arXiv Machine Learning By Yan Yang

Loss Landscape Diagnosis for Gradient-Based Gray-Scott System Inversion: Disentangling the Roles of PINN Components

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arXiv:2606. 11258v1 Announce Type: new Abstract: Gradient-based inversion of reaction-diffusion systems is typically approached via surrogate models or physics-informed neural networks (PINNs), while the most direct route, backpropagation through the PDE's structure itself, has largely been avoided.

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arXiv Machine Learning
Sep 22

Learning Physics from an Imperfect Ancestor

arXiv:2609.24947v1 Announce Type: new Abstract: Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed n...

By S. Mohammad Mousavi, Teeratorn Kadeethum, Nikolaos Bouklas, Somdatta Goswami
arXiv Machine Learning
Aug 31

Examining the robustness of Physics-Informed Neural Networks to noise for Inverse Problems

The paper evaluates the robustness of Physics‑Informed Neural Networks (PINNs) against noisy data in inverse problems, comparing them to a finite element method (FEM) plus optimizer baseline. Experiments on viscosity identification in 1D Burgers’ equation and 2D/3D Taylor‑Green Vortex with additive Gaussian noise show that PINNs, while requiring less human expertise, are outperformed by the traditional FEM approach in accuracy (e.g., RMSE 0.01 vs. 0.0013 for 2D Taylor‑Green with σ=1). PINNs do, however, exhibit better scaling with problem complexity, and the study highlights specific training failures that must be addressed for PINNs to become more competitive.

By Aleksandra Jekic, Afroditi Natsaridou, Signe Riemer-S{\o}rensen, Helge Langseth, Odd Erik Gundersen