Karen Willcox

MNZM – Director, Oden Institute for Computational Engineering and SciencesThe University of Texas at Austin | Associate Vice President for Research | Professor of Aerospace Engineering and Engineering Mechanics | W. A. “Tex” Moncrief, Jr. Chair in Simulation-Based Engineering and Sciences | Peter O’Donnell, Jr. Centennial Chair in Computing Systems. US.

“Digital Twin: Graph Formulations for Managing Complexity and Uncertainty“

18 February 2025

Abstract

Our work has proposed graphical models and graph-based methods as fundamental enablers of digital twins. Graph-based representations are well known to be suited for describing complex systems where the connections between entities are as important as the entities themselves. The interconnections within and across data, models, and decisions are central to a digital twin’s value. Not only does a graph emphasize the scalable representation of such interrelationships, it also provides a natural mathematical setting for addressing uncertainty and complexity — arguably the two biggest barriers to scalable deployment and adoption of digital twins. We discuss how recent advances in theory and algorithms for large-scale knowledge graphs and graphical models can be combined in a multi-layered formulation to provide a powerful foundation for achieving scalable digital twins for complex systems. We illustrate our approaches by creating an educational digital twin to support decision-making around transfer student pathways for the state of Texas. The educational digital twin represents the dynamic academic pathways of millions of students across hundreds of demographic and academic dimensions.

Bio

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. 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 in 2017 was appointed Member of the New Zealand Order of Merit (MNZM) for services to aerospace engineering and education. In 2022 she was elected to the National Academy of Engineering (NAE).

MW25 Slides