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A model-based approach to forecasting chaotic dynamical systems utilizesknowledge of the physical processes governing the dynamics to build anapproximate mathematical model of the system. In contrast, machine learningtechniques have demonstrated promising results for forecasting chaotic systemspurely from past time series measurements of system state variables (trainingdata), without prior knowledge of the system dynamics. The motivation for thispaper is the potential of machine learning for filling in the gaps in ourunderlying mechanistic knowledge that cause widely-used knowledge-based modelsto be inaccurate. Thus we here propose a general method that leverages theadvantages of these two approaches by combining a knowledge-based model and amachine learning technique to build a hybrid forecasting scheme. Potentialapplications for such an approach are numerous (e.g., improving weatherforecasting). We demonstrate and test the utility of this approach using aparticular illustrative version of a machine learning known as reservoircomputing, and we apply the resulting hybrid forecaster to a low-dimensionalchaotic system, as well as to a high-dimensional spatiotemporal chaotic system.These tests yield extremely promising results in that our hybrid technique isable to accurately predict for a much longer period of time than either itsmachine-learning component or its model-based component alone.

Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model