Complementing Imperfect Models with Data for the Prediction of Extreme Events in Turbulent Systems*

A major challenge in projection-based order reduction methods for nonlinear dynamical systems lies in choosing a set of modes that can faithfully represent the overall dynamics. Modes lacking in number or dynamical importance may lead to significant compromise in accuracy, or worse, completely different dynamical behaviors in the model. In this work, we present a framework for using data-driven models to assist dynamical models, obtained through projection, when the reduced set of modes are not necessarily optimal. We make use of the long short-term memory (LSTM), a recurrent neural network architecture, to extract latent information from the reduced-order time series data and derive dynamics not explicitly accounted for by the projection. We apply the framework to projected dynamical models of differing fidelities for prediction of intermittent events in turbulent systems such as the Kolmogorov flow.