  We report the application of machine learning methods for predicting the
effective diffusivity (De) of two-dimensional porous media from images of their
structures. Pore structures are built using reconstruction methods and
represented as images, and their effective diffusivity is computed by lattice
Boltzmann (LBM) simulations. The datasets thus generated are used to train
convolutional neural network (CNN) models and evaluate their performance. The
trained model predicts the effective diffusivity of porous structures with
computational cost orders of magnitude lower than LBM simulations. The
optimized model performs well on porous media with realistic topology, large
variation of porosity (0.28-0.98), and effective diffusivity spanning more than
one order of magnitude (), e.g., >95% of predicted De have truncated relative
error of <10% when the true De is larger than 0.2. The CNN model provides
better prediction than the empirical Bruggeman equation, especially for porous
structure with small diffusivity. The relative error of CNN predictions,
however, is rather high for structures with De < 0.1. To address this issue,
the porosity of porous structures is encoded directly into the neural network
but the performance is enhanced marginally. Further improvement, i.e., 70% of
the CNN predictions for structures with true De < 0.1 have relative error <30%,
is achieved by removing trapped regions and dead-end pathways using a simple
algorithm. These results suggest that deep learning augmented by field
knowledge can be a powerful technique for predicting the transport properties
of porous media. Directions for future research of machine learning in porous
media are discussed based on detailed analysis of the performance of CNN models
in the present work.
