The statistical physics of data assimilation and machine learning / Henry D. I. Abarbanel.

Format:

Book

Author/Creator:

Abarbanel, H. D. I., author.

Language:

English

Subjects (All):

Statistical physics--Data processing.

Statistical physics.

Discrete-time systems.

Supervised learning (Machine learning)--Mathematical models.

Supervised learning (Machine learning).

Stochastic processes.

Physical Description:

1 online resource (xvii, 187 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge ; New York, NY : Cambridge University Press, 2022.

Summary:

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.

Contents:

Prologue: Linking "the future" with the present

A data assimilation reminder

Remembrance of things path

SDA variational principles; Euler-Lagrange equations and Hamiltonian formulation

Using waveform information

Annealing in the model precision Rf

Discrete time integration in data assimilation variational principles; Lagrangian and Hamiltonian formulations

Monte Carlo methods

Machine learning and its equivalence to statistical data assimilation

Two examples of the practical use of data assimilation

Unfinished business.

Notes:

Title from publisher's bibliographic system (viewed on 28 Jan 2022).

ISBN:

1-009-02170-2

1-009-02484-1

OCLC:

1268543359