Topological Data Analysis combined with Machine Learning for Predicting Permeability of Porous Media

Flow in porous media is difficult to address using standard analytical or numerical methods due to its complexity. However, since synthetic representations of porous media are easy to produce and data from physical experiments are becoming more widely available, the problem is well-suited to studies that include machine learning (ML) techniques. We discuss a number of features that can be extracted from such data, and their utility as input variables into a standard ML algorithm. These features include structural measures describing the geometry of the porous media, topological measures describing the connectivity, and network measures obtained by modeling the porous media as simplified pore networks. These features enable the prediction of the permeability of the considered (synthetic) porous materials using ML techniques that also leverage the separately computed exact permeability (ground truth). Comparing results obtained using different input variables helps develop a better understanding of the utility of various measures for predicting permeability based on the porous media structure. We show, in particular, that topological data analysis (TDA) provides a useful set of features that can be easily combined with ML to yield meaningful results.