DAN -- An optimal Data Assimilation framework based on machine learning Recurrent Networks

Data assimilation algorithms aim at forecasting the state of a dynamical system by combining a mathematical representation of the system with noisy observations thereof. We propose a fully data driven deep learning architecture generalizing recurrent Elman networks and data assimilation algorithms which provably reaches the same prediction goals as the latter. On numerical experiments based on the well-known Lorenz system and when suitably trained using snapshots of the system trajectory (i.e. batches of state trajectories) and observations, our architecture successfully reconstructs both the analysis and the propagation of probability density functions of the system state at a given time conditioned to past observations.