arXiv AI August 10, 2026 By Zhentao Tan, Ruijie Quan, Yi Yang

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.

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.

benchmarks

arXiv AI

Jul 15

Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance

arXiv:2607. 11974v1 Announce Type: cross Abstract: Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen.

By Zixuan Shen (Central South University), Bingchuan Wang (Central South University), Zhi Wang (Nanjing University), Yong Wang (Central South University)

diffusion

arXiv Machine Learning

Aug 31

Beyond Pairwise Graphs in Science: Hypergraph Adaptive Wavelet Operators for Parametric PDEs

arXiv:2608.27883v1 Announce Type: new Abstract: Physical systems are often modeled by solution operators that map input fields, parameters, geometries, or past states to steady or future physical sta...

By Rajat Sarkar, Venkataramana Runkana, Souvik Chakraborty

llms benchmarks

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 AI

Jun 3

Physics-informed diffusion models in spectral space

arXiv:2602. 09708v2 Announce Type: replace-cross Abstract: We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems.

By Davide Gallon, Philippe von Wurstemberger, Patrick Cheridito, Arnulf Jentzen

diffusion

arXiv Machine Learning

Jun 3

Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing

arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.

By Yilong Dai, Shengyu Chen, Xiaowei Jia, Runlong Yu

diffusion safety

arXiv Machine Learning

Jun 16

Manifold-Orthogonal Dual-spectrum Extrapolation for Parameterized Physics-Informed Neural Networks

arXiv:2603. 13751v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) have achieved notable success in modeling dynamical systems governed by partial differential equations (PDEs).

By Zhangyong Liang, Huanhuan Gao

diffusion fine-tuning multimodal benchmarks

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Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance

Beyond Pairwise Graphs in Science: Hypergraph Adaptive Wavelet Operators for Parametric PDEs

Joint Spatiotemporal Spectral Neural Operators for Learning PDEs on Irregular Domains

Physics-informed diffusion models in spectral space

Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing

Manifold-Orthogonal Dual-spectrum Extrapolation for Parameterized Physics-Informed Neural Networks