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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.
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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