Enhancing reservoir predictions of chaotic time series by incorporating delayed values of input and reservoir variables.

Abstract

Time series generated by chaotic dynamical systems can be effectively predicted using readouts from driven reservoir dynamics. In practical scenarios, however, only time series measurements with partial knowledge of the chaotic system's state are usually available. To address this aspect, we evaluate and compare the performance of reservoir computing in predicting time series under both conditions of complete and partial knowledge of the state. Our results show that memory improves the prediction accuracy only when the system state is partially known. For cases with partial state knowledge, we extend the mean prediction horizon by including delayed values of both the input and reservoir variables. To ensure the robustness of this result, we test it in systems with varying degrees of complexity. Finally, we show that the inclusion of delayed values can also facilitate the optimization of hyperparameters for predictions based on full knowledge of the system state.