Optical tomography: forward and inverse problems

SR Arridge, JC Schotland - Inverse problems, 2009 - iopscience.iop.org
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 …

Inverse problems: From regularization to Bayesian inference

D Calvetti, E Somersalo - Wiley Interdisciplinary Reviews …, 2018 - Wiley Online Library
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 …

Systems biology informed deep learning for inferring parameters and hidden dynamics

A Yazdani, L Lu, M Raissi… - PLoS computational …, 2020 - journals.plos.org
Mathematical models of biological reactions at the system-level lead to a set of ordinary
differential equations with many unknown parameters that need to be inferred using …

[图书][B] Uncertainty quantification: theory, implementation, and applications

RC Smith - 2024 - SIAM
Uncertainty quantification serves a central role for simulation-based analysis of physical,
engineering, and biological applications using mechanistic models. From a broad …

Analysis of electrochemical impedance spectroscopy data using the distribution of relaxation times: A Bayesian and hierarchical Bayesian approach

F Ciucci, C Chen - Electrochimica Acta, 2015 - Elsevier
Electrochemical impedance spectroscopy (EIS) is one of the most important experimental
techniques employed in electrochemistry because it can be used to deconvolve physico …

[图书][B] Discrete inverse problems: insight and algorithms

PC Hansen - 2010 - SIAM
Inverse problems are mathematical problems that arise when our goal is to recover “interior”
or “hidden” information from “outside”—or otherwise available—noisy data. For example, an …

[图书][B] Parameter estimation and inverse problems

RC Aster, B Borchers, CH Thurber - 2018 - books.google.com
Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at
New Mexico Tech and is designed to be accessible to typical graduate students in the …

Bayesian and hierarchical bayesian based regularization for deconvolving the distribution of relaxation times from electrochemical impedance spectroscopy data

MB Effat, F Ciucci - Electrochimica Acta, 2017 - Elsevier
The distribution of relaxation times (DRT) is a fast-growing methodology that is used to
interpret data obtained from electrochemical impedance spectroscopy (EIS) experiments …

Parameter and state model reduction for large-scale statistical inverse problems

C Lieberman, K Willcox, O Ghattas - SIAM Journal on Scientific Computing, 2010 - SIAM
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 …

Non‐linear model reduction for uncertainty quantification in large‐scale inverse problems

D Galbally, K Fidkowski, K Willcox… - International journal for …, 2010 - Wiley Online Library
We present a model reduction approach to the solution of large‐scale statistical inverse
problems in a Bayesian inference setting. A key to the model reduction is an efficient …