A comparison between Reservoir Computing with Recurrent Analogs in predicting dynamical systems

Reservoir computer (RC) is an attractive neural computing framework that can well predict the dynamics of nonlinear systems, which is promissing to address the nonlinear nature of climatic time series. While in dynamical systems theory, estimating recurrent analog (RA) trajectory in state space is as a reliable method to fit and predict the nonlinear time series. Here we would present an investigation on comparing performances of the RC and RA in predicting climatic time series. We find that the RC outperforms the RA in case of the complete observations for a dynamical system, and a combination between the RC and RA can significantly improve their ability to predict the system in case of partial observation. Additionally, we extend their comparision to the framework of inferring causality from the time series, i.e., a RC-based causality detection framework proposed by us, and the convergent cross mapping causality method based on the RA. The results demonstrate that, in terms of accuracy, computation efficiency and robustness to the noise, the causality method based on the RC outperforms that on the RA. These results could provide indications for future developments and applications of the RC in addressing climatic time series.