arXiv Machine Learning June 2, 2026 By Satoshi Noguchi, Yoshinobu Kawahara

Mesh Field Theory: Port-Hamiltonian Formulation of Mesh-Based Physics

Read the original on arXiv Machine Learning →

arXiv:2605. 00394v3 Announce Type: replace Abstract: We present Mesh Field Theory (MeshFT) and its neural realization, MeshFT-Net: a structure-preserving framework for mesh-based continuum physics that cleanly separates the physics' topological structure from its metric structure.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

safety

arXiv Machine Learning

2d ago

HI-MeshGraphNets: Efficient and Accurate Mesh-based Physics Learning with Hierarchical Multi-scale Graph Neural Networks

arXiv:2608. 13827v1 Announce Type: new Abstract: Machine-learned physical surrogate models have become promising alternatives to mesh-based numerical solvers.

By SiHun Lee, Dong-Hyuk Park, Taesoo Bang, Seung-Hoon Kang

benchmarks

arXiv AI

Jun 10

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.

By Benjamin D. Shaffer, Shawn Koohy, Brooks Kinch, M. Ani Hsieh, Nathaniel Trask

llms benchmarks safety

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

Jul 10

PGD-NO: A Neural Operator with Precomputed Geometry Decomposition for 3D Million-scale Physics Simulations

arXiv:2607. 08025v1 Announce Type: new Abstract: While neural PDE solvers have demonstrated significant potential for accelerating engineering simulations, existing architectures remain constrained by high memory consumption and the single node bottleneck, where the maximum processable mesh resolution is strictly limited by the VRAM of a single compute unit.

By Weiheng Zhong, Jing Bi, Victor Oancea, Hadi Meidani

benchmarks safety

arXiv Machine Learning

Jul 10

Neural non-canonical Hamiltonian dynamics for long-time simulations

arXiv:2510. 01788v2 Announce Type: replace Abstract: This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes.

By Cl\'ementine Court\`es (IRMA, MACARON), Emmanuel Franck (MACARON), Michael Kraus (IPP), Laurent Navoret (IRMA, MACARON), L\'eopold Tr\'emant (LML)

arXiv Machine Learning

Jul 21

WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains

arXiv:2605. 24651v2 Announce Type: replace-cross Abstract: We propose a Weak-form Physics-Informed Neural Operator (WINO), a data-free framework that combines the efficiency of neural operators with the geometric flexibility of the $\varphi$-finite element method ($\varphi$-FEM).

By Bokai Zhu, Yizheng Wang, Qinghui Zhang, Timon Rabczuk

benchmarks

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HI-MeshGraphNets: Efficient and Accurate Mesh-based Physics Learning with Hierarchical Multi-scale Graph Neural Networks

Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs

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

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Neural non-canonical Hamiltonian dynamics for long-time simulations

WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains