Data-Driven Forward Discretizations for Bayesian Inversion

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.

References in corpus (6)

• Dimension-independent likelihood-informed MCMC
• Data-Driven Model Reduction for the Bayesian Solution of Inverse Problems
• Adaptive construction of surrogates for the Bayesian solution of inverse problems
• Bayesian Probabilistic Numerical Methods
• The Bayesian Formulation and Well-Posedness of Fractional Elliptic Inverse Problems
• On the Consistency of Graph-based Bayesian Learning and the Scalability of Sampling Algorithms

Cited by in corpus (2)

• Operator Learning Using Random Features: A Tool for Scientific Computing
• Graph-based Prior and Forward Models for Inverse Problems on Manifolds with Boundaries