Karen E. Willcox is Director of the Oden Institute for Computational Engineering and Sciences, Associate Vice President for Research, and Professor of Aerospace Engineering and Engineering Mechanics at the University of Texas at Austin. She is also External Professor at the Santa Fe Institute. At UT, 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. Before joining the Oden Institute 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.

Willcox has co-authored more than 150 papers in peer-reviewed journals and advised more than 60 graduate students. She is a Fellow of the Society for Industrial and Applied Mathematics (SIAM), a Fellow of the American Institute of Aeronautics and Astronautics (AIAA), and a Fellow of the US Association for Computational Mechanics (USACM). She is the recipient of the 2024 Theodore von Karman Prize and the 2023 J.T. Oden Medal. In 2022 she was elected to the U.S. National Academy of Engineering (NAE) and in 2017 she was appointed Member of the New Zealand Order of Merit (MNZM) for services to aerospace engineering and education.

Willcox Research GroupのWebページ（外部サイト）

Reduced-order models as a foundation for predictive digital twins

Abstract

A digital twin is a computational model or set of coupled models that evolves over time to persistently represent the structure, behavior, and context of a unique physical system. A dynamic bidirectional flow between the physical world and the digital world is central to the digital twin concept. Mathematically, these bidirectional flows manifest as dynamic data assimilation, control, and optimization tasks. Reduced-order models are a key enabling technology for predictive digital twins, since they provide the computational speedups needed to solve these tasks in real-time (or near real-time) dynamic settings.

This talk presents our Operator Inference approach for reduced-order modeling. Operator Inference combines classical theory of projection-based reduced-order modeling with a modern algorithmic perspective from data-driven scientific machine learning. The result is a scalable, non-intrusive, physics-informed approach to deriving reduced-order models that embed structure dictated by the underlying physics. An attractive property of the Operator Inference approach is its flexibility in expressing the reduced-order model in a linear subspace or a nonlinear (polynomial) manifold. Operator Inference is shown to be successful in achieving predictive reduced-order models for challenging digital twin applications where training data are sparse and expensive to acquire.