This article addresses the inference of physics models from data, from the perspectives of
inverse problems and model reduction. These fields develop formulations that integrate data …

This paper surveys an important class of methods that combine iterative projection methods
and variational regularization methods for large-scale inverse problems. Iterative methods …

Methane is a greenhouse gas emitted by a range of natural and anthropogenic sources.
Atmospheric methane has been measured continuously from space since 2003, and new …

We present a computational framework for estimating the uncertainty in the numerical
solution of linearized infinite-dimensional statistical inverse problems. We adopt the …

We address the solution of large-scale statistical inverse problems in the framework of
Bayesian inference. The Markov chain Monte Carlo (MCMC) method is the most popular …

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 …

Many Bayesian inference problems require exploring the posterior distribution of high-
dimensional parameters that represent the discretization of an underlying function. This work …

We present an extensible software framework, hIPPYlib, for solution of large-scale
deterministic and Bayesian inverse problems governed by partial differential equations …

Many-query problems–arising from, eg, uncertainty quantification, Bayesian inversion,
Bayesian optimal experimental design, and optimization under uncertainty–require …

We propose derivative-informed neural operators (DINOs), a general family of neural
networks to approximate operators as infinite-dimensional mappings from input function …