  Modeling the subgrid-scale dynamics of reduced models is a long standing open
problem that finds application in ocean, atmosphere and climate predictions
where direct numerical simulation (DNS) is impossible. While neural networks
(NNs) have already been applied to a range of three-dimensional flows with
success, two dimensional flows are more challenging because of the backscatter
of energy from small to large scales. We show that learning a model jointly
with the dynamical solver and a meaningful \textit{a posteriori}-based loss
function lead to stable and realistic simulations when applied to
quasi-geostrophic turbulence.
