Machine learning techniques for fractured media

This is primarily an account of the role of machine learning, including the role played by graph theory, in the development of reduced-order models (ROM) of flow and transport through fractured media that are modeled with the DFN approach. We describe the construction of a DFN, the necessary governing equations for flow and transport through DFN and various graph representations of it. The development of ROMs in DFN is then traced and divided into different unifying themes. We set out, in general terms, the role of machine learning in constructing reduced-order models of DFN, place three different machine learning approaches that have been developed in this context into an abstract perspective, and explain the fundamental ideas of each approach. We show that the approaches differ in the identity of the elements being classified, and the rule for assigning labels to elements. By choosing the elements as paths, rather than fractures, a truly physics-informed machine learning method results that preserves network connectivity in the reduced networks.