  We consider the commonly encountered situation (e.g., in weather forecasting)
where the goal is to predict the time evolution of a large, spatiotemporally
chaotic dynamical system when we have access to both time series data of
previous system states and an imperfect model of the full system dynamics.
Specifically, we attempt to utilize machine learning as the essential tool for
integrating the use of past data into predictions. In order to facilitate
scalability to the common scenario of interest where the spatiotemporally
chaotic system is very large and complex, we propose combining two
approaches:(i) a parallel machine learning prediction scheme; and (ii) a hybrid
technique, for a composite prediction system composed of a knowledge-based
component and a machine-learning-based component. We demonstrate that not only
can this method combining (i) and (ii) be scaled to give excellent performance
for very large systems, but also that the length of time series data needed to
train our multiple, parallel machine learning components is dramatically less
than that necessary without parallelization. Furthermore, considering cases
where computational realization of the knowledge-based component does not
resolve subgrid-scale processes, our scheme is able to use training data to
incorporate the effect of the unresolved short-scale dynamics upon the resolved
longer-scale dynamics ("subgrid-scale closure").
