Hybridizing Traditional and Next-Generation Reservoir Computing to
  Accurately and Efficiently Forecast Dynamical Systems
Ravi Chepuri Dael Amzalag Thomas Antonsen Jr. Michelle Girvan
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.