Learning on Graphs for Predictions of Fracture Propagation, Flow and Transport

Microstructural information plays a key role in governing the dominant physics for various applications involving fracture networks. Resolving the interactions of thousands of interconnected sub-micron scale fractures is computationally intensive, and is intractable with current technologies. Coarsening of the domain and simplification of the physics are two commonly used workarounds, but these methods often eliminate features critical to accurately predicting macroscale behavior. Additionally, traditional Uncertainty Quantification (UQ) methods which account for parametric and model uncertainties have been shown to be inadequate in failure predictions that do not include these subgrid scale effects. We propose to overcome this hurdle by exploiting the fact that fracture networks have an underlying discrete structure that can be compactly represented and propagated via graphs. We have outlined two separate approaches for two separate applications -- prediction of flow in the subsurface and brittle failure at the macroscale. In the first approach, we expect to discover accurate graph representations of previously neglected microscale physics. An alternate approach would be using machine learning algorithms to mimic the detailed physics at the microscale. The resulting workflow using either approach will be memory/computationally efficient by at least one to two orders of magnitude over existing methods.