Operator Learning for Predicting Fracture Paths in Brittle Random Media

We present an operator learning approximation framework for brittle fracture. The proposed approach aims to alleviate the computational cost associated with full-scale, phase-field simulations in studying brittle fracture in heterogenous materials. Our strategy relies on the combination of dimensionality reduction and learning between function spaces. We first explore optimal strategies to encode and decode smooth and non-smooth physical fields, including the use of linear and nonlinear reduction techniques. A probabilistic learning technique is subsequently leveraged to map between the latent spaces. The accuracy of the method is finally demonstrated considering fracture path simulations in a random medium exhibiting stochastic spatially varying toughness.