  Convolution Neural Networks (CNN) are well-suited to model the nonlinear
relationship between the microscale geometry of porous media and the
corresponding flow distribution, thereby accurately and efficiently coupling
the flow behavior at the micro- and macro- scale levels. In this paper, we have
identified the challenges involved in implementing CNNs for macroscale model
closure in the turbulent flow regime, particularly in the prediction of the
drag force components arising from the microscale level. We report that
significant error is incurred in the crucial data preparation step when the
Reynolds averaged pressure and velocity distributions are interpolated from
unstructured stretched grids used for Large Eddy Simulation (LES) to the
structured uniform grids used by the CNN model. We show that the range of the
microscale velocity values is 10 times larger than the range of the pressure
values. This invalidates the use of the mean squared error loss function to
train the CNN model for multivariate prediction. We have developed a CNN model
framework that addresses these challenges by proposing a conservative
interpolation method and a normalized mean squared error loss function. We
simulated a model dataset to train the CNN for turbulent flow prediction in
periodic porous media composed of cylindrical solid obstacles with square
cross-section by varying the porosity in the range 0.3 to 0.88. We demonstrate
that the resulting CNN model predicts the pressure and viscous drag forces with
less than 10% mean absolute error when compared to LES while offering a speedup
of O(10^6).
