arXiv Machine Learning August 11, 2026 By Jeeeun Lee, Denis Korolev, Miro Duhovic, Seong Su Kim

Finite basis physics-informed neural networks with hard constraints for viscous fluid flow in highly perforated domains

Read the original on arXiv Machine Learning →

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).

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

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arXiv Machine Learning

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LRX-PINN: A Layer-Resolving XNet Physics-Informed Neural Network with Integrated Cauchy Activations for Convection-Dominated Problems

arXiv:2607. 03682v1 Announce Type: cross Abstract: Convection-dominated convection-diffusion problems often develop thin layers, where the solution has sharp transition profiles and its derivatives are highly localized.

By Zihao Guo, Xin Li, Zhihong Xia

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Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning

arXiv:2601. 00473v4 Announce Type: replace-cross Abstract: We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms.

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arXiv Machine Learning

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Petrov-Galerkin Variational Physics-Informed Neural Network Framework for Two-Dimensional Singularly Perturbed Problems

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By Vijay Kumar, Gautam Singh

arXiv Machine Learning

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Multi-dimensional training-priority weighting based on physical information propagation paths: a unified residual-weighting framework for physics-informed neural networks

arXiv:2607. 11094v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs); however, their synchronous optimization treats residuals of different regions and constraints equally, which is inconsistent with the progressive "from source to response" physical information propagation path, degrading training stability and accuracy.

By Zhangyi Lian, Xinda Dong, Wenxuan Huo, Weifeng Huang, Gang Zhu, Qiang He

benchmarks

arXiv Machine Learning

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A Convex Quasilinearization Method for Solving Nonlinear PDEs with Physics-Informed Neural Networks

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By Gbenga T. Awojinrin, Abdul-Akeem Olawoyin, Rami M. Younis

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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

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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)

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