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  3. Inverse Problems and Data Assimilation
  • Cited by 19
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)
Information

Book description

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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