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Data-driven computational methods: parameter and operator estimations

By: Harlim, John.
Material type: materialTypeLabelBookPublisher: Cambridge Cambridge University Press 2018Description: xi, 158 p. Includes bibliographical references and index.ISBN: 9781108472470.Subject(s): Mathematical statistics | Stochastic analysis | Computer science | Stochastic modelsDDC classification: 519.2 Summary: Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-principles modelling paradigm. This book bridges this transition, connecting the theory of probability, stochastic processes, functional analysis, numerical analysis, and differential geometry. It describes two classes of computational methods to leverage data for modelling dynamical systems. The first is concerned with data fitting algorithms to estimate parameters in parametric models that are postulated on the basis of physical or dynamical laws. The second is on operator estimation, which uses the data to nonparametrically approximate the operator generated by the transition function of the underlying dynamical systems. This self-contained book is suitable for graduate studies in applied mathematics, statistics, and engineering. Carefully chosen elementary examples with supplementary MATLAB® codes and appendices covering the relevant prerequisite materials are provided, making it suitable for self-study. Grants quick access to techniques, but provides a solid theoretical understanding for those who want to go further Gives an overview of various topics usually scattered across disciplines Background material is provided in several short appendices. https://www.cambridge.org/in/academic/subjects/mathematics/computational-science/data-driven-computational-methods-parameter-and-operator-estimations?format=HB
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Table of Contents

1. Introduction
2. Markov chain Monte Carlo
3. Ensemble Kalman filters
4. Stochastic spectral methods
5. Karhunen–Loève expansion
6. Diffusion forecast
Appendix A. Elementary probability theory
Appendix B. Stochastic processes
Appendix C. Elementary differential geometry
References
Index.

Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-principles modelling paradigm. This book bridges this transition, connecting the theory of probability, stochastic processes, functional analysis, numerical analysis, and differential geometry. It describes two classes of computational methods to leverage data for modelling dynamical systems. The first is concerned with data fitting algorithms to estimate parameters in parametric models that are postulated on the basis of physical or dynamical laws. The second is on operator estimation, which uses the data to nonparametrically approximate the operator generated by the transition function of the underlying dynamical systems. This self-contained book is suitable for graduate studies in applied mathematics, statistics, and engineering. Carefully chosen elementary examples with supplementary MATLAB® codes and appendices covering the relevant prerequisite materials are provided, making it suitable for self-study.
Grants quick access to techniques, but provides a solid theoretical understanding for those who want to go further
Gives an overview of various topics usually scattered across disciplines
Background material is provided in several short appendices.

https://www.cambridge.org/in/academic/subjects/mathematics/computational-science/data-driven-computational-methods-parameter-and-operator-estimations?format=HB

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