arXiv Machine Learning

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.

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 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

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

arXiv Machine Learning

Jul 8

PGOT: A Physics-Geometry Operator Transformer for Complex PDEs

arXiv:2512. 23192v4 Announce Type: replace Abstract: While Transformers have demonstrated remarkable potential in modeling Partial Differential Equations (PDEs), modeling large-scale unstructured meshes with complex geometries remains a significant challenge.

By Zhuo Zhang, Xi Yang, Ying Miao, Xiaobin Hu, Yifu Gao, Yong Yang, Canqun Yang, Boocheong Khoo

llms benchmarks

arXiv Machine Learning

Jun 9

Mesh Graph Neural Network Framework for Accelerating Finite Element Simulation for Arbitrary Geometries

arXiv:2606. 08287v1 Announce Type: new Abstract: Finite element analysis (FEA) is essential for structural design but remains computationally expensive, particularly when evaluating multiple design iterations or load scenarios.

By Josiah D. Kunz, Kamal Choudhary

arXiv Machine Learning

Jun 17

INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities

arXiv:2606. 18032v1 Announce Type: cross Abstract: We propose a new weak-form Physics-Informed Neural Network approach (named INI-VPINN).

By Shayan Dodge (DESTeC, University of Pisa, Pisa, Italy), Alessandro Formisano (Department of Engineering, University of Campania Luigi Vanvitelli, Aversa, Italy), Sami Barmada (DESTeC, University of Pisa, Pisa, Italy)

arXiv Machine Learning

Jun 29

Recovering Sharp Conductivity Features in the Finite-Data Calder\'on Problem with Physics-Informed Neural Networks

arXiv:2606. 28158v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have recently emerged as a promising framework for addressing the Calder\'on inverse problem from limited boundary data.

By Ali AlHadi Kalout, Pablo Tejerina-P\'erez, Konstantin Karchev, Pedro Taranc\'on-\'Alvarez, Leonid Sarieddine, Raul Jimenez, Max Engelstein, Guy David

arXiv AI

2d ago

ArGEnT: Arbitrary Geometry-encoded Transformer for Operator Learning

arXiv:2602. 11626v3 Announce Type: replace-cross Abstract: Learning solution operators on arbitrary geometries remains a central challenge in scientific machine learning, especially for many-query simulation, physics-informed learning, and evolving geometries requiring accurate, geometry-aware predictions at arbitrary spatial locations.

By Wenqian Chen, Zhi-Feng Wei, Yucheng Fu, Michael Penwarden, Pratanu Roy, Panos Stinis

llms benchmarks

arXiv Machine Learning

Aug 4

Self-composing neural operators for high-frequency and multiscale PDE surrogates

arXiv:2508. 20650v2 Announce Type: replace Abstract: Addressing the computational challenges of high-frequency and multiscale partial differential equations (PDEs), this work introduces a self-composing neural operator (SC-NO) framework.

By Juncai He, Xinliang Liu, Jinchao Xu

safety

arXiv Machine Learning

Jun 2

Sparse FEONet: A Low-Cost, Memory-Efficient Operator Network via Finite-Element Local Sparsity for Parametric PDEs

arXiv:2601. 00672v2 Announce Type: replace-cross Abstract: In this paper, we study the finite element operator network (FEONet), an operator-learning method for parametric problems, originally introduced in J.

By Seungchan Ko, Jiyeon Kim, Dongwook Shin

efficiency

arXiv Machine Learning

Jun 11

HAMNO: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems

arXiv:2606. 11963v1 Announce Type: new Abstract: Neural operators provide a powerful framework for learning solution mappings of partial differential equations directly in function space.

By Mostafa Bamdad, Mohammad Sadegh Eshaghi, Timon Rabczuk

arXiv Machine Learning

Jul 14

OpenEM: Large-scale multi-structural 3D datasets for electromagnetic methods

arXiv:2510. 21859v3 Announce Type: replace Abstract: Electromagnetic (EM) methods, owing to their efficiency and non-invasive nature, have become one of the most widely used techniques in geological exploration.

By Shuang Wang, Xuben Wang, Fei Deng, Peifan Jiang, Jian Chen, Gianluca Fiandaca

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