2025-07-23 –, Main Room 2
We present OptimalUncertaintyQuantification.jl: A SciML package for end-to-end distributionally robust uncertainty quantification of static and dynamic systems models. The tool performs a worst-case analysis so as to make certification/decertification decisions on engineering models defined in ModelingToolkit.jl as demonstrated on a variety of aerospace and structural engineering applications.
Uncertainty Quantification (UQ) methods explicitly account for the influence of various sources of uncertainty (e.g., input parameters, model structure, numerical simulation errors) on the predictions made by a model. Traditional techniques, such as Monte Carlo simulation, often rely on a priori assumptions regarding the probability distributions of uncertain parameters. These methods involve drawing a large number of samples from these assumed distributions and propagating them through the model. However, such distributional assumptions can be brittle and unsuitable especially for safety-critical applications for instance in aerospace [1]. The Optimal Uncertainty Quantification (OUQ) framework, pioneered by Owhadi et al. [2] avoids making these unwarranted assumptions but instead introduces partial information about the model in a systematic way. OUQ casts the problem into an optimization problem searching over the space of probability distributions with constraints encoding the known information (such as moments or bounds of the random variables). Furthermore, it leverages certain reduction theorems and transformations to generate a computationally tractable finite optimization problem. Since a primary application of OUQ is to provide worst-case certificates for safety-critical systems, the use of rigorous global optimization algorithms is essential to guarantee provable and tight bounds. This work presents OptimalUncertaintyQuantification.jl: An end-to-end framework for OUQ integrated with Julia’s SciML ecosystem.
We demonstrate the following workflow for practically relevant engineering applications:
1. Developing a system model using the ModelingToolkit.jl package.
2. Bounding this system model leveraging tools from reachability analysis such as TaylorModels.jl
3. Construction of the OUQ problem and transformation to a tractable finite dimensional optimization problem
4. Global optimization using both custom and external solvers as appropriate.
5. Certification/Decertification of the model based on optimization results
[1]: Stark, P. "Your prior can bite you on the posterior: contrasting Bayesian and frequentist measures of uncertainty." In JPL Science Visitor and Colloquium Program-Earth Science Seminar, Sept. 1, 2020. 2020.
[2]: Owhadi, H., Scovel, C., Sullivan, T.J., McKerns, M. and Ortiz, M., 2013. Optimal uncertainty quantification. Siam Review, 55(2), pp.271-345.
Distribution Statement A: Approved for Public Release; Distribution is Unlimited. PA# AFRL-2025-0776, 11 Feb 2025
Benjamin Chung is a modeling & simulation consultant with JuliaHub. Previously, he was a postdoc at the University of Washington with Behcet Acikmese working on aerospace trajectory optimization after finishing his PhD with Jan Vitek on type systems for Julia.
Dr. Von Moll is a researcher with the Control Science Center, Aerospace Systems Directorate, Air Force Research Laboratory. He holds a B.S. in Aerospace Engineering from Ohio State (2012), an M.S. in Aerospace Engineering from Georgia Institute of Technology (2016), and a Ph.D. in Electrical Engineering from University of Cincinnati (2022). Alex was a Department of Defense SMART Scholar, awarded in 2011 and again in 2014. His research interests include multi-agent systems, cooperative control, and differential games.