Fourier neural networks as function approximators and differential equation solvers

We present a Fourier neural network (FNN) that can be mapped directly to the decomposition. The choice of activation and loss function yields results replicate series expansion closely while preserving straightforward architecture with single hidden layer. simplicity this facilitates integration any other higher-complexity networks, at data pre- or postprocessing stage. validate FNN on naturally periodic smooth functions piecewise continuous functions. showcase use for modeling solving partial differential equations boundary conditions. main advantages current approach are validity solution outside training region, interpretability trained model, use.