Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspective

Understand

In solving partial differential equations (PDEs), Fourier Neural Operators (FNOs) have exhibited notable effectiveness.

• However, FNO is observed to be ineffective with large Fourier kernels that parameterize more frequencies.
• Current solutions rely on setting small kernels, restricting FNO's ability to capture complex PDE data in real-world applications.
• This paper offers empirical insights into FNO's difficulty with large kernels through spectral analysis: FNO exhibits a unique Fourier parameterization bias, excelling at learning dominant frequencies in target data while struggling with non-dominant frequencies.