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

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 differentialequations, 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.