Enhancing Stability of Physics-Informed Neural Network Training Through Saddle-Point Reformulation

Dmitry Bylinkin; Mikhail Aleksandrov; Savelii Chezhegov; Aleksandr Beznosikov

ICLR 2026poster0 citations

Enhancing Stability of Physics-Informed Neural Network Training Through Saddle-Point Reformulation

Dmitry Bylinkin, Mikhail Aleksandrov, Savelii Chezhegov, Aleksandr Beznosikov

Abstract

Physics-informed neural networks (PINNs) have gained prominence in recent years and are now effectively used in a number of applications. However, their performance remains unstable due to the complex landscape of the loss function. To address this issue, we reformulate PINN training as a nonconvex-strongly concave saddle-point problem. After establishing the theoretical foundation for this approach, we conduct an extensive experimental study, evaluating its effectiveness across various tasks and architectures. Our results demonstrate that the proposed method outperforms the current state-of-the-art techniques.

Physics-informed neural networksMulti-task learningSaddle-point problemsScientific machine learning

BibTeX

@inproceedings{
bylinkin2026enhancing,
title={Enhancing Stability of Physics-Informed Neural Network Training Through Saddle-Point Reformulation},
author={Dmitry Bylinkin and Mikhail Aleksandrov and Savelii Chezhegov and Aleksandr Beznosikov},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=EQNp3sFrY3}
}