Deep learning-enhanced ensemble-based data assimilation for high-dimensional nonlinear dynamical systems *

Recent advances in data-driven modeling with deep learning have seen a surge of interest in predicting the spatio-temporal evolution of high-dimensional chaotic dynamical systems and turbulent flow. In applications to such prediction tasks, models (data-driven or otherwise) are often constrained via sparse and noisy observations available from the system, which allows one to obtain improved initial conditions for prediction via data assimilation. However, data assimilation algorithms require a large ensemble of predicted trajectories to accurately compute the background covariance matrix from which these improved initial conditions are derived, thus, becoming computationally intractable for high-dimensional systems. This work presents a hybrid data-driven and numerical modeling framework that leverages deep learning to generate a large ensemble of predicted trajectories to accurately compute the background covariance matrix that enables efficient and accurate data assimilation for predicting the spatio-temporal evolution of high-dimensional geophysical turbulence.