  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 training data requirements. However, NGRCs have
their own practical difficulties, 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 dynamical systems. We show that our
hybrid approach can produce accurate short term predictions and capture the
long term statistics of chaotic dynamical systems in situations where the RC
and NGRC components alone are insufficient, e.g., due to constraints from
limited computational resources, sub-optimal hyperparameters, sparsely-sampled
training data, etc. Under these conditions, we show for multiple model chaotic
systems that the hybrid RC-NGRC method with a small reservoir can achieve
prediction performance approaching that of a traditional RC with a much larger
reservoir, illustrating that the hybrid approach can offer significant gains in
computational efficiency over traditional RCs while simultaneously addressing
some of the limitations of NGRCs. Our results suggest that hybrid RC-NGRC
approach may be particularly beneficial in cases when computational efficiency
is a high priority and an NGRC alone is not adequate.
