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

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.

34 pages, 4 tables, 3 figures, 4 theorems; code available at https://anonymous.4open.science/r/pinns-bgda-00D6/README.md