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
arXiv:2609.35938v1 Announce Type: new
Abstract: This paper proposes an interpretable neural operator framework, the Kernel Operator Network (KernelOnet), which incorporates kernel functions explicitl...
By Yuan Guo, Hanshu Chen, Qiang Xi, Timon Rabczuk, Zhuojia Fu
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
arXiv:2609.14841v1 Announce Type: new
Abstract: Scientific machine learning methods such as physics-informed neural networks (PINNs) increasingly rely on domain decomposition for better scalability w...
By Sidharth S. Menon, Irina Tezaur, Ameya D. Jagtap
The paper presents Finite Basis Physics-Informed Neural Networks (FBPINNs) and their multilevel extensions as a new approach to solving the Helmholtz equation. By decomposing the computational domain into overlapping sub‑domains, each governed by a local neural network, the method aims to improve accuracy and computational efficiency for high‑frequency wave problems in complex two‑dimensional domains. The authors evaluate the technique on the homogeneous Helmholtz case, showing its potential to overcome limitations of traditional finite difference and finite element methods.
By Victorita Dolean, Daria Hrebenshchykova, St\'ephane Lanteri, Victor Michel-Dansac
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