The Bayesian Approach To Inverse Problems

TL;DR

This paper discusses the Bayesian framework for inverse problems in differential equations, emphasizing its mathematical and computational aspects for uncertainty quantification in model-data integration.

Contribution

It provides a comprehensive overview of the Bayesian approach, including algorithms and structure, for solving inverse problems in differential equations.

Findings

Highlights the importance of Bayesian methods in uncertainty quantification

Details algorithms for Bayesian inverse problems

Connects mathematical structure with computational techniques

Abstract

These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental in the quantification of uncertainty within applications involving the blending of mathematical models with data.