In many situations across computational science and engineering, multiple computational
models are available that describe a system of interest. These different models have varying …

This is a comprehensive, critical, and pedagogical review of volumetric emission
tomography for combustion processes. Many flames that are of interest to scientists and …

Biomedical photoacoustic tomography, which can provide high-resolution 3D soft tissue
images based on optical absorption, has advanced to the stage at which translation from the …

In recent years, deep learning has achieved remarkable empirical success for image
reconstruction. This has catalyzed an ongoing quest for the precise characterization of the …

Numerical simulation of large-scale dynamical systems plays a fundamental role in studying
a wide range of complex physical phenomena; however, the inherent large-scale nature of …

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 …

This is a review of recent mathematical and computational advances in optical tomography.
We discuss the physical foundations of forward models for light propagation on microscopic …

A number of technological processes and natural phenomena are accompanied by heat
transfer concerned with media thermal radiation. Generally, thermal radiation is thought to …

Inverse problems deal with the quest for unknown causes of observed consequences,
based on predictive models, known as the forward models, that associate the former …

A greedy algorithm for the construction of a reduced model with reduction in both parameter
and state is developed for an efficient solution of statistical inverse problems governed by …