A Nonchalant Intro to Fourier Neural Operator

The Fourier Neural Operator (FNO) may seem cryptic, but at its core is intuitive, which we'll show it step by step. First, we go over the approximation of linear and non-linear functions, and how this is done using Neural Networks. Next, we introduce operators and how to learn them from data, notably using the Fast-Fourier-Transform (FFT) which has computational advantages with respect to other methods. The FFT motivates the derivation of the FNO, which with the additions activation functions and the bypass convolution, can be used to learn non-linear operators. We verify the core properties of the FNO with a bare-bones version to learn the linear operator governing a smooth pulse propagation problem. Finally, the FNO is used to learn a non-linear constitutive friction model.