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

•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 effect...

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Bibliographic Details
Published in:	Journal of computational physics Vol. 449; p. 110768
Main Authors:	Wang, Sifan, Yu, Xinling, Perdikaris, Paris
Format:	Journal Article
Language:	English
Published:	Cambridge Elsevier Inc 15.01.2022 Elsevier Science Ltd
Subjects:	Algorithms Computational physics Convergence Eigenvalues Empirical equations Gradient descent Inverse problems Kernels Lenses Multi-task learning Neural networks Partial differential equations Physics-informed neural networks Scientific machine learning Spectral bias Training Spectral bias Gradient descent Scientific machine learning Multi-task learning Physics-informed neural networks
ISSN:	0021-9991, 1090-2716
Online Access:	Get full text
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