Title: Hybridizing Traditional and Next-Generation Reservoir Computing to Accurately and Efficiently Forecast Dynamical Systems

Abstract: Reservoir computers (RCs) are powerful machine learning architectures for time series prediction. Recently, next generation reservoir computers (NGRCs) have been introduced, offering distinct advantages over RCs, such as reduced computational expense and lower data requirements. However, NGRCs have their own practical difficulties distinct from those of RCs, including sensitivity to sampling time and type of nonlinearities in the data. Here, we introduce a hybrid RC-NGRC approach for time series forecasting of complex and chaotic dynamical systems. We show that our hybrid approach can produce accurate short term predictions and capture the long term statistics of dynamical systems in situations where the RC and NGRC components alone are insufficient. The advantage of the hybrid RC-NGRC approach is most pronounced when both components are limited in their prediction capabilities, e.g. for a small RC and a large sampling time in the training data. Under these conditions, we show for several chaotic systems that the hybrid RC-NGRC method with a small reservoir ($N \approx 100$) can achieve prediction performance rivaling that of a pure RC with a much larger reservoir ($N \approx 1000$), illustrating that the hybrid approach offers significant gains in computational efficiency over traditional RCs while simultaneously addressing some of the limitations of NGRCs.