Past Event: Oden Institute Seminar

Model reduction: Systems-theoretic perspective

Serkan Gugercin, Professor, Department of Mathematics, Virginia Tech

Abstract

Numerical simulation of large-scale dynamical systems plays a crucial role in studying a great variety of complex physical phenomena. However, simulations in these large-scale settings present significant computational difficulties. Model reduction aims to resolve this computational burden by constructing simpler (reduced order) models, which are much easier and faster to simulate and yet accurately represent the original system. These simpler reduced order models can then serve as efficient surrogates for the original, replacing them, for example, in optimal control and design. In this talk, we will focus on systems theoretical methods for model reduction, with a special emphasis on interpolatory methods based on rational approximation. After reviewing the concept of interpolation in the setting of dynamical systems, we will discuss how to construct optimal interpolants. If time allows, we will also describe recent extensions to nonlinear dynamics. We will use various examples to illustrate the theoretical discussion. Bio Serkan Gugercin is a professor of Mathematics at Virginia Tech. He holds the the A.V. Morris Professorship and is a core faculty member in the Division of Computational Modeling and Data Analytics. In 1992, he received his B.S. degree in Electrical and Electronics Engineering from Middle East Technical University, Ankara, Turkey; and his M.S. and Ph.D. degrees in Electrical Engineering from Rice University, in 1999 and 2003, respectively. His primary research interests are model reduction, data-driven modeling, numerical linear algebra, approximation theory, and systems and control theory. Dr. Gugercin received the Ralph Budd Award for Research in Engineering from Rice University in 2003 for the best doctoral thesis in the School of Engineering; Teaching Award from Jacobs University Bremen, in 2003; the National Science Foundation Early CAREER Award in Computational and Applied Mathematics in 2007; and the Alexander von Humboldt Research Fellowship in 2016. He is currently serving as an Associate Editor for SIAM Journal on Scientific Computing, and Systems and Control Letters.