Adversarial Training Improves PINNs: A Neural Tangent Kernel Analysis

A novel analytical framework for adversarial training in physics-informed neural networks (PINNs) has been introduced by researchers, drawing from the Neural Tangent Kernel perspective. This framework elucidates the theoretical basis for the effectiveness of adversarial training and presents a cohesive analysis of various GANs used in this context, culminating in a new practical algorithm. Empirical findings indicate notable enhancements in training PINNs, especially for solutions that are high-frequency or multiscale. Additionally, this research tackles challenges related to spectral bias, stiffness, and inaccuracies commonly encountered in PINNs.