Quantifying Topological Uncertainty in Fractured Systems using Graph Theory and Machine Learning

Fractured systems are ubiquitous in natural and engineered applications as diverse as hydraulic fracturing, underground nuclear test detection, corrosive damage in materials and brittle failure of metals and ceramics. Microstructural information (fracture size, orientation, etc.) plays a key role in governing the dominant physics for these systems but can only be known statistically. Current models either ignore or idealize microscale information at these larger scales because we lack a framework that efficiently utilizes it in its entirety to predict macroscale behavior in brittle materials. We propose a method that integrates computational physics, machine learning and graph theory to make a paradigm shift from computationally intensive high-fidelity models to coarse-scale graphs without loss of critical structural information. We exploit the underlying discrete structure of fracture networks in systems considering flow through fractures and fracture propagation. We demonstrate that compact graph representations require significantly fewer degrees of freedom (dof) to capture micro-fracture information and further accelerate these models with Machine Learning. Our method has been shown to improve accuracy of predictions with up to four orders of magnitude speedup.