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Toward a Better Understanding of Fourier Neural Operators: Analysis and Improvement from a Spectral Perspective
April 11, 2024, 4:42 a.m. | Shaoxiang Qin, Fuyuan Lyu, Wenhui Peng, Dingyang Geng, Ju Wang, Naiping Gao, Xue Liu, Liangzhu Leon Wang
cs.LG updates on arXiv.org arxiv.org
Abstract: In solving partial differential equations (PDEs), Fourier Neural Operators (FNOs) have exhibited notable effectiveness compared to Convolutional Neural Networks (CNNs). This paper presents clear empirical evidence through spectral analysis to elucidate the superiority of FNO over CNNs: FNO is significantly more capable of learning low-frequencies. This empirical evidence also unveils FNO's distinct low-frequency bias, which limits FNO's effectiveness in learning high-frequency information from PDE data. To tackle this challenge, we introduce SpecBoost, an ensemble learning …
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