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arXiv Machine Learning

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

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).

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arXiv Machine Learning
Sep 22

Adaptive Physics-Informed Neural Networks for the Blasius Boundary-Layer Problem

The paper presents an adaptive physics-informed neural network (PINN) framework for solving the Blasius boundary‑layer equation. By combining gradient‑norm‑based loss weighting, nonuniform residual‑based collocation, and a sequential Adam–L‑BFGS optimization, the authors achieve a highly accurate prediction of the wall‑shear coefficient, with an absolute error of $1.896 imes10^{-5}$ for $f''(0)$. A comparative study of network architectures shows that a two‑hidden‑layer model yields the lowest wall‑shear error, while deeper networks reduce the weighted loss but increase physical error. "whyItMatters":"The adaptive framework demonstrates that coordinated adjustments to loss weighting, collocation strategy, and optimization can substantially improve the physical accuracy of PINNs for classical fluid dynamics problems."

By Mehari Fentahun Endalew, Xiaoming John Zhang
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arXiv Machine Learning
Jul 14

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
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arXiv Machine Learning
Jun 17

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

arXiv:2606. 18175v1 Announce Type: cross Abstract: We present a numerical method for the forward solution of nonlinear partial differential equations (PDEs) in which Bellman-Kalaba quasilinearization reduces the nonlinear problem to a sequence of linear subproblems, each discretized by collocation onto a trial space that is linear in its parameters and solved by a single direct linear least-squares QR factorization.

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

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)
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arXiv Machine Learning
Aug 27

Physics-Informed Error Field Learning: A Post-Training Optimization Framework for Physics-Informed Neural Networks

Physics-Informed Error Field Learning (PIEFL) is a post‑training optimization framework for Physics‑Informed Neural Networks (PINNs). After a primary network reaches satisfactory accuracy, PIEFL introduces an auxiliary error network that learns the discrepancy between the current approximation and the exact solution by deriving error control equations under physical constraints. The learned error correction is then combined with the primary prediction, improving solution accuracy without modifying the primary network architecture and focusing computational resources on correcting existing prediction errors.

By Jiuyun Sun, Yong Zhang
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