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

Lulu Zhang; Wei Cai; Zhi-Qin John Xu

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

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arxiv 2501.09987 v1 pith:UIY6SKTG submitted 2025-01-17 math.NA cs.NA

Zhi-Qin John Xu , Lulu Zhang , Wei Cai This is my paper · ORCID

classification math.NAcs.NA

keywords learningdeepmethodsnetworkneuralspectralapproachesbias

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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.

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