Abstract
This paper considers learning a dynamical system using a recurrent neural network (RNN) with hidden units. Such an RNN does not produce a dynamical system on the visible state space unless a mapping from the visible state space to the hidden state space is successfully specified. We propose an affine neural dynamical system (A-NDS) as a dynamical system that an RNN can actually produce on the visible state space to approximate a target dynamical system. An n-dimensional A-NDS is parametrically represented by a suitable pair of an RNN with n visible units and r hidden units, and an affine mapping from the n-dimensional space to the r-dimensional space. However, this parametric representation has redundancy. We construct a unique parametric representation of an A-NDS with the aim of building efficient learning algorithms of a dynamical system using an RNN.
