  Data assimilation is concerned with sequentially estimating a
temporally-evolving state. This task, which arises in a wide range of
scientific and engineering applications, is particularly challenging when the
state is high-dimensional and the state-space dynamics are unknown. This paper
introduces a machine learning framework for learning dynamical systems in data
assimilation. Our auto-differentiable ensemble Kalman filters (AD-EnKFs) blend
ensemble Kalman filters for state recovery with machine learning tools for
learning the dynamics. In doing so, AD-EnKFs leverage the ability of ensemble
Kalman filters to scale to high-dimensional states and the power of automatic
differentiation to train high-dimensional surrogate models for the dynamics.
Numerical results using the Lorenz-96 model show that AD-EnKFs outperform
existing methods that use expectation-maximization or particle filters to merge
data assimilation and machine learning. In addition, AD-EnKFs are easy to
implement and require minimal tuning.
