On understanding and overcoming spectral biases of deep neural network learning methods for solving PDEs

TL;DR

This paper reviews recent methods to address the spectral bias of deep neural networks, which favor low-frequency solutions, in solving partial differential equations, and discusses open problems and future research directions.

Contribution

It provides a comprehensive survey of techniques to overcome spectral bias in neural PDE solvers and highlights open challenges for future work.

Findings

Survey of recent approaches to spectral bias

Identification of open problems in neural PDE methods

Discussion of future research directions

Abstract

In this review, we survey the latest approaches and techniques developed to overcome the spectral bias towards low frequency of deep neural network learning methods in learning multiple-frequency solutions of partial differential equations. Open problems and future research directions are also discussed.