Approximation of dynamical systems by continuous time recurrent neural networks

Abstract

In this paper, we prove that any finite time trajectory of a given n-dimensional dynamical system can be approximately realized by the internal state of the output units of a continuous time recurrent neural network with n output units, some hidden units, and an appropriate initial condition. The essential idea of the proof is to embed the n-dimensional dynamical system into a higher dimensional one which defines a recurrent neural network. As a corollary, we also show that any continuous curve can be approximated by the output of a recurrent neural network.