A general representation of dynamical systems for reservoir computing

TL;DR

This paper introduces a unified neural network framework to represent various dynamical systems, like cellular automata, for reservoir computing, enabling optimization and generalization across different systems and applications.

Contribution

It presents a novel neural network-based representation of dynamical systems, facilitating their use in reservoir computing and enabling evolution and optimization of these systems.

Findings

Implemented cellular automata as neural networks for reservoir computing

Demonstrated the framework's ability to generalize to other dynamical systems

Enabled evolution of dynamical systems for optimized computational performance

Abstract

Dynamical systems are capable of performing computation in a reservoir computing paradigm. This paper presents a general representation of these systems as an artificial neural network (ANN). Initially, we implement the simplest dynamical system, a cellular automaton. The mathematical fundamentals behind an ANN are maintained, but the weights of the connections and the activation function are adjusted to work as an update rule in the context of cellular automata. The advantages of such implementation are its usage on specialized and optimized deep learning libraries, the capabilities to generalize it to other types of networks and the possibility to evolve cellular automata and other dynamical systems in terms of connectivity, update and learning rules. Our implementation of cellular automata constitutes an initial step towards a general framework for dynamical systems. It aims to evolve such systems to optimize their usage in reservoir computing and to model physical computing substrates.