The subject of inverse problems in differential equations is of enormous practical
importance, and has also generated substantial mathematical and computational …

We describe and compare two formulations of inverse problems for a physics-based process
model in the context of uncertainty and random variability: the Bayesian inverse problem …

This text provides a framework in which the main objectives of the field of uncertainty
quantification (UQ) are defined and an overview of the range of mathematical methods by …

We introduce a simple, rigorous, and unified framework for solving nonlinear partial
differential equations (PDEs), and for solving inverse problems (IPs) involving the …

A central research challenge for the mathematical sciences in the twenty-first century is the
development of principled methodologies for the seamless integration of (often vast) data …

These lecture notes highlight the mathematical and computational structure relating to the
formulation of, and development of algorithms for, the Bayesian approach to inverse …

We address the numerical solution of infinite-dimensional inverse problems in the
framework of Bayesian inference. In Part I of this paper [T. Bui-Thanh, O. Ghattas, J. Martin …

Over forty years ago average-case error was proposed in the applied mathematics literature
as an alternative criterion with which to assess numerical methods. In contrast to worst-case …

This paper introduces a new method for performing computational inference on log-
Gaussian Cox processes. The likelihood is approximated directly by making use of a …

We study the problem of sampling high and infinite dimensional target measures arising in
applications such as conditioned diffusions and inverse problems. We focus on those that …