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.