Past Event: Babuška Forum

Reduced-order modeling of parametrized large-scale systems

Tan Bui Thanh, Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin

Abstract

Most reduced-order modeling (aka model reduction) techniques employ a reduced-space basis on which the large-scale mathematical problem is projected to become a much smaller system whose solution can be obtained in a fraction of the cost of the original problem. The basis is usually formed as the span of a set of solutions of the large-scale system, which are computed for selected values (samples) of parameters and forcing inputs. In this talk, a basis idea behind reduced-order modeling will be presented and a connection to the fundamental mathematical tools such as Fourier expansion and Karhunen-Loeve expansion will be highlighted. The important connection with compressive sensing will be also outlined. For problems where canonical bases are not efficient, adaptive/empirical bases are necessary. To that end, the proper orthogonal decomposition (POD) method will be presented as an effective tool. The relationship between POD, PCA (principle component analysis), and SVD (singular value decomposition) will be outlined. Various successful applications to complex problems in science and engineering will be shown to demonstrate the effectiveness of reduced-order models towards real time simulations. If time permits, challenging topics such as how to find the "best" reduced basis and how to construct reduced models for nonlinear problems will be discussed. Bio Tan Bui received his PhD in 2007 in computational fluid dynamics from the Department of Aeronautics and Astronautics at MIT. He joined ICES as a postdoc in 2008, and became a faculty in the Department of Aerospace Engineering and Engineering Mechanics, UT Austin, in 2013. His research in computational mechanics include: Inverse problem, uncertainty quantification, optimization, and high-order finite element methods. His research has been supported by DOE, NSF, DTRA, AFOSR, KAUST, Exxon Mobil.