The Statistical Physics of Data Assimilation and Machine Learning

The theory of data assimilation and machine learning is introduced in an accessible manner for undergraduate and graduate students.

Henry D. I. Abarbanel (Author)

9781316519639, Cambridge University Press

Hardback, published 17 February 2022

204 pages
25 x 17.3 x 1.4 cm, 0.52 kg

Data assimilation is a hugely important mathematical technique, relevant in fields as diverse as geophysics, data science, and neuroscience. This modern book provides an authoritative treatment of the field as it relates to several scientific disciplines, with a particular emphasis on recent developments from machine learning and its role in the optimisation of data assimilation. Underlying theory from statistical physics, such as path integrals and Monte Carlo methods, are developed in the text as a basis for data assimilation, and the author then explores examples from current multidisciplinary research such as the modelling of shallow water systems, ocean dynamics, and neuronal dynamics in the avian brain. The theory of data assimilation and machine learning is introduced in an accessible and unified manner, and the book is suitable for undergraduate and graduate students from science and engineering without specialized experience of statistical physics.

1. Prologue: linking 'The Future' with the present
2. A data assimilation reminder
3. Remembrance of things path
4. SDA variational principles
Euler–Lagrange equations and Hamiltonian formulation
5. Using waveform information
6. Annealing in the model precision Rf
7. Discrete time integration in data assimilation variational principles
Lagrangian and Hamiltonian formulations
8. Monte Carlo methods
9. Machine learning and its equivalence to statistical data assimilation
10. Two examples of the practical use of data assimilation
11. Unfinished business
Bibliography
Index.

Subject Areas: Machine learning [UYQM], Data capture & analysis [UNC], Statistical physics [PHS]