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Convolution Neural Networks (CNN) are well-suited to model the nonlinearrelationship between the microscale geometry of porous media and thecorresponding flow distribution, thereby accurately and efficiently couplingthe flow behavior at the micro- and macro- scale levels. In this paper, we haveidentified the challenges involved in implementing CNNs for macroscale modelclosure in the turbulent flow regime, particularly in the prediction of thedrag force components arising from the microscale level. We report thatsignificant error is incurred in the crucial data preparation step when theReynolds averaged pressure and velocity distributions are interpolated fromunstructured stretched grids used for Large Eddy Simulation (LES) to thestructured uniform grids used by the CNN model. We show that the range of themicroscale velocity values is 10 times larger than the range of the pressurevalues. This invalidates the use of the mean squared error loss function totrain the CNN model for multivariate prediction. We have developed a CNN modelframework that addresses these challenges by proposing a conservativeinterpolation method and a normalized mean squared error loss function. Wesimulated a model dataset to train the CNN for turbulent flow prediction inperiodic porous media composed of cylindrical solid obstacles with squarecross-section by varying the porosity in the range 0.3 to 0.88. We demonstratethat the resulting CNN model predicts the pressure and viscous drag forces withless than 10% mean absolute error when compared to LES while offering a speedupof O(10^6).

Convolution Neural Network Model Framework to Predict Microscale Drag Force for Turbulent Flow in Porous Media