Forward Uncertainty Quantification
John Jakeman
Sandia National Laboratories
Optimization and Uncertainty Quantification
Numerical models are essential for predicting the behavior of fusion energy systems, yet they are subject to multiple sources of uncertainty whose effects on model predictions must be quantified. This 75-minute, hands-on tutorial introduces forward Uncertainty Quantification (UQ): propagating uncertain inputs through a simulation to produce probability distributions of quantities of interest, enabling faster and more defensible decisions than point predictions alone. Participants will learn to (1) specify uncertainty using prior distributions, including independent and correlated parameterizations; (2) estimate expected response, variability, and failure probabilities using Monte Carlo and quasi--Monte Carlo sampling; and (3) accelerate UQ with surrogate models that enable rapid evaluation and efficient estimation of moments. The tutorial concludes with a practical introduction to multi-fidelity variance reduction via control variates, illustrating how a high-accuracy surrogate can be paired with a limited number of expensive model evaluations to achieve order-of-magnitude efficiency gains. Exercises are implemented in PyApprox and emphasize repeatable workflows for uncertainty specification, sampling, surrogate construction, and statistical estimation.