While most approaches for modelling flows in porous media rely on Darcy’s law, a computational homogenization approach where both fine scale and coarse scale equations are of Navier-Stokes type has recently been developed. This alternative approach is promising as it eases the extension to inertial flows under a principle of multiscale virtual power. Its drawback, however, is that its implementation is quite involved. At each integration point of the Finite Element (FE) mesh of the coarse scale domain, indeed, are attached fine scale domains with their own meshes. Although solving this FExFE or FE² problem at each time increment of the simulation involves a computational complexity that is decreased by several orders as compared to what a single-scale approach would entail, it is still quite demanding. In this work, a deep learning model is developed in order to reduce the computational cost of the fine scale problems. This model is based on a recurrent neural network previously developed for fracture mechanics. In the present work, however, because the objective is to integrate this model within the computational homogenization scheme, several new challenging issues are addressed. Among them, it is ensured that the model is intrinsically constrained for convexity and incompressibility. Solutions for coupling an FE code with a neural network are assessed as well. This presentation will briefly summarize the computational homogenization scheme for porous media flows, and then detail the deep learning model and its coupling with the FE code. The capabilities of the proposed approach as compared to single-scale and then FE² simulations will be demonstrated both in terms of accuracy and computation time.