Explicit construction of recurrent neural networks effectively approximating discrete dynamical systems

TL;DR

This paper presents an explicit method for constructing recurrent neural networks that can effectively approximate discrete dynamical systems derived from bounded time series data.

Contribution

It introduces a novel explicit construction technique for RNNs tailored to approximate arbitrary bounded discrete dynamical systems.

Findings

Constructed RNNs effectively approximate the target dynamical systems.

The method applies to arbitrary bounded discrete time series.

Provides a systematic approach for RNN design in dynamical systems modeling.

Abstract

We consider arbitrary bounded discrete time series originating from dynamical system with recursivity. More precisely, we provide an explicit construction of recurrent neural networks which effectively approximate the corresponding discrete dynamical systems.