English

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

Numerical Analysis 2025-01-20 v1 Numerical Analysis

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.

Keywords

Cite

@article{arxiv.2501.09987,
  title  = {On understanding and overcoming spectral biases of deep neural network learning methods for solving PDEs},
  author = {Zhi-Qin John Xu and Lulu Zhang and Wei Cai},
  journal= {arXiv preprint arXiv:2501.09987},
  year   = {2025}
}