University of Texas at Austin

Past Event: Babuška Forum

Learning low-dimensional models: Nonlinear model reduction via lifting transformations and proper orthogonal decomposition

Karen Willcox, Director, ICES, UT Austin

10 – 11AM
Friday Sep 28, 2018

POB 6.304

Abstract

Analysis of the physical governing equations of a system can reveal variable transformations that transform a general nonlinear model into a model with more structure. In particular, the introduction of auxiliary variables can convert a general nonlinear model to a model with polynomial nonlinearities, a so-called "lifted" system. The lifted model is equivalent to the original model; it uses a change of variables, but introduces no approximations. We present an approach that combines lifting with proper orthogonal decomposition model reduction. The approach uses a data-driven formulation to learn the low-dimensional model from high-fidelity simulation data, but a key aspect of the approach is that the state-space in which the learning is achieved is derived using the problem physics. A key benefit of the approach is that there is no need for additional approximations of the nonlinear terms, in contrast with existing nonlinear model reduction methods that require sparse sampling or hyper-reduction. A second benefit is that the lifted problem structure opens new pathways for rigorous analysis and input-independent model reduction. The method is demonstrated for nonlinear systems of partial differential equations arising in rocket combustion applications. ** Note that Professor Willcox has an open GRA position for research related to this topic. Bio Karen E. Willcox is Director of the Institute for Computational Engineering and Sciences (ICES) and a Professor of Aerospace Engineering and Engineering Mechanics at the University of Texas at Austin. She holds the W. A. “Tex” Moncrief, Jr. Chair in Simulation-Based Engineering and Sciences and the Peter O'Donnell, Jr. Centennial Chair in Computing Systems. Prior to joining ICES in 2018, she spent 17 years as a professor at the Massachusetts Institute of Technology, where she served as the founding Co-Director of the MIT Center for Computational Engineering and the Associate Head of the MIT Department of Aeronautics and Astronautics. Prior to joining the MIT faculty, she worked at Boeing Phantom Works with the Blended-Wing-Body aircraft design group. Her research at MIT has produced scalable computational methods for design of next-generation engineered systems, with a particular focus on model reduction as a way to learn principled approximations from data and on multi-fidelity formulations to leverage multiple sources of uncertain information. She is a Fellow of SIAM and Associate Fellow of AIAA.

Event information

Date
10 – 11AM
Friday Sep 28, 2018
Location POB 6.304
Hosted by Thomas O'Leary-Roseberry