Machine learning framework for analysis of transport through complex networks in porous, granular media: A focus on permeability.

We present a data-driven framework to study the relationship between fluid flow at the macroscale and the internal pore structure, across the micro- and mesoscales, in porous, granular media. Sphere packings with varying particle size distribution and confining pressure are generated using the discrete element method. For each sample, a finite element analysis of the fluid flow is performed to compute the permeability. We construct a pore network and a particle contact network to quantify the connectivity of the pores and particles across the mesoscopic spatial scales. Machine learning techniques for feature selection are employed to identify sets of microstructural properties and multiscale complex network features that optimally characterize permeability. We find a linear correlation (in log-log scale) between permeability and the average closeness centrality of the weighted pore network. With the pore network links weighted by the local conductance, the average closeness centrality represents a multiscale measure of efficiency of flow through the pore network in terms of the mean geodesic distance (or shortest path) between all pore bodies in the pore network. Specifically, this study objectively quantifies a hypothesized link between high permeability and efficient shortest paths that thread through relatively large pore bodies connected to each other by high conductance pore throats, embodying connectivity and pore structure.