Functional neural networks for scalar prediction

We introduce a methodology for integrating functional data into densely connected feed-forward neural networks. The model is defined for scalar responses with at least one functional covariate and some number of scalar covariates. A by-product of the method is a set of functional parameters that are dynamic to the learning process which leads to interpretability. The model is shown to perform well in a number of contexts including prediction of new data and recovery of the true underlying coefficient function; these results were confirmed through cross-validations and simulation studies. A collection of useful functions are built on top of the Keras/Tensorflow architecture allowing for general use of the approach.