Effect of temporal resolution on the reproduction of chaotic dynamics via reservoir computing

TL;DR

This paper investigates how different sampling frequencies affect reservoir computing's ability to generate chaotic time series, identifying optimal sampling ranges for accurate reproduction of chaotic dynamics.

Contribution

It provides a quantitative analysis of sampling effects on reservoir computing's chaotic time series generation, highlighting optimal sampling windows and underlying mechanisms.

Findings

Excessively coarse sampling degrades performance

Excessively dense sampling is also unsuitable

Identified a suitable sampling frequency window

Abstract

Reservoir computing is a machine learning paradigm that uses a structure called a reservoir, which has nonlinearities and short-term memory. In recent years, reservoir computing has expanded to new functions such as the autonomous generation of chaotic time series, as well as time series prediction and classification. Furthermore, novel possibilities have been demonstrated, such as inferring the existence of previously unseen attractors. Sampling, in contrast, has a strong influence on such functions. Sampling is indispensable in a physical reservoir computer that uses an existing physical system as a reservoir because the use of an external digital system for the data input is usually inevitable. This study analyzes the effect of sampling on the ability of reservoir computing to autonomously regenerate chaotic time series. We found, as expected, that excessively coarse sampling degrades the system performance, but also that excessively dense sampling is unsuitable. Based on quantitative indicators that capture the local and global characteristics of attractors, we identify a suitable window of the sampling frequency and discuss its underlying mechanisms.