  We present a novel machine learning approach for data assimilation applied in
fluid mechanics, based on adjoint-optimization augmented by Graph Neural
Networks (GNNs) models. We consider as baseline the Reynolds-Averaged
Navier-Stokes (RANS) equations, where the unknown is the meanflow and a closure
model based on the Reynolds-stress tensor is required for correctly computing
the solution. An end-to-end process is cast; first, we train a GNN model for
the closure term. Second, the GNN model is introduced in the training process
of data assimilation, where the RANS equations act as a physics constraint for
a consistent prediction. We obtain our results using direct numerical
simulations based on a Finite Element Method (FEM) solver; a two-fold interface
between the GNN model and the solver allows the GNN's predictions to be
incorporated into post-processing steps of the FEM analysis. The proposed
scheme provides an excellent reconstruction of the meanflow without any
features selection; preliminary results show promising generalization
properties over unseen flow configurations.
