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We consider the commonly encountered situation (e.g., in weather forecasting)where the goal is to predict the time evolution of a large, spatiotemporallychaotic dynamical system when we have access to both time series data ofprevious system states and an imperfect model of the full system dynamics.Specifically, we attempt to utilize machine learning as the essential tool forintegrating the use of past data into predictions. In order to facilitatescalability to the common scenario of interest where the spatiotemporallychaotic system is very large and complex, we propose combining twoapproaches:(i) a parallel machine learning prediction scheme; and (ii) a hybridtechnique, for a composite prediction system composed of a knowledge-basedcomponent and a machine-learning-based component. We demonstrate that not onlycan this method combining (i) and (ii) be scaled to give excellent performancefor very large systems, but also that the length of time series data needed totrain our multiple, parallel machine learning components is dramatically lessthan that necessary without parallelization. Furthermore, considering caseswhere computational realization of the knowledge-based component does notresolve subgrid-scale processes, our scheme is able to use training data toincorporate the effect of the unresolved short-scale dynamics upon the resolvedlonger-scale dynamics ("subgrid-scale closure").

chaos

Combining Machine Learning with Knowledge-Based Modeling for Scalable  Forecasting and Subgrid-Scale Closure of Large, Complex, Spatiotemporal  Systems