Higher Order Dynamic Mode Decomposition and Its Applications

Jose Manuel Vega, Soledad Le Clainche

• Publisher: Academic Press
• Year: 2020
• Print ISBN: 9780128197431
• eBook ISBN: 9780128227664
• Topic: Technology & Engineering
• Subtopic: Fluid Mechanics
• Index: Technology & Engineering

Higher Order Dynamic Mode Decomposition and Its Applications provides detailed background theory, as well as several fully explained applications from a range of industrial contexts to help readers understand and use this innovative algorithm. Data-driven modelling of complex systems is a rapidly evolving field, which has applications in domains including engineering, medical, biological, and physical sciences, where it is providing ground-breaking insights into complex systems that exhibit rich multi-scale phenomena in both time and space.Starting with an introductory summary of established order reduction techniques like POD, DEIM, Koopman, and DMD, this book proceeds to provide a detailed explanation of higher order DMD, and to explain its advantages over other methods. Technical details of how the HODMD can be applied to a range of industrial problems will help the reader decide how to use the method in the most appropriate way, along with example MATLAB codes and advice on how to analyse and present results.- Includes instructions for the implementation of the HODMD, MATLAB codes, and extended discussions of the algorithm- Includes descriptions of other order reduction techniques, and compares their strengths and weaknesses- Provides examples of applications involving complex flow fields, in contexts including aerospace engineering, geophysical flows, and wind turbine design

Chapter 1: General introduction and scope of the book

Abstract

This chapter addresses some preliminary data processing tools that are needed in the remainder of the book. These tools include singular value decomposition in its various versions (economy, compact, and truncated singular value decomposition), proper orthogonal decomposition, and higher order singular value decomposition in its various versions (economy, compact, and truncated higher order singular value decomposition). These tools are illustrated with some toy models. An introduction to reduced order models, both data-driven and projection-based, is also included. The organization of the book is summarized at the end of the chapter. Some selected practice problems are proposed in Annex 1.1. Some MATLAB functions are also given in Annex 1.2 that allow for computing the various versions of singular value decomposition and higher order singular value decomposition.

Keywords

Multidimensional databases; Post-processing tools; Singular value decomposition; Proper orthogonal decomposition; Higher order singular value decomposition; Data-driven reduced order models; Projection-based reduced order models

1.1 Introduction to post-processing tools

Database post-processing tools for matrices (namely, two-dimensional databases) and higher than two order tensors (namely, higher-dimensional databases) are used for various purposes, including filtering out errors in noisy databases, decreasing the database size (compression), and extracting the underlying relevant patterns. These tools can also be used for constructing purely data-driven reduced order models (ROMs), which allow for the fast online simulation of the physical systems from which the database...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication
• Biography
• Preface
• Chapter 1: General introduction and scope of the book
• Chapter 2: Higher order dynamic mode decomposition
• Chapter 3: HODMD applications to the analysis of flight tests and magnetic resonance
• Chapter 4: Spatio-temporal Koopman decomposition
• Chapter 5: Application of HODMD and STKD to some pattern forming systems
• Chapter 6: Applications of HODMD and STKD in fluid dynamics
• Chapter 7: Applications of HODMD and STKD in the wind industry
• Chapter 8: HODMD and STKD as data-driven reduced order models
• Chapter 9: Conclusions
• References
• Index