Data-driven forward discretizations for Bayesian inversion. (25th September 2020)

• Record Type: Journal Article
• Authors: Bigoni, D; Chen, Y; Trillos, N Garcia; Marzouk, Y; Sanz-Alonso, D
• Is Part Of: Inverse problems. Volume 36:Number 10(2020)
• Publication Date: 2020-09-25
• Subjects: Bayesian inverse problems -- data-driven discretizations -- hierarchical learning; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abb2fa
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: This paper suggests a framework for the learning of discretizations of expensive forward models in Bayesian inverse problems. The main idea is to incorporate the parameters governing the discretization as part of the unknown to be estimated within the Bayesian machinery. We numerically show that in a variety of inverse problems arising in mechanical engineering, signal processing and the geosciences, the observations contain useful information to guide the choice of discretization.