2022/06/29 by Ghazal Farhani, Farhani, Ghazal, Alexander Kazachek +2 · 2 citations
Computer Science · Physics and Astronomy · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning and ELM #Model Reduction and Neural Networks #Neural Networks and Applications
paper · pdf · doi:10.48550/arxiv.2206.14862
openalex publication_date 2022/06/29 · openalex created_date 2022/07/03 · openalex updated_date 2026/07/28
Physics-informed neural network (PINN) algorithms have shown promising results in solving a wide range of problems involving partial differential equations (PDEs). However, they often fail to converge to desirable solutions when the target function contains high-frequency features, due to a phenomenon known as spectral bias. In the present work, we exploit neural tangent kernels (NTKs) to investigate the training dynamics of PINNs evolving under stochastic gradient descent with momentum (SGDM). This demonstrates SGDM significantly reduces the effect of spectral bias. We have also examined why training a model via the Adam optimizer can accelerate the convergence while reducing the spectral bias. Moreover, our numerical experiments have confirmed that wide-enough networks using SGDM still converge to desirable solutions, even in the presence of high-frequency features. In fact, we show that the width of a network plays a critical role in convergence.