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

Dmitry Bylinkin, Mikhail Aleksandrov, Savelii Chezhegov, Aleksandr Beznosikov

Keywords: Physics-informed neural networks, Multi-task learning, Saddle-point problems, Scientific machine learning

TL;DR: Adaptive weighting of losses corresponding to equations and boundary conditions during PINN training

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.

Primary Area: optimization

Submission Number: 7302