Nonlinear Functional Modeling Using Neural Networks

We introduce a new class of non-linear models for functional data based on neural networks. Deep learning has been very successful in modeling, but there little work done the setting. propose two variations our framework: network with continuous hidden layers, called Functional Direct Neural Network (FDNN), and second version that utilizes basis expansions Basis (FBNN). Both are designed explicitly to exploit structure inherent data. To fit these we derive gradient optimization algorithm. The effectiveness proposed methods handling complex is demonstrated by comprehensive simulation studies real examples.