  In recent years, convolutional neural networks (CNNs) have experienced an
increasing interest in their ability to perform a fast approximation of
effective hydrodynamic parameters in porous media research and applications.
This paper presents a novel methodology for permeability prediction from
micro-CT scans of geological rock samples. The training data set for CNNs
dedicated to permeability prediction consists of permeability labels that are
typically generated by classical lattice Boltzmann methods (LBM) that simulate
the flow through the pore space of the segmented image data. We instead perform
direct numerical simulation (DNS) by solving the stationary Stokes equation in
an efficient and distributed-parallel manner. As such, we circumvent the
convergence issues of LBM that frequently are observed on complex pore
geometries, and therefore, improve the generality and accuracy of our training
data set. Using the DNS-computed permeabilities, a physics-informed CNN PhyCNN)
is trained by additionally providing a tailored characteristic quantity of the
pore space. More precisely, by exploiting the connection to flow problems on a
graph representation of the pore space, additional information about confined
structures is provided to the network in terms of the maximum flow value, which
is the key innovative component of our workflow. The robustness of this
approach is reflected by very high prediction accuracy, which is observed for a
variety of sandstone samples from archetypal rock formations.
