arXiv Machine Learning By Duc Tien Nguyen, Hang Tran, Trinh Minh Tuan, Nguyen Duc Manh, Dinh Gia Ninh

Reliability-Aware Hard--Soft Physics-Informed Neural Networks for Robust Learning of Challenging Partial Differential Equations

Read the original on arXiv Machine Learning →

arXiv:2607. 19377v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) provide a mesh-free framework for solving partial differential equations, but their training is often affected by loss imbalance, optimization stiffness, and difficulty in capturing localized or multi-mode solution structures.

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

arXiv Machine Learning
Jun 4

Loss-Conditional PINNs for Parametric PDE Families

arXiv:2606. 04420v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) approximate solutions of ODEs and PDEs by minimising a weighted combination of residual, boundary, initial, and data losses.

By Anna Lazareva, Alexander Tarakanov
Hugging Face Trending Papers
Jul 13

SPARC-Net: A Spectral, Causality-Aware, and Hard-Constrained Physics-Informed Architecture for Stiff and Shock-Dominated Partial Differential Equations

Physics-Informed Neural Networks (PINNs) provide a meshless approach for solving partial differential equations (PDEs), but suffer severe degradation in stiff and shock-dominated problems, where small PDE residuals can correspond to globally inaccurate solutions. We show these failures are multi-causal, arising from the concurrent interplay of (i) spectral bias against sharp features, (ii) imbalanced multi-term optimization and loss-weight collapse, (iii) violation of temporal causality, and (iv) under-resolved collocation.

arXiv Machine Learning
Jul 14

SPARC-Net: A Spectral, Causality-Aware, and Hard-Constrained Physics-Informed Architecture for Stiff and Shock-Dominated Partial Differential Equations

arXiv:2607. 11310v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) provide a meshless approach for solving partial differential equations (PDEs), but suffer severe degradation in stiff and shock-dominated problems, where small PDE residuals can correspond to globally inaccurate solutions.

By Divyavardhan Singh, Dimple Sonone, Hammad Mohammad, Kishor Upla
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