stanislas Pamela, Robert Akers, Marc Peter Deisenroth, Anima Anandkumar

Learnable Splines for Unstructured Neural Operators

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The paper introduces L‑SplineFNO, a memory‑efficient neural operator that combines a Fourier neural operator backbone with a learnable tensor‑product B‑spline transfer to map unstructured meshes to a latent Cartesian grid. By using a local normalised scatter, the method preserves spline properties without geometry‑dependent solves, enabling efficient training on up to 26.6 million nodes and inference on 46 million nodes on a single A100 GPU. L‑SplineFNO achieves strong predictive accuracy across six 3D engineering benchmarks, supports zero‑shot super‑resolution, efficient closed‑form spatial derivatives, and provides rigorous prediction bounds via Bernstein convex hulls and Taylor models on a large tokamak model.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

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