BAYESIAN INVERSION USING GLOBAL-LOCAL FORWARD MODELS APPLIED TO FRACTURE PROPAGATION IN POROUS MEDIA

In this work, we are interested in parameter estimation in fractured media using Bayesian inversion. Therein, to reduce the computational costs of the forward model, a nonintrusive global-local approach is employed, rather than using fine-scale high-fidelity simulations. The crack propagates within the local region, and a linearized coarse model is employed in the global region. Here, a predictor-corrector mesh refinement approach is adopted, in which the local domain is dynamically adjusted to the current fracture state. Both subdomains change during the fluid injection time. Our algorithmic developments are substantiated with some numerical tests using phase-field descriptions of hydraulic fractures. The obtained results indicate that the global-local approach is an efficient technique for Bayesian inversion. It has the same accuracy as the full approach; however, the computational time is significantly lower.