Abarbanel H. The Statistical Physics of Data..Machine Learn.2022

Textbook in PDF format

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.
Frontmatter
Preface
A Data Assimilation Reminder
Remembrance of Things Path
SDA Variational Principles
Using Waveform Information
Annealing in the Model Precision Rf
Discrete Time Integration in Data Assimilation Variational Principles Lagrangian and Hamiltonian For
Monte Carlo Methods
Machine Learning and Its Equivalence to Statistical Data Assimilation
Two Examples of the Practical Use of Data Assimilation
Unfinished Business
Bibliography
Index