Inverse Problems and Data Assimilation

ISBN-13: 9781009414326 / Twarda / 2023 / 221 str.

Armeen (University of Washington) Taeb

Opis

A clear and concise mathematical introduction to the subjects of inverse problems and data assimilation, and their inter-relations.

Spis treści

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.