Work

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

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2501.09987

Authors: Xu, Zhi-Qin John, Zhang, Lulu, Cai, Wei

Institutions: Shanghai Jiao Tong University, Southern Methodist University

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Natural Science Foundation of China, Shanghai Jiao Tong University, Division of Mathematical Sciences

Awards: G1339871232, G377228980, Deep Neural Network Machine Learning for Oscillatory Navier-Stokes Flows and Nonlinear Operators, and High Dimensional Fokker-Planck Equations, G8721642152

OpenAlex ID: W4406603949

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