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Fourier Neural Operator (FNO) is a neural network-based approach that combines deep learning with the Fourier transform to solve partial differential equations. It leverages the power of neural networks to learn the complex relationships between input data and the corresponding PDE solutions. FNO trains a neural network to directly approximate the Fourier coefficients of the solution.

While torch, julia and many other languages have enables calling fast Fourier transform (FFT) in their deep learning toolbox, and making FNO easily accessible, I wonder how one can call FFT in mathematica deep learning toobox, or how to implement neural operator learning?

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  • $\begingroup$ No, but Mathematica has FourierMatrix, FourierDCTMatrix, FourierDSTMatrix, HadamardMatrix, etc. perhaps there is a way to feed in these as constant arrays to perform the transform on fixed length vectors within the network using dot product layers. $\endgroup$
    – flinty
    Commented May 29, 2023 at 18:00

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