arXiv:2606. 16510v1 Announce Type: cross Abstract: This study proposes a Petrov-Galerkin based Variational Physics-Informed Neural Network (VPINN) for efficiently solving two-dimensional singularly perturbed problems (SPPs) with one and two small perturbation parameters.
By Vijay Kumar, Gautam Singh
The paper introduces a hybrid iterative deep Ritz method (H-IDRM) for solving interface problems involving second-order elliptic operators. It uses a mixed formulation that reduces the problem to a sequence of convex minimization tasks and employs a level‑set neural network to represent the interface, thereby handling piecewise smooth solutions without explicit interface sampling. The authors analyze errors from neural network, Monte Carlo, iterative, and penalty sources, and demonstrate through numerical experiments that H-IDRM outperforms existing neural solvers on high‑dimensional, complex interface problems.
By Tianhao Hu, Bangti Jin, Fengru Wang, Yifeng Xu
The paper explores neural network solvers for infinity and p‑Laplace problems, employing Physics‑Informed Neural Networks (PINNs) and Deep Operator Networks (DeepONets). It addresses computational challenges for large p values (2 to 1000) across 2D and 3D domains, showing advantages over traditional mesh‑based solvers, especially in three dimensions. The authors provide conditional convergence results for PINNs, a universal approximation theorem for DeepONet on the parametric p‑Poisson problem, and validate their methods with numerical experiments comparing performance to conventional approaches.
By Tak Shing Au Yeung, Ka Chun Cheung, Hannah Potgieter, Steven J. Ruuth, Simon See
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:2608. 08114v1 Announce Type: cross Abstract: In this work, viscous fluid flow governed by the Stokes equations in highly perforated domains is studied using physics-informed neural networks (PINNs).
By Jeeeun Lee, Denis Korolev, Miro Duhovic, Seong Su Kim
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