Higher Order Dynamic Mode Decomposition and Its Applications

1st Edition - September 22, 2020
Authors: Jose Manuel Vega, Soledad Le Clainche
Language: English
Paperback ISBN:
9 7 8 - 0 - 1 2 - 8 1 9 7 4 3 - 1
eBook ISBN:
9 7 8 - 0 - 1 2 - 8 2 2 7 6 6 - 4

Higher Order Dynamic Mode Decomposition and Its Applications provides detailed background theory, as well as several fully explained applications from a range of industria… Read more

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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.

Cover image
Title page
Table of Contents
Copyright
Dedication
Biography
Professor José M. Vega
Doctor Soledad Le Clainche
Preface
References
Chapter 1: General introduction and scope of the book
Abstract
1.1. Introduction to post-processing tools
1.2. Introduction to reduced order models
1.3. Organization of the book
1.4. Some concluding remarks
1.5. Annexes to Chapter 1
References
Chapter 2: Higher order dynamic mode decomposition
Abstract
2.1. Introduction to standard DMD and HODMD
2.2. DMD and HODMD: methods and algorithms
2.3. Periodic and quasi-periodic phenomena
2.4. Some toy models
2.5. Some concluding remarks
2.6. Annexes to Chapter 2
References
Chapter 3: HODMD applications to the analysis of flight tests and magnetic resonance
Abstract
3.1. Introduction to flutter in flight tests
3.2. Introduction to nuclear magnetic resonance
3.3. Some concluding remarks
3.4. Annexes to Chapter 3
References
Chapter 4: Spatio-temporal Koopman decomposition
Abstract
4.1. Introduction to the spatio-temporal Koopman decomposition method
4.2. Traveling waves and standing waves
4.3. The STKD method
4.4. Some key points about the use of the STKD method
4.5. Some toy models
4.6. Some concluding remarks
4.7. Annexes to Chapter 4
References
Chapter 5: Application of HODMD and STKD to some pattern forming systems
Abstract
5.1. Introduction to pattern forming systems
5.2. The one-dimensional CGLE
5.3. Thermal convection
5.4. Some concluding remarks
5.5. Annexes to Chapter 5
References
Chapter 6: Applications of HODMD and STKD in fluid dynamics
Abstract
6.1. Introduction to fluid dynamics and global instability analysis
6.2. The two- and three-dimensional cylinder wake
6.3. Flow structures in the three-dimensional cylinder wake
6.4. The zero-net-mass-flux jet
6.5. Exercise: apply HODMD to analyze the three-dimensional cylinder wake
6.6. Some concluding remarks
6.7. Annexes to Chapter 6
References
Chapter 7: Applications of HODMD and STKD in the wind industry
Abstract
7.1. On the relevance of extracting spatio-temporal patterns in wind turbine wakes
7.2. Flow structures in vertical wind turbines using the HODMD method
7.3. Analysis of the flow structures in a wind turbine with horizontal axis using STKD
7.4. LiDAR experimental data: wind velocity spatial predictions
7.5. Some concluding remarks
7.6. Annexes to Chapter 7
References
Chapter 8: HODMD and STKD as data-driven reduced order models
Abstract
8.1. Introduction to data driven reduced order models
8.2. Data-driven reduced order models based on HODMD and STKD
8.3. Data-driven adaptive ROM: HODMD on the Fly
8.4. Exercises: data-driven reduced order models for the Lorenz system
8.5. Some concluding remarks
8.6. Annexes to Chapter 8
References
Chapter 9: Conclusions
Abstract
9.1. Brief summary of the content of the book
9.2. The HODMD method
9.3. The STKD method
9.4. Scientific and industrially oriented applications
References
References
References
Index

Jose Manuel Vega

Professor Vega currently holds a Professorship in Applied Mathematics at the School of Aerospace Engineering of the Universidad Politécnica de Madrid (UPM). He received a Master and a PhD, both in Aeronautical Engineering at UPM, and a Master in Mathematics at the Universidad Complutense de Madrid. Along the years, his research has focused on applied mathematics at large, including applications to physics, chemistry, and aerospace and mechanical engineering. The main topics were connected to the analysis of partial differential equations, nonlinear dynamical systems, pattern formation, water waves, reaction–diffusion problems, interfacial phenomena, and, more recently, reduced order models and data processing tools. The latter two topics are related, precisely, to the content of this book. Specifically, he developed (with Dr. Le Clainche as collaborator) the higher order dynamic mode decomposition method, and also several extensions, including the spatio-temporal Koopman decomposition method. His research activity resulted in the publication of more than one hundred and twenty research papers in first class referred journals, as well as around forty publications resulting from scientific meetings and conferences.

Affiliations and expertise

Professor, School of Aerospace Engineering, Universidad Politecnica de Madrid, Spain

Soledad Le Clainche

Dr. Soledad Le Clainche holds a Lectureship in Applied Mathematics at the School of Aerospace Engineering of UPM. She received three Masters of Science: in Mechanical Engineering by UPCT, in Aerospace Engineering by UPM, and in Fluid Mechanics by the Von Karman Institute. In 2013 she completed her PhD in Aerospace Engineering at UPM. Her research focuses on computational fluid dynamics and in the development of novel tools for data analysis enabling the detection of spatio-temporal patterns. More specifically, she has co-developed (with Prof. Vega) the higher order dynamic mode decomposition and variants. Additionally, she has exploited these data-driven tools to develop reduced order models that help to understand the complex physics of dynamical systems. She has also contributed to the fields of flow control, global stability analysis, synthetic jets, analysis of flow structures in complex flows (transitional and turbulent) using data-driven methods, and prediction of temporal patterns using machine learning and soft computing techniques.

Affiliations and expertise

Lecturer, School of Aerospace Engineering, Universidad Politecnica de Madrid, Spain

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