Predicting High-Dimensional Chaotic Time Series by Employing Hybridized Local State Reservoir Computing

Abstract

Reservoir Computing (RC) has been shown to be one of the most promising methods for the prediction of chaotic spatiotemporal systems. Recently it has been demonstrated that by combining knowledge-based models (KBMs) with fully data-driven RC, prediction performance exceeding both methods can be achieved. Additionally, this approach is compatible with a parallel prediction scheme based on local states, making forecasting of high-dimensional chaotic spatiotemporal systems of arbitrarily large extent possible. We demonstrate this using three of the most common RC techniques, namely classical RC, Next Generation RC (NGRC), and Minimal RC (MRC), as well as three hybrid methods: input hybrid (IH), output hybrid (OH), and full hybrid (FH). A find that NGRC and MRC yield equivalent prediction performance with up to two orders of magnitude less computing time and training data than classical RC. Furthermore, our implementation of these techniques in the publicly available software package “SCAN” (Software for Chaos Analysis using Networks) enables the processing of generalized system topologies. We discuss different examples for the prediction of spatially extended systems, whether on a two-dimensional plane or a network (e.g. power grid data), and outline possible applications.