  The permeability of complex porous materials can be obtained via direct flow
simulation, which provides the most accurate results, but is very
computationally expensive. In particular, the simulation convergence time
scales poorly as simulation domains become tighter or more heterogeneous.
Semi-analytical models that rely on averaged structural properties (i.e.
porosity and tortuosity) have been proposed, but these features only summarize
the domain, resulting in limited applicability. On the other hand, data-driven
machine learning approaches have shown great promise for building more general
models by virtue of accounting for the spatial arrangement of the domains solid
boundaries. However, prior approaches building on the Convolutional Neural
Network (ConvNet) literature concerning 2D image recognition problems do not
scale well to the large 3D domains required to obtain a Representative
Elementary Volume (REV). As such, most prior work focused on homogeneous
samples, where a small REV entails that that the global nature of fluid flow
could be mostly neglected, and accordingly, the memory bottleneck of addressing
3D domains with ConvNets was side-stepped. Therefore, important geometries such
as fractures and vuggy domains could not be well-modeled. In this work, we
address this limitation with a general multiscale deep learning model that is
able to learn from porous media simulation data. By using a coupled set of
neural networks that view the domain on different scales, we enable the
evaluation of large images in approximately one second on a single Graphics
Processing Unit. This model architecture opens up the possibility of modeling
domain sizes that would not be feasible using traditional direct simulation
tools on a desktop computer.
