Data-Driven Computational Methods
Data-Driven Computational Methods
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Résumé
The mathematics behind, and the practice of, computational methods that leverage data for modelling dynamical systems are described in this book. It will teach readers how to fit data on the assumed model and how to use data to determine the underlying model. Suitable for graduate students in applied mathematics, statistics, and engineering.
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Data-Driven Computational Methods by John Harlim
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 modeling 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 modeling 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(R) codes and appendices covering the relevant prerequisite materials are provided, making it suitable for self-study.
'The MATLAB code used for the examples in the book can be downloaded from the publisher's website; the scripts are short, well commented and can be understood without difficulty (even if you are not a MATLAB expert)' Fabio Mainardi, MAA Reviews
'… this book is useful for students or researchers entering in the topic of data assimilation or interested in statistical and computational methods for stochastic differential equations. It complements nicely other recent books in the field and gives a concise overview of some recent research activity in a very comprehensive style.' Nikolas Kantas, SIAM Review
'… this book is useful for students or researchers entering in the topic of data assimilation or interested in statistical and computational methods for stochastic differential equations. It complements nicely other recent books in the field and gives a concise overview of some recent research activity in a very comprehensive style.' Nikolas Kantas, SIAM Review
John Harlim is a Professor of Mathematics and Meteorology at the Pennsylvania State University. His research interests include data assimilation and stochastic computational methods. In 2012, he received the Frontiers in Computational Physics award from the Journal of Computational Physics for his research contributions on computational methods for modeling Earth systems. He has previously co-authored another book, Filtering Complex Turbulent Systems (Cambridge, 2012).
| SKU | Non disponible |
| ISBN 13 | 9781108472470 |
| ISBN 10 | 1108472478 |
| Titre | Data-Driven Computational Methods |
| Auteur | John Harlim |
| État | Non disponible |
| Type de reliure | Hardback |
| Éditeur | Cambridge University Press |
| Année de publication | 2018-07-12 |
| Nombre de pages | 168 |
| Note de couverture | La photo du livre est présentée à titre d'illustration uniquement. La reliure, la couverture ou l'édition réelle peuvent varier. |
| Note | Non disponible |