Inverse Problems and Data Assimilation

Daniel Sanz-Alonso; Andrew Stuart; Armeen Taeb

doi:10.1017/9781009414319

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Lyu, Kaiyu and Cheng, Hao 2024. Recovering a space-dependent source term for distributed order time-space fractional diffusion equation. Numerical Algorithms,

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Sanz-Alonso, Daniel and Waniorek, Nathan 2024. Analysis of a Computational Framework for Bayesian Inverse Problems: Ensemble Kalman Updates and MAP Estimators under Mesh Refinement. SIAM/ASA Journal on Uncertainty Quantification, Vol. 12, Issue. 1, p. 30.

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Carrillo, J. A. Hoffmann, F. Stuart, A. M. and Vaes, U. 2024. The Mean-Field Ensemble Kalman Filter: Near-Gaussian Setting. SIAM Journal on Numerical Analysis, Vol. 62, Issue. 6, p. 2549.

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Daniel Sanz-Alonso, University of Chicago, Andrew Stuart, California Institute of Technology, Armeen Taeb, University of Washington

Publisher:: Cambridge University Press
Online publication date:: July 2023
Print publication year:: 2023
Online ISBN:: 9781009414319
DOI:: https://doi.org/10.1017/9781009414319

Subjects:: Mathematics (general), Mathematics, Computational Science, Computational Statistics, Machine Learning and Information Science, Statistics and Probability
Series:: London Mathematical Society Student Texts (107)

29.99 (GBP)

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This concise introduction provides an entry point to the world of inverse problems and data assimilation for advanced undergraduates and beginning graduate students in the mathematical sciences. It will also appeal to researchers in science and engineering who are interested in the systematic underpinnings of methodologies widely used in their disciplines. The authors examine inverse problems and data assimilation in turn, before exploring the use of data assimilation methods to solve generic inverse problems by introducing an artificial algorithmic time. Topics covered include maximum a posteriori estimation, (stochastic) gradient descent, variational Bayes, Monte Carlo, importance sampling and Markov chain Monte Carlo for inverse problems; and 3DVAR, 4DVAR, extended and ensemble Kalman filters, and particle filters for data assimilation. The book contains a wealth of examples and exercises, and can be used to accompany courses as well as for self-study.

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Inverse Problems and Data Assimilation

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-iv

Dedication
pp v-vi

Contents
pp vii-x

Preface
pp xi-xii

Introduction
pp xiii-xvi

Part I - Inverse Problems
pp 1-2

1 - Bayesian Inverse Problems andWell-Posedness
pp 3-20

2 - The Linear-Gaussian Setting
pp 21-31

3 - Optimization Perspective
pp 32-48

4 - Gaussian Approximation
pp 49-58

5 - Monte Carlo Sampling and Importance Sampling
pp 59-72

6 - Markov Chain Monte Carlo
pp 73-90

Exercises for Part I
pp 91-98

Part II - Data Assimilation
pp 99-100

7 - Filtering and Smoothing Problems and Well-Posedness
pp 101-111

8 - The Kalman Filter and Smoother
pp 112-124

9 - Optimization for Filtering and Smoothing: 3DVAR and 4DVAR
pp 125-132

10 - The Extended and Ensemble Kalman Filters
pp 133-143

11 - Particle Filter
pp 144-152

12 - Optimal Particle Filter
pp 153-163

Exercises for Part II
pp 164-170

Part III - Kalman Inversion
pp 171-172

13 - Blending Inverse Problems and Data Assimilation
pp 173-191

References
pp 192-204

Index
pp 205-210

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Inverse Problems and Data Assimilation

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