Data-Driven Forward Discretizations for Bayesian Inversion

Daniele Bigoni, Yuming Chen, Nicolas Garcia Trillos, Youssef Marzouk, Daniel Sanz-Alonso

Abstract: This paper suggests a framework for the learning of discretizations of expensive forwardmodels in Bayesian inverse problems. The main idea is to incorporate the parameters governingthe discretization as part of the unknown to be estimated within the Bayesian machinery. Wenumerically show that in a variety of inverse problems arising in mechanical engineering, signalprocessing and the geosciences, the observations contain useful information to guide the choiceof discretization.