The Statistical Physics of Data Assimilation and Machine Learning
The Statistical Physics of Data Assimilation and Machine Learning

Author: Henry D. I. Abarbanel

Publisher: Cambridge University Press

Published: 2022-02-17

Total Pages: 208

ISBN-13: 1009021702

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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.

Data Assimilation
Data Assimilation

Author: Kody Law

Publisher: Springer

Published: 2015-09-05

Total Pages: 256

ISBN-13: 3319203258

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This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online. The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material is organized; the next four are concerned with discrete time dynamical systems and discrete time data; the last four are concerned with continuous time dynamical systems and continuous time data and are organized analogously to the corresponding discrete time chapters. This book is aimed at mathematical researchers interested in a systematic development of this interdisciplinary field, and at researchers from the geosciences, and a variety of other scientific fields, who use tools from data assimilation to combine data with time-dependent models. The numerous examples and illustrations make understanding of the theoretical underpinnings of data assimilation accessible. Furthermore, the examples, exercises and MATLAB software, make the book suitable for students in applied mathematics, either through a lecture course, or through self-study.

Machine Learning with Neural Networks
Machine Learning with Neural Networks

Author: Bernhard Mehlig

Publisher: Cambridge University Press

Published: 2021-10-28

Total Pages: 262

ISBN-13: 1108849563

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This modern and self-contained book offers a clear and accessible introduction to the important topic of machine learning with neural networks. In addition to describing the mathematical principles of the topic, and its historical evolution, strong connections are drawn with underlying methods from statistical physics and current applications within science and engineering. Closely based around a well-established undergraduate course, this pedagogical text provides a solid understanding of the key aspects of modern machine learning with artificial neural networks, for students in physics, mathematics, and engineering. Numerous exercises expand and reinforce key concepts within the book and allow students to hone their programming skills. Frequent references to current research develop a detailed perspective on the state-of-the-art in machine learning research.

Data Assimilation and Control: Theory and Applications in Life Sciences
Data Assimilation and Control: Theory and Applications in Life Sciences

Author: Axel Hutt

Publisher: Frontiers Media SA

Published: 2019-08-16

Total Pages: 116

ISBN-13: 2889459853

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The understanding of complex systems is a key element to predict and control the system’s dynamics. To gain deeper insights into the underlying actions of complex systems today, more and more data of diverse types are analyzed that mirror the systems dynamics, whereas system models are still hard to derive. Data assimilation merges both data and model to an optimal description of complex systems’ dynamics. The present eBook brings together both recent theoretical work in data assimilation and control and demonstrates applications in diverse research fields.

Predicting Storm Surges: Chaos, Computational Intelligence, Data Assimilation and Ensembles
Predicting Storm Surges: Chaos, Computational Intelligence, Data Assimilation and Ensembles

Author: Michael Siek

Publisher: CRC Press

Published: 2011-12-16

Total Pages: 239

ISBN-13: 1466553480

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Accurate predictions of storm surge are of importance in many coastal areas in the world to avoid and mitigate its destructive impacts. For this purpose the physically-based (process) numerical models are typically utilized. However, in data-rich cases, one may use data-driven methods aiming at reconstructing the internal patterns of the modelled p

Introduction to Environmental Data Science
Introduction to Environmental Data Science

Author: William W. Hsieh

Publisher: Cambridge University Press

Published: 2022-12-31

Total Pages: 650

ISBN-13: 1009301802

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Statistical and machine learning methods have many applications in the environmental sciences, including prediction and data analysis in meteorology, hydrology and oceanography, pattern recognition for satellite images from remote sensing, management of agriculture and forests, assessment of climate change, and much more. With rapid advances in machine learning in the last decade, this book provides an urgently needed, comprehensive guide to machine learning and statistics for students and researchers interested in environmental data science. It includes intuitive explanations covering the relevant background mathematics, with examples drawn from the environmental sciences. A broad range of topics are covered, including correlation, regression, classification, clustering, neural networks, random forests, boosting, kernel methods, evolutionary algorithms, and deep learning, as well as the recent merging of machine learning and physics. End-of-chapter exercises allow readers to develop their problem-solving skills and online data sets allow readers to practise analysis of real data.

Inverse Problems and Data Assimilation
Inverse Problems and Data Assimilation

Author: Daniel Sanz-Alonso

Publisher: Cambridge University Press

Published: 2023-07-31

Total Pages: 228

ISBN-13: 100941433X

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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.

Data Assimilation: Methods, Algorithms, and Applications
Data Assimilation: Methods, Algorithms, and Applications

Author: Mark Asch

Publisher: SIAM

Published: 2016-12-29

Total Pages: 310

ISBN-13: 1611974542

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Data assimilation is an approach that combines observations and model output, with the objective of improving the latter. This book places data assimilation into the broader context of inverse problems and the theory, methods, and algorithms that are used for their solution. It provides a framework for, and insight into, the inverse problem nature of data assimilation, emphasizing why and not just how. Methods and diagnostics are emphasized, enabling readers to readily apply them to their own field of study. Readers will find a comprehensive guide that is accessible to nonexperts; numerous examples and diverse applications from a broad range of domains, including geophysics and geophysical flows, environmental acoustics, medical imaging, mechanical and biomedical engineering, economics and finance, and traffic control and urban planning; and the latest methods for advanced data assimilation, combining variational and statistical approaches.