Reservoir Computing with Diverse Timescales for Prediction of Multiscale Dynamics

Abstract

Machine learning approaches have recently been leveraged as a substitute or an aid for physical/mathematical modeling approaches to dynamical systems. To develop an efficient machine learning method dedicated to modeling and prediction of multiscale dynamics, we propose a reservoir computing (RC) model with diverse timescales by using a recurrent network of heterogeneous leaky integrator (LI) neurons. We evaluate computational performance of the proposed model in two time series prediction tasks related to four chaotic fast-slow dynamical systems. In a one-step-ahead prediction task where input data are provided only from the fast subsystem, we show that the proposed model yields better performance than the standard RC model with identical LI neurons. Our analysis reveals that the timescale required for producing each component of target multiscale dynamics is appropriately and flexibly selected from the reservoir dynamics by model training. In a long-term prediction task, we demonstrate that a closed-loop version of the proposed model can achieve longer-term predictions compared to the counterpart with identical LI neurons depending on the hyperparameter setting.