Modeling dynamical systems using neural networks and random linear projections

Abstract

We focus our attention on two stable models of nonlinear dynamic systems (external dynamic approach): NFIR (nonlinear finite impulse response) and simple version of NARX (nonlinear autoregressive model with external inputs), and their linear counterparts. The main idea investigated in the paper is to project the vector of past inputs un’s onto random directions drawn uniformly from the unit sphere, (instead of estimated) and select only those projections that are relevant for proper neural networks based models.