Higher Order Dynamic Mode Decomposition and Its Applications

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 Front-Matter_2021_Higher-Order-Dynamic-Mode-Decomposition-and-Its-Applicatio Copyright_2021_Higher-Order-Dynamic-Mode-Decomposition-and-Its-Applications Dedication_2021_Higher-Order-Dynamic-Mode-Decomposition-and-Its-Applications Contents_2021_Higher-Order-Dynamic-Mode-Decomposition-and-Its-Applications Contents Biography_2021_Higher-Order-Dynamic-Mode-Decomposition-and-Its-Applications Biography Professor José M. Vega Doctor Soledad Le Clainche Preface_2021_Higher-Order-Dynamic-Mode-Decomposition-and-Its-Applications Preface Chapter-1---General-introduction-a_2021_Higher-Order-Dynamic-Mode-Decomposit 1 General introduction and scope of the book 1.1 Introduction to post-processing tools 1.1.1 Singular value decomposition 1.1.2 A toy model to illustrate SVD 1.1.3 Proper orthogonal decomposition 1.1.4 Higher order SVD 1.1.5 A toy model to illustrate HOSVD 1.1.6 Applications of SVD and HOSVD 1.2 Introduction to reduced order models 1.2.1 Data-driven ROMs 1.2.2 Projection-based ROMs 1.3 Organization of the book 1.4 Some concluding remarks 1.5 Annexes to Chapter 1 A. Compact SVD B. Truncated SVD C. Economy HOSVD D. Compact HOSVD E. Truncated HOSVD Chapter-2---Higher-order-dynamic-_2021_Higher-Order-Dynamic-Mode-Decompositi 2 Higher order dynamic mode decomposition 2.1 Introduction to standard DMD and HODMD 2.2 DMD and HODMD: methods and algorithms 2.2.1 The standard (optimized) DMD method: the DMD-1 algorithm 2.2.2 The DMD-d algorithm with d>1 2.2.3 HODMD for spatially multidimensional data, involving more than one spatial variables 2.2.4 Iterative HODMD 2.2.5 Some key points to successfully use the DMD-d algorithm with d>=1 2.3 Periodic and quasi-periodic phenomena 2.3.1 Approximate commensurability 2.3.2 Semi-analytic representation of periodic dynamics and invariant periodic orbits in phase space 2.3.3 Semi-analytic representation of quasi-periodic dynamics and the associated invariant tori in phase space 2.4 Some toy models 2.5 Some concluding remarks 2.6 Annexes to Chapter 2 A. HODMD algorithm: the main program B. DMD-d algorithm C. DMD-1 algorithm D. Reconstruction of the original field E. Approximate commensurability Chapter-3---HODMD-applications-to-the-anal_2021_Higher-Order-Dynamic-Mode-De 3 HODMD applications to the analysis of flight tests and magnetic resonance 3.1 Introduction to flutter in flight tests 3.1.1 Training the method using a toy model for flight tests 3.1.2 Using the method in actual flight tests experimental data 3.2 Introduction to nuclear magnetic resonance 3.2.1 Training the method using a magnetic resonance toy model 3.2.2 Using the method with synthetic magnetic resonance experimental data 3.3 Some concluding remarks 3.4 Annexes to Chapter 3 A. Flight test experiments: toy model B. Nuclear magnetic resonance: toy model Chapter-4---Spatio-temporal-Koop_2021_Higher-Order-Dynamic-Mode-Decompositio 4 Spatio-temporal Koopman decomposition 4.1 Introduction to the spatio-temporal Koopman decomposition method 4.2 Traveling waves and standing waves 4.3 The STKD method 4.3.1 A scalar state variable in one space dimension 4.3.2 Vector state variable with one longitudinal and one transverse coordinate 4.3.3 Vector state variable with two transverse and one longitudinal coordinates 4.3.4 Vector state variable with one transverse and two longitudinal coordinates 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 A. The STKD algorithm: main function B. Spatio-temporal DMD C. DMD-d for STKD D. DMD-1 for STKD E. Reconstruction F. Dispersion diagram Chapter-5---Application-of-HODMD-and-ST_2021_Higher-Order-Dynamic-Mode-Decom 5 Application of HODMD and STKD to some pattern forming systems 5.1 Introduction to pattern forming systems 5.2 The one-dimensional CGLE 5.2.1 Properties of the CGLE 5.2.2 The one-dimensional CGLE with Neumann boundary conditions 5.2.3 The one-dimensional CGLE with periodic boundary conditions 5.3 Thermal convection 5.3.1 The Lorenz system 5.3.2 Thermal convection in a three-dimensional rotating spherical shell 5.4 Some concluding remarks 5.5 Annexes to Chapter 5 Chapter-6---Applications-of-HODMD-a_2021_Higher-Order-Dynamic-Mode-Decomposi 6 Applications of HODMD and STKD in fluid dynamics 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 A. Iterative, multi-dimensional HODMD in the wake of a three- dimensional circular cylinder B. Calculate HOSVD Chapter-7---Applications-of-HODMD-an_2021_Higher-Order-Dynamic-Mode-Decompos 7 Applications of HODMD and STKD in the wind industry 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 7.4.1 HODMD for spatial forecasting: toy model 7.4.2 HODMD for spatial forecasting: LiDAR experiments 7.5 Some concluding remarks 7.6 Annexes to Chapter 7 A. Toy model B. Spatial data forecasting Chapter-8---HODMD-and-STKD-as-data-d_2021_Higher-Order-Dynamic-Mode-Decompos 8 HODMD and STKD as data-driven reduced order models 8.1 Introduction to data driven reduced order models 8.2 Data-driven reduced order models based on HODMD and STKD 8.2.1 Data-driven ROM for temporal forecasting in the three-dimensional wake of a circular cylinder 8.2.2 Spatio-temporal forecasting in a toy model 8.3 Data-driven adaptive ROM: HODMD on the Fly 8.3.1 Application of the HODMD on the Fly data driven ROM to the one-dimensional complex Ginzburg-Landau equation 8.4 Exercises: data-driven reduced order models for the Lorenz system 8.4.1 Standard data driven ROM 8.4.2 Partially adaptive data driven ROM 8.5 Some concluding remarks 8.6 Annexes to Chapter 8 A. STKD for extrapolation in a toy model: the toy model B. HODMD to construct a standard HODMD-based data driven ROM for extrapolation in Lorenz system C. HODMD to construct a standard HODMD-based data driven ROM for extrapolation in Lorenz system. Additional function Chapter-9---Conclusi_2021_Higher-Order-Dynamic-Mode-Decomposition-and-Its-Ap 9 Conclusions 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 9.4.1 Flight tests and magnetic resonance 9.4.2 Application of the HODMD and STKD methods to pattern forming systems 9.4.3 Applications of HODMD in fluid dynamics 9.4.4 Applications of HODMD and STKD in the wind industry 9.4.5 Data-driven reduced order models obtained via the HODMD and STKD methods References_2021_Higher-Order-Dynamic-Mode-Decomposition-and-Its-Applications References Index_2021_Higher-Order-Dynamic-Mode-Decomposition-and-Its-Applications Index