Modeling of nonlinear nonstationary dynamic systems with a novel class of artificial neural networks

This paper introduces a novel neural-network architecture that can be used to model time varying Volterra systems from input-output data. The Volterra systems constitute a very broad class of stable nonlinear dynamic systems that can be extended to cover nonstationary (time-varying) cases. This novel architecture is composed of parallel subnets of three-layer perceptrons with polynomial activation functions, with the output of each subnet modulated by an appropriate time function that gives the summative output its time-varying characteristics. The paper shows the equivalence between this network architecture and the class of time-varying Volterra systems, and demonstrates the range of applicability of this approach with computer-simulated examples and real data. Although certain types of nonstationarities may not be amenable to this approach, it is hoped that this methodology will provide the practical tools for modeling some broad classes of nonlinear, nonstationary systems from input-output data, thus advancing the state of the art in a problem area that is widely viewed as a daunting challenge.