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Look Inside Inverse Problems and Data Assimilation

Inverse Problems and Data Assimilation

Part of London Mathematical Society Student Texts

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

Date Published: August 2023
availability: Not yet published - available from October 2024
format: Paperback
isbn: 9781009414296

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About the Authors

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.
- Provides a gentle introduction to inverse problems and data assimilation emphasizing the unity between both subjects and the potential for an exchange of ideas between them
- Includes numerous pointers to the wider literature
- Features examples and exercises for classroom teaching and self-guided learning
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Customer reviews

17th Oct 2024 by UName-1388979
This title of this book is very attractive, since it connects inverse problems and data assimilation two very important topics.

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Product details
- Date Published: August 2023
- format: Paperback
- isbn: 9781009414296
- length: 221 pages
- dimensions: 226 x 152 x 15 mm
- weight: 0.33kg
- availability: Not yet published - available from October 2024
Table of Contents
Introduction
Part I. Inverse Problems:
1. Bayesian inverse problems and well-posedness
2. The linear-Gaussian setting
3. Optimization perspective
4. Gaussian approximation
5. Monte Carlo sampling and importance sampling
6. Markov chain Monte Carlo
Exercises for Part I
Part II. Data Assimilation:
7. Filtering and smoothing problems and well-posedness
8. The Kalman filter and smoother
9. Optimization for filtering and smoothing:
3DVAR and 4DVAR
10. The extended and ensemble Kalman filters
11. Particle filter
12. Optimal particle filter
Exercises for Part II
Part III. Kalman Inversion:
13. Blending inverse problems and data assimilation
References
Index.
Look Inside
Authors
Daniel Sanz-Alonso, University of Chicago
Daniel Sanz-Alonso is Assistant Professor in the Committee on Computational and Applied Mathematics within the Department of Statistics at the University of Chicago. His contributions to inverse problems and data assimilation have been recognized with a José Luis Rubio de Francia prize and an NSF CAREER award.
Andrew Stuart, California Institute of Technology
Andrew Stuart is Professor in the Computing and Mathematical Sciences Department within the Division of Engineering and Applied Sciences at Caltech. He is well known for his work in applied and computational mathematics, in the areas of dynamical systems, inverse problems, data assimilation, and machine learning.
Armeen Taeb, University of Washington
Armeen Taeb is Assistant Professor in the Department of Statistics at the University of Washington. His work focuses on developing efficient methods for graphical modeling and latent-variable modeling, learning causal relations from data, and model selection in contemporary data analysis settings. His PhD thesis received the W. P. Carey & Co. Prize for outstanding dissertation in applied mathematics.