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 codes and appendices covering the relevant prerequisite materials are provided, making it suitable for self-study. Read more...
Abstract:
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. Read more...
Author(s): Harlim, JohnYYeauthor
Publisher: Cambridge University Press
Year: 2018
Language: English
Pages: 158
Content: 1. Introduction
2. Markov chain Monte Carlo
3. Ensemble Kalman filters
4. Stochastic spectral methods
5. Karhunen-Loeve expansion
6. Diffusion forecast
Appendix A. Elementary probability theory
Appendix B. Stochastic processes
Appendix C. Elementary differential geometry
References
Index.
