  Performing Data Assimilation (DA) at a low cost is of prime concern in Earth
system modeling, particularly at the time of big data where huge quantities of
observations are available. Capitalizing on the ability of Neural Networks
techniques for approximating the solution of PDE's, we incorporate Deep
Learning (DL) methods into a DA framework. More precisely, we exploit the
latent structure provided by autoencoders (AEs) to design an Ensemble Transform
Kalman Filter with model error (ETKF-Q) in the latent space. Model dynamics are
also propagated within the latent space via a surrogate neural network. This
novel ETKF-Q-Latent (thereafter referred to as ETKF-Q-L) algorithm is tested on
a tailored instructional version of Lorenz 96 equations, named the augmented
Lorenz 96 system: it possesses a latent structure that accurately represents
the observed dynamics. Numerical experiments based on this particular system
evidence that the ETKF-Q-L approach both reduces the computational cost and
provides better accuracy than state of the art algorithms, such as the ETKF-Q.
