  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.
