arXiv Machine Learning

Joint Spatiotemporal Spectral Neural Operators for Learning PDEs on Irregular Domains

arXiv AI

Jul 14

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.

By Noam Koren, Rafael Moschopoulos, Kira Radinsky, Elad Hazan

diffusion benchmarks

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 AI

Jun 3

EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs

arXiv:2606. 03260v1 Announce Type: cross Abstract: Deep learning surrogates for 3D Partial Differential Equations (PDEs) often fail to generalize across geometric transformations because they depend heavily on specific coordinate systems.

By Sungwon Kim, Juho Song, Seungmin Shin, Guimok Cho, Sangkook Kim, Chanyoung Park

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

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 4

Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning

arXiv:2407. 00809v4 Announce Type: replace Abstract: This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for function-space approximation of operators (maps from functions to functions).

By Matthew Lowery, John Turnage, Zachary Morrow, John D. Jakeman, Akil Narayan, Shandian Zhe, Varun Shankar

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 17

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning

arXiv:2606. 17513v1 Announce Type: cross Abstract: Neural operators provide fast surrogates for PDEs but their deterministic predictions limit their use in tasks requiring uncertainty quantification (UQ), especially under geometric variability.

By Oriol Vendrell-Gallart, Nima Negarandeh, Ramin Bostanabad

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 AI

Aug 13

Geometry-aware Incremental Neural Operator for Long-Horizon PDE prediction

arXiv:2608. 11237v1 Announce Type: new Abstract: Neural operators have shown strong potential for learning solution operators of partial differential equations (PDEs).

By Jiaquan Zhang, Shuxu Chen, Haifan Meng, Yi Lu, Zhihan Lyu, Fan Mo, Wei Dong, Yang Yang, Chaoning Zhang

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 9

Intrinsic Green's Learning: Supervised Learning on Manifolds via Inverse PDE

arXiv:2607. 07034v1 Announce Type: cross Abstract: We introduce Intrinsic Green's Learning (IGL), a framework that models a target function on a manifold as the solution to a linear PDE whose source term is learned from data.

By Alexandre Quemy

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