  Variational data assimilation and deep learning share many algorithmic
aspects in common. While the former focuses on system state estimation, the
latter provides great inductive biases to learn complex relationships. We here
design a hybrid architecture learning the assimilation task directly from
partial and noisy observations, using the mechanistic constraint of the 4DVAR
algorithm. Finally, we show in an experiment that the proposed method was able
to learn the desired inversion with interesting regularizing properties and
that it also has computational interests.
