Dimension of Reservoir Computers

Abstract

A reservoir computer is a complex dynamical system, often created by coupling nonlinear nodes in a network. The nodes are all driven by a common driving signal. In this work, three dimension estimation methods, false nearest neighbor, covariance and Kaplan-Yorke dimensions, are used to estimate the dimension of the reservoir dynamical system. It is shown that the signals in the reservoir system exist on a relatively low dimensional surface. Changing the spectral radius of the reservoir network can increase the fractal dimension of the reservoir signals, leading to an increase in testing error.

arXiv commentsubmitted to Chaos

References in corpus (6)

• Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations
• Attractor Reconstruction by Machine Learning
• Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronisation and cryptography
• Network Structure Effects in Reservoir Computers
• Rapid Time Series Prediction with a Hardware-Based Reservoir Computer
• Testing Dynamical System Variables for Reconstruction

Cited by in corpus (6)

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• Effects of cavity nonlinearities and linear losses on silicon microring-based reservoir computing
• Reservoir Computers with Random and Optimized Time-Shifts
• Adding Filters to Improve Reservoir Computer Performance
• Functional differentiations in evolutionary reservoir computing networks
• (Thesis) Reservoir Computing With Dynamical Systems