Elucidating the performance of data assimilation neural networks for chaotic dynamics

Abstract. Recent work has shown that the analysis operator in sequential data assimilation designed to track chaotic dynamics, can be learned with deep learning from the sole knowledge of a true state trajectory and observations thereof. This approach to learning the analysis is computationally more challenging, yet conceptually more fundamental than approaches that learn a direct mapping from forecasts and observations to the corresponding analysis increments. Such learned scheme has been demonstrated to achieve accuracy comparable to that of the ensemble Kalman filter when applied to low-order dynamics. Strikingly, the same accuracy can be reached with a single state forecast instead of an ensemble, hence bypassing the need to explicitly represent forecast uncertainty.

In this study, we extend the investigation of such learned analysis operators beyond the preliminary experiments reported so far. First, we analyse the emergence of local patterns encoded in the operator, which accounts for the remarkable scalability of the approach to high-dimensional state spaces. Second, we assess the performance of the learned operators in stronger nonlinear regimes of the chaotic dynamics. We show that they can match the efficiency of the iterative ensemble Kalman filter, the baseline in this context, while avoiding the need for nonlinear iterative optimisation. Throughout the paper, we seek underlying reasons for the efficiency of the approach, drawing on insights from both machine learning and nonlinear data assimilation.