  In many branches of earth sciences, the problem of rock study on the
micro-level arises. However, a significant number of representative samples is
not always feasible. Thus the problem of the generation of samples with similar
properties becomes actual. In this paper, we propose a novel deep learning
architecture for three-dimensional porous media reconstruction from
two-dimensional slices. We fit a distribution on all possible three-dimensional
structures of a specific type based on the given dataset of samples. Then,
given partial information (central slices), we recover the three-dimensional
structure around such slices as the most probable one according to that
constructed distribution. Technically, we implement this in the form of a deep
neural network with encoder, generator and discriminator modules. Numerical
experiments show that this method provides a good reconstruction in terms of
Minkowski functionals.
