A Multi-Input Multi-Output Functional Artificial Neural Network

Abstract

A generic two-layer feed forward functional neural network is proposed that processes functions rather than point evaluations of functions. Specifically, the network receives n functions as inputs and delivers m real values as outputs. Its architecture is derived using the nonlinear system identification techniques of Zyla and de Figueiredo. As such, neurons are represented by Volterra functions in Fock space, which is a reproducing kernel Hilbert space, with synaptic weights that are functions themselves. The main advantage is that this functional network can be used in the modeling of real-world (continuous-time parameter) nonlinear systems, capturing the dynamics presented in them, as well as in the simulation of their behavior in a computer-based environment.