To evaluate the variability of multiphase flow properties of porous media at the pore scale, it is necessary to
acquire a number of representative samples of the void-solid structure. While modern x-ray computer tomography
has made it possible to extract three-dimensional images of the pore space, assessment of the variability in the
inherent material properties is often experimentally not feasible. We present a method to reconstruct the
solid-void structure of porous media by applying a generative neural network that allows an implicit description
of the probability distribution represented by three-dimensional image data sets. We show, by using an adversarial
learning approach for neural networks, that this method of unsupervised learning is able to generate representative
samples of porous media that honor their statistics. We successfully compare measures of pore morphology, such
as the Euler characteristic, two-point statistics, and directional single-phase permeability of synthetic realizations
with the calculated properties of a bead pack, Berea sandstone, and Ketton limestone. Results show that generative
adversarial networks can be used to reconstruct high-resolution three-dimensional images of porous media at
different scales that are representative of the morphology of the images used to train the neural network.
The fully convolutional nature of the trained neural network allows the generation of large samples while
maintaining computational efficiency. Compared to classical stochastic methods of image reconstruction, the
implicit representation of the learned data distribution can be stored and reused to generate multiple realizations
of the pore structure very rapidly