Understanding how fluid flows through heterogeneous materials, and how it can make these materials fail, are among the hardest challenges in materials science. Experiments and simulations show that flow through subsurface rock is mostly limited to a small subnetwork, or backbone, of fractures. Identifying this backbone would allow for a large speedup in flow and transport simulations, but the process of identifying it can itself be computationally intensive. I will discuss a machine learning approach, developed in a CGU Math Clinic project with Los Alamos National Laboratory, that rapidly finds relevant subnetworks based on graph structure and training data from simulations. Time permitting, I will also describe a method that uses graph convolutional neural networks to predict, with high accuracy, how fractures grow in brittle materials. This provides an automated approach for learning how the fractures can radiate through the material, and ultimately cause it to fail.