arXiv AI June 3, 2026 By Sungwon Kim, Juho Song, Seungmin Shin, Guimok Cho, Sangkook Kim, Chanyoung Park

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.

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arXiv Machine Learning

Sep 1

Rotational Equivariance in Machine Learning: A Comprehensive Tutorial

arXiv:2608.31045v1 Announce Type: new Abstract: Rotational symmetry is one of the most important structural principles in machine learning on 3D data. In applications ranging from physics and materia...

By Peter Lippmann, Fred A. Hamprecht

computer-vision

arXiv AI

Jun 30

Representation Learning for Equivariant Inference with Guarantees

arXiv:2505. 19809v3 Announce Type: replace-cross Abstract: In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency.

By Daniel Ordo\~nez-Apraez, Vladimir Kosti\'c, Alek Fr\"ohlich, Vivien Brandt, Karim Lounici, Massimiliano Pontil

robotics

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

Jun 17

Variational autoencoders with latent high-dimensional steady geometric flows for dynamics

arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.

By Andrew Gracyk

diffusion

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 AI

Sep 1

Equivariant Sheaf Neural Networks: Learning Geometric Transport on Graphs

arXiv:2608.28853v1 Announce Type: cross Abstract: Equivariant graph neural networks provide a principled way to model geometric systems, but efficient first-order architectures remain limited in how...

By Alessio Borgi, Mario Severino, Fabrizio Silvestri, Pietro Li\`o

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