Karen E. Willcox, PhD, NAE, MNZM

Director, Oden Institute for Computational Engineering and Sciences | 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 | External Professor, Santa Fe Institute

Research in Multi-fidelity uncertainty quantification, multi-fidelity optimization under uncertainty, adaptive reduced models, predictive digital twins, scientific machine learning, and data to decisions in aerospace engineering

201 E 24th Street, POB 4.102
University of Texas at Austin
Austin, TX 78712
(512) 471-3312
Presenting Digital twins at TEDxUTAustin in March 2022

Presenting Digital twins: A personalized future of computing for complex systems at TEDxUTAustin. Link to Youtube video.


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 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 the Oden Institute in 2018, she spent 17 years as a professor at the Massachusetts Institute of Technology, where she served as Professor of Aeronautics and Astronautics, the founding Co-Director of the MIT Center for Computational Engineering, and the Associate Head of the MIT Department of Aeronautics and Astronautics. She is also an External Professor at the Santa Fe Institute. Willcox holds a Bachelor of Engineering Degree from the University of Auckland, New Zealand, and masters and PhD degrees from MIT. Prior to becoming a professor at MIT, she worked at Boeing Phantom Works with the Blended-Wing-Body aircraft design group.

In 2022, Willcox was elected to the National Academy of Engineering "for contributions to computational engineering methods for the design and optimal control of high-dimensional systems with uncertainties." In 2017, she was awarded Member of the New Zealand Order of Merit (MNZM) for services to aerospace engineering and education. She is Fellow of the Society for Industrial and Applied Mathematics (SIAM), Fellow of the American Institute of Aeronautics and Astronautics (AIAA), and member of the American Society for Engineering Education (ASEE). She is currently co-chair of the NSF Advisory Committee on Cyberinfrastructure, vice-chair of Institute for Mathematical and Statistical Innovation (IMSI) Board of Advisors, and chair of the Committee to Visit Harvard University Information Technology. She is currently a member of the AIAA Board of Trustees and the National Academies Board on Mathematical Sciences and Analytics. She has served on five National Academies studies and review panels, including being a current member of the National Academies Study on Post-Exascale Computing for the National Nuclear Security Administration. She has served in multiple leadership positions within AIAA and SIAM, including leadership roles in the SIAM Activity Group on Computational Science and Engineering, the SIAM Activity Group on Data Science, and the AIAA Multidisciplinary Design Optimization Technical Committee. She is formerly Section Editor of SIAM Journal on Scientific Computing and current Editorial Board member of AIAA Journal.

Willcox's research has produced scalable computational methods for design of next-generation engineered systems, with a particular focus on reduced-order modeling as a way to learn principled physics-based approximations from data, multifidelity formulations to leverage multiple sources of information in decision-making and uncertainty quantification, and scalable methods for predictive digital twins. Her model reduction and multifidelity methods are widely applied across the scientific and engineering community, and have been incorporated into industry/government codes for aircraft system design and environmental policy decision-making. She currently has funded projects supported by the US Air Force Office of Scientific Research, Air Force Research Laboratory, ARPA-E, Department of Energy, Lockheed Martin, NASA, and Sandia National Laboratories. Willcox currently leads several multi-institution research teams: she is Co-director of the Department of Energy AEOLUS Multifaceted Mathematics Capability Center on Advances in Experimental Design, Optimal Control, and Learning for Uncertain Complex Systems; she leads an Air Force MURI team on Machine Learning for Physics-based Systems; and she leads the Rise of the Machines team developing robust, interpretable, scalable, efficient methods for digital twins under the Department of Energy AI and Decision Support for Complex Systems program. Willcox has co-authored more than 130 papers in peer-reviewed journals and advised 54 graduate students, including 22 PhD students.

In addition to her research pursuits, Willcox is active in education innovation. She served as co-Chair of the MIT Online Education Policy Initiative, co-Chair of the 2013-2014 Institute wide Task Force on the Future of MIT Education, and Chair of the MIT OpenCourseWare Faculty Advisory Board. She is a recognized innovator in the U.S. education landscape, where she is a 2015 recipient of a First in the World Department of Education grant that developed and deployed educational technologies in community colleges. She continues to direct the Mapping Lab, which develops technologies for the future of digital education.


About me

I was born and raised in Auckland, New Zealand. I am a first-generation college student, the daughter of an air-conditioning fitter and a secretary, neither of whom finished high school. The first time I left New Zealand was in 1994, when I travelled to Boston to begin graduate school at MIT. As the first of my entire family and extended family to attend college, I fully appreciate the challenges facing today's first-generation college students: the overwhelming uncertainty of choosing a degree path, the financial need to work a part-time job during studies, the difficulty in navigating all those extra things like finding a summer internship, the challenge of being far from home, and the general burden of meeting your family's expectations while knowing that they can't possibly understand what you're going through. I am incredibly fortunate to have had some amazing mentors through my career, and that has instilled in me a lifelong commitment to mentoring.

I am passionate about engineering and the contribution it makes to society. Engineers have literally built the world around us. They have made our lives better in countless ways and they have enabled the human race to make superhuman achievements. I am inspired to advance the impact of engineering on the world through my research that sits at the interfaces of engineering, mathematics, and computation. I also have a strong commitment to teaching and education. Every day I am inspired to be a part of educating the next generation of engineers. I am also passionate about the role that engineering thinking and technology can play in advancing education more broadly. I have an unwavering commitment to building a more diverse and more inclusive professional community. Diversity of perspective is a driving part of my research group — the group brings together students with different backgrounds (engineering, mathematics, computer science, physics), different nationalities (Belgium, Canada, Colombia, Germany, India, Iran, Italy, New Zealand, Romania, Ukraine, USA), and different life experiences. We all learn from each other every day, and that drives us towards excellence.

Recent News

October 2022

We have released the Operator Inference in Python package, with new documentation and tutorial examples.

Congratulations to postdoc Rudy Geelen on having his paper Operator inference for non-intrusive model reduction with nonlinear manifolds accepted for publication in Computer Methods in Applied Mechanics and Engineering. A collaboration with Steve Wright, this paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models.

Karen will deliver the 2022 Leçons Jacques-Louis Lions at the Sorbonne. The mini-course "Learning physics-based models from data: Perspectives from projection-based model reduction" will take place October 25, 26 and 27. The colloquium "Mathematical and computational foundations for enabling predictive digital twins at scale" will take place on October 28.

September 2022

Karen presented Digital twins: A personalized future of computing for complex systems at TEDxUTAustin in March 2022. The invited talk is now published on Youtube.

August 2022

Congratulations to CSEM PhD student Sean McBane on the successful defense of his PhD thesis "Topology optimization and uncertainty quantification using component-wise reduced order modeling." Sean's thesis shows the power of decomposition approaches together with component-based reduced-order modeling to address the challenges of complex systems with high-dimensional parameter spaces. Sean will start a job at Cadence this month.

July 2022

On July 1, Karen starts a six-year term as a member of the International Association for Computational Mechanics (IACM) Executive Council.

June 2022

Karen is giving an invited keynote talk at the Department of Energy AI for Science, Engineering and Security workshop.

May 2022

Congratulations to postdoc Parisa Khodabakhshi, who will start a tenure track position in the fall at Lehigh University. In the past three years working with me, Parisa has made some excellent contributions in the development of reduced-order modeling for additive manufacturing and multifidelity uncertainty quantification methods for nonlocal problems.

Congratulations to postdoc Marco Tezzele for winning the ECCOMAS prize for best thesis of 2021 for his thesis Data-driven parameter and model order reduction for industrial optimisation problems with applications in naval engineering, which he completed with SISSA Professor Gianlugi Rozza.

April 2022

The Oden Institute will be co-hosting Rising Stars in Computational and Data Sciences in Albuquerque April 20-21. We had so many outstanding nominations that it was very difficult to choose the 32 attendees. I can't wait to meet all these amazing young women for two days of research presentations, career discussions and networking.

March 2022

Congratulations to Elizabeth Qian and Ionut Farcas for having their paper Reduced operator inference for nonlinear partial differential equations accepted to SIAM Journal on Scientific Computing. The paper develops the Operator Inference reduced-order modeling approach in the continuous (i.e., PDE) setting and applies the method to a large-scale 3D combustion problem.

Farewell to postdoc Michael Kapteyn, who leaves us to pursue the next stage of his career. Michael's PhD work in digital twins has laid the groundwork for so many exciting new projects. Best of luck Michael!

February 2022

Karen has been elected to the National Academy of Engineering "for contributions to computational engineering methods for the design and optimal control of high-dimensional systems with uncertainties." I am so appreciative of all the opportunities I have had throughout my career, made possible only by working with the most amazing students, postdocs, collaborators, colleagues and staff.

Congratulations to Michael Kapteyn for having his paper A Probabilistic Graphical Model Foundation for Enabling Predictive Digital Twins at Scale selected for the Nature Computational Science one-year anniversary collection.

January 2022

Karen was honored to give the AIAA Structures, Structural Dynamics, and Materials (SDM) Lecture, presented at AIAA SciTech Forum. Here is a link to her slides for her talk titled From reduced-order modeling to scientific machine learning: How computational science is enabling the design of next-generation aerospace systems.

December 2021

Welcome to new postdoc Marco Tezzele who joins us from SISSA. Marco is an expert on reduced-order modeling and design optimization. He will be joining our NASA ULI project and leading the effort to build digital twins in support of scalable autonomous cargo operations.

November 2021

Welcome to new postdoc Matteo Croci who joins us from Oxford. Matteo is an expert on multilevel Monte Carlo and numerical methods for PDEs. He will be joining the PSAAP project.

Congratulations to Rudy Geelen for having his paper Localized non-intrusive reduced-order modeling in the operator inference framework accepted for publication in Philosophical Transactions of the Royal Society A. The paper presents data-driven learning of localized reduced models. Instead of a global reduced basis, the approach employs multiple local approximation subspaces. This localization permits adaptation of a reduced model to local dynamics, thereby keeping the reduced dimension small. This is particularly important for reduced models of nonlinear systems of partial differential equations, where the solution may be characterized by different physical regimes or exhibit high sensitivity to parameter variations. Localization has been used in a number of model reduction approaches in the past; the key contribution here is the non-intrusive formulation via Operator Inference.

Congratulations to Parisa Khodabakhshi for having her paper Non-intrusive data-driven model reduction for differential algebraic equations derived from lifting transformations accepted for publication in Computer Methods in Applied Mechanics and Engineering. The paper presents a non-intrusive data-driven approach for model reduction of nonlinear systems. The approach considers the particular case of nonlinear PDEs that form systems of partial differential algebraic equations when lifted to polynomial form. Such systems arise, for example, when the governing equations include Arrhenius reaction terms (e.g., in reacting flow models) and thermodynamic terms (e.g., the Helmholtz free energy terms in a phase-field solidification model).

October 2021

Welcome to new postdoc Aniketh Kalur. Aniketh just completed his PhD at the University of Minnesota on "Reduced-Complexity Modeling for Control and Nonlinear Analysis of Transitional Flows."

Karen will be giving a keynote talk on Predictive Digital Twins at The 13th International Symposium on NDT in Aerospace 2021.

Karen will be giving a plenary talk on Research Needs and Future Directions in Aviation Digital Twins: Applications and Opportunities, hosted by the MITRE Corporation.

September 2021

Welcome to new Willcox group students Ben Zastrow (Aerospace Engineering) and Valentyn Visyn (Computational Science, Engineering and Mathematics).

Congratulations to former Kiwi group graduate student and HKUST Assistant Professor Rhea Liem for being selected as the 2021 recipient of Hong Kong's University Grants Committee Teaching Award!

Michael, Ionut and Anirban will all be giving a technical talks at the Conference on Mechanistic Machine Learning and Digital Twins for Computational Science, Engineering and Technology.

Karen will be giving a keynote talk on Predictive Digital Twins at the Computing in Engineering Forum, hosted by the University of Wisconsin-Madison.

August 2021

Omar Ghattas and I have a paper in the 2021 volume of Acta Numerica. Learning physics-based models from data: Perspectives from inverse problems and model reduction gives a 110-page introduction to inverse problems and model reduction, representing some of our 16 years of collaboration. The paper is available open access.

Congratulations to Julie Pham for being named one of Aviation Week Network’s 20 Twenties!

Congratulations to Anirban Chaudhuri and Boris Kramer for having their paper Certifiable Risk-Based Engineering Design Optimization accepted to AIAA Journal. This paper proposes two notions of certifiability: the first is based on accounting for the magnitude of failure to ensure data-informed conservativeness, and the second is the ability to provide optimization convergence guarantees by preserving convexity. Satisfying these notions leads to certifiable risk-based design optimization (CRiBDO).

July 2021

Michael Kapteyn's digital twin research is highlighted on the Department of Energy Office of Science website.

Our paper Modeling COVID-19 disruptions via network mapping of the Common Core Mathematics Standards is a finalist for Best Paper in the Computers in Education section of the ASEE Annual Conference & Exposition. Congratulations to Luwen Huang and Kayla Bicol!

Karen is giving an Invited Plenary talk at the European Control Conference (ECC21) on Thursday July 1.

June 2021

Best wishes to postdoc James Koch who is leaving to start a staff research position at Pacific Northwest National Laboratory.

Congratulations to Stefanie Salinger for completing her master's thesis "Toward Predictive Digital Twins for Self-Aware Unmanned Aerial Vehicles: Non-Intrusive Reduced Order Models and Experimental Data Analysis." Stefanie performed an amazing pivot to reduced order modeling when the pandemic shut down her UAV hardware experiments. Stefanie will be starting a position at Lockheed Martin in Fort Worth.

Welcome to new Oden Institute master's student Vignesh Sella.

May 2021

I was honored to testify to Congress for the Subcommittee on Energy of the House Committee on Science, Space, and Technology hearing on Accelerating Discovery: the Future of Scientific Computing at the Department of Energy. My written testimony is posted here.

Congratulations to PhD student Michael Kapteyn for having his paper A Probabilistic Graphical Model Foundation for Enabling Predictive Digital Twins at Scale published in Nature Computational Science. This paper proposes a probabilistic graphical model as a formal mathematical representation of a digital twin and its associated physical asset. This formulation naturally integrates data, predictive models, and decisions. We illustrate the approach by building a structural digital twin of our group's unmanned aerial vehicle (UAV) hardware asset and show how the digital twin enables dynamic mission re-planning in response to in-flight structural damage.

Our perspective Scaling Digital Twins from the Artisanal to the Industrial was published in Nature Computational Science. This opinion piece makes the case that advancing the mathematical and algorithm foundations is essential to achieving digital twins at scale. It draws from examples in cardiology and aerospace engineering.

Congratulations to Michael Kapteyn for a successful PhD defense!

April 2021

PhD student Michael Kapteyn's research will be presented next week at a NATO Science and Technology Organization (STO) Applied Vehicle Technology Panel (AVT) Research Workshop on Intelligent Solutions for Improved Mission Readiness of Military UxVs.

Congratulations to postdoc Parisa Khodabakhshi for having her paper A multifidelity method for a nonlocal diffusion model accepted for publication in Applied Mathematics Letters. This paper puts forward the idea that the horizon δ in a nonlocal model can be used to generate a hierarchy of multifidelity models, similar to using the grid size h to create multilevel models. The paper develops this idea in the context of forward uncertainty quantification using a multifidelity Monte Carlo formulation. Another great collaboration with Max Gunzburger!

March 2021

Together with Patrick Heimbach and Omar Ghattas, Karen co-authored a comment piece The imperative of physics-based modeling and inverse theory in computational science in Nature Computational Science. We make the case that inverse theory has a key role to play in the data-driven future of computational science, especially for applications in the physical/nature world where data are sparse.

Congratulations to MIT Mapping Lab researcher Luwen Huang for having her paper Network models and sensor layers to design adaptive learning using educational mapping accepted in Design Science. This paper defines "Micro-outcomes" as extremely fine-grained statements of learning ability and then shows how network modeling can be used to design a sensor layer of high-resolution assessments. When put together, this forms the mathematical and computational foundation for intelligent tutoring, intelligent teaching assistants, and data-driven teaching feedback. We describe our deployment of the ideas in College Algebra and Introductory Accounting subjects at Arapahoe Community College and Quinsigamond Community College, and in the MIT sophomore Aerospace Engineering class Signals and Systems.

Congratulations to former visiting PhD student Max Ehre for having his paper Conditional reliability analysis in high dimensions based on controlled mixture importance sampling and information reuse accepted for publication in Computer Methods in Applied Mechanics and Engineering. This paper employs information reuse to reduce the computational cost of conditional reliability analysis.

Karen is giving an Invited Plenary talk on "A Probabilistic Graphical Model Foundation for Enabling Predictive Digital Twins at Scale" at the SIAM Conference on Computational Science and Engineering (CSE21) on Tuesday March 2.

Elizabeth, Graham, Ionut, Mengwu, Michael, Parisa, Sean and Shane will all be presenting at SIAM Conference on Computational Science and Engineering (CSE21) March 1-5. The group's favorite conference; sorry to miss it in person!

February 2021

Congratulations to postdoc Mengwu Guo who this month starts his tenure-track faculty position as Assistant Professor in the Department of Applied Mathematics at University of Twente. Best wishes Mengwu!

Congratulations to former postdoc Qifeng Liao who just received tenure at ShanghaiTech. Best wishes for the next phase of your career Qifeng!

January 2021

Congratulations to former PhD student Victor Singh for having his paper Decision Making Under Uncertainty for a Digital Thread Enabled Design Process accepted for publication in the Journal of Mechanical Design. This paper presents a formulation of decision under uncertainty with Digital Thread, using Bayesian statistics and decision theory.

Karen is giving a keynote talk on "Aerospace Design in the Age of Big Data and Big Compute" at the AIAA Scitech Forum on Tuesday January 19.

Congratulations to PhD student Shane McQuarrie for having his paper Data-driven reduced-order models via regularized operator inference for a single-injector combustion process accepted for publication in the Journal of the Royal Society of New Zealand. This paper derives predictive reduced-order models for rocket engine combustion dynamics via our Operator Inference approach, a scientific machine learning approach that blends data-driven learning with physics-based modeling. The codes and example problems are available on Github.

December 2020

Karen is giving an invited talk the Machine Learning for Engineering Modeling, Simulation and Design workshop at NeurIPS 2020.

Congratulations to Elizabeth Qian for a successful PhD defense!

November 2020

Congratulations to PhD student Michael Kapteyn for winning the 2020 AIAA Best MDO Paper Prize for his paper Toward predictive digital twins via component-based reduced-order models and interpretable machine learning. This award is presented to the paper selected from among all AIAA papers published at MDO sessions in 2020 AIAA conferences.

Congratulations to Anirban for having his paper mfEGRA: Multifidelity Efficient Global Reliability Analysis through Active Learning for Failure Boundary Location accepted to Structural and Multidisciplinary Optimization. The paper develops a multifidelity version of the popular EGRA method, which is used for locating contours (e.g., failure boundaries, stability boundaries). The multifidelity formulation provides significant computational speedups.

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