When and why PINNs fail to train: A neural tangent kernel perspective

Sifan Wang, Xinling Yu, Paris Perdikaris

Abstract: Highlights•We analyze the training dynamics of PINNs using neural tangent kernel theory.•We derive the NTK of PINNs and study its limiting behavior.•Our analysis reveals a remarkable discrepancy in the convergence rate of PINNs loss functions.•We propose a novel NTK-guided gradient descent algorithm to effectively resolve this pathology.•We demonstrate significant and consistent accuracy improvements across a range of benchmarks.