arXiv AI July 14, 2026 By Noam Koren, Rafael Moschopoulos, Kira Radinsky, Elad Hazan

SFO: Learning PDE Operators via Spectral Filtering

arXiv:2601. 17090v2 Announce Type: replace-cross Abstract: Partial differential equations (PDEs) govern complex systems, yet neural operators often struggle to efficiently capture the long-range, nonlocal interactions inherent in their solution maps.

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.

arXiv Machine Learning

Sep 1

Joint Spatiotemporal Spectral Neural Operators for Learning PDEs on Irregular Domains

arXiv:2608.29892v1 Announce Type: new Abstract: Learning solution operators for partial differential equations (PDEs) on irregular and geometry-dependent domains remains a central challenge in scient...

By Abdolmehdi Behroozi, Chaopeng Shen

rag benchmarks

arXiv Machine Learning

Jul 21

Adaptive Mamba Neural Operators

arXiv:2607. 18043v1 Announce Type: new Abstract: Accurately solving partial differential equations (PDEs) on arbitrary geometries and a variety of meshes is an important task in science and engineering applications.

By Zeyuan Song, Zheyu Jiang

benchmarks

arXiv Machine Learning

Aug 26

Physics-Integrated Operator Learning via Gaussian Splatting Representations

arXiv:2608.24049v1 Announce Type: new Abstract: Neural operators provide efficient surrogates for spatiotemporal PDE systems, but purely data-driven formulations often accumulate substantial errors d...

By Jihao Zhang, Junyi Guo, Jian-Xun Wang

diffusion benchmarks

arXiv AI

Jul 16

Spectral-Informed Neural Networks Outperform Spectral Methods in High-dimensional PDEs

arXiv:2607. 13566v1 Announce Type: cross Abstract: For low-dimensional problems ($d\leq3$), spectral methods can achieve exceptionally high accuracy.

By Tianchi Yu, Ivan Oseledets

rag

arXiv AI

Jun 29

Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs

arXiv:2606. 28122v1 Announce Type: cross Abstract: Neural operators provide deep neural networks for learning mappings between function spaces.

By Alex Colagrande, Paul Caillon, Eva Feillet, Alexandre Allauzen

llms benchmarks safety

arXiv AI

Aug 10

From Points to Edges: Edge-Conditioned Spectral Operators for Physics-Sensitive PDE Learning

arXiv:2608. 06894v1 Announce Type: new Abstract: Neural operators have become a central tool for solving partial differential equations (PDEs), with spectral operators offering efficient global mixing across spatial locations.

By Zhentao Tan, Ruijie Quan, Yi Yang

benchmarks

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Joint Spatiotemporal Spectral Neural Operators for Learning PDEs on Irregular Domains

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Physics-Integrated Operator Learning via Gaussian Splatting Representations

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