arXiv AI June 10, 2026 By Benjamin D. Shaffer, Shawn Koohy, Brooks Kinch, M. Ani Hsieh, Nathaniel Trask

Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs

arXiv:2602. 02788v2 Announce Type: replace-cross Abstract: We aim to develop physics foundation models for science and engineering that provide real-time solutions to Partial Differential Equations (PDEs) which preserve structure and accuracy under adaptation to unseen geometries.

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arXiv Machine Learning

1d ago

Geometry-physics confounding impairs PDE learning across varying domains

arXiv:2609.38623v1 Announce Type: new Abstract: Learning partial differential equation (PDE) dynamics across varying domains is central to predictive modelling and data-driven discovery of governing...

By Yinghao Cheng, Gengxiang Chen, Xu Liu, Qinglu Meng, Yixin Jing, Xiangguo Tang, Wenping Mou, Lihui Wang, Yingguang Li

benchmarks

arXiv Machine Learning

Jul 31

Learning the Helmholtz equation operator with DeepONet for non-parametric 2D geometries

arXiv:2605. 00760v2 Announce Type: replace Abstract: This paper deals with solving the 2D Helmholtz equation on non-parametric domains, leveraging a physics-informed neural operator network, the DeepONet framework.

By Rodolphe Barlogis, Ferhat Tamssaouet, Quentin Falcoz, St\'ephane Grieu

arXiv Machine Learning

Jul 27

Latent PDE mapping for efficient physics-informed learning across geometries with limited data

arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.

By Ingvild Askim Adde, Mary M. Maleckar, Gabriel Balaban

benchmarks

arXiv Machine Learning

Jun 11

Structure-Preserving Neural Surrogates with Tractable Uncertainty Quantification

arXiv:2606. 11650v1 Announce Type: new Abstract: Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation.

By Handi Zhang, Adrienne M. Propp, Brooks Kinch, Houman Owhadi, Nathaniel Trask

llms

arXiv Statistics ML

2d ago

Warm-starting PDE solvers with any-dimensional machine learning

arXiv:2609.38916v1 Announce Type: new Abstract: Any-dimensional machine learning models, such as graph neural networks (GNNs), can be naturally trained and evaluated on inputs of different sizes and...

By Wilson G. Gregory, George A. Kevrekidis, Ben Blum-Smith, Soledad Villar

arXiv Machine Learning

3d ago

Preconditioned Physics-Informed Neural Operator Training

arXiv:2609.36216v1 Announce Type: new Abstract: Neural operators are typically trained in a supervised fashion, which requires a dataset to be generated with a classical solver. Training them physics...

By Shizheng Wen, Siddhartha Mishra, Marius Zeinhofer

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