Synthetic and reticulated foam solid and velocity data used to train and validate CNN models

Data-driven deep learning models are emerging as a new method to predict the flow and transport through porous media with very little computational power required. Previous deep learning models, however, experience difficulty or require additional computations to predict the 3D velocity field which is essential to characterize porous media at the pore-scale. We design a deep learning model and incorporate a physicsinformed loss function to relate the spatial information of the 3D binary image to the 3D velocity field of porous media. We demonstrate that our model, trained only with synthetic porous media as binary data without additional image processing, can predict the 3D velocity field of real reticulated foams which have microstructures different from porous media that are studied in previous works. We also show that our loss function enforces the law of mass conservation in incompressible flows. Our study provides deep learning framework for predicting the velocity field of porous media and conducting subsequent transport analysis for various engineering applications. As an example, we conduct heat transfer analysis using the predicted velocity fields and demonstrate the accuracy and advantage of our deep learning model.