Uncertainty Quantification and Reduction for the AIAA Aerodynamics Challenge Using Sensitivity-Based and Diffusion Model Updating

This paper presents the principles and techniques employed to address the AIAA Second Uncertainty Quantification Challenge Problem for Aerodynamics. Two distinct model updating strategies for uncertainty quantification and reduction are investigated, a sensitivity-based approach and a data-driven diffusion model-based approach. Both methods aim to infer the posterior distributions of key aerodynamic input parameters, which are subsequently propagated through either a surrogate model or XFOIL to obtain posterior-predictive lift, drag, and moment coefficients. The diffusion model shows consistent posterior-predictive responses across both the surrogate and XFOIL, whereas the sensitivity-based approach produces sharply concentrated parameter posteriors that may represent a more limited uncertainty range. Across multiple operating configurations, the two approaches produce coherent predictive aerodynamic responses despite their differing parameter posterior structures. The findings underscore that, in UQ challenges of this type, it is not only essential to characterise multiple sources of uncertainty, but equally, if not more, critical to employ an appropriate inverse uncertainty-reduction mechanism capable of leveraging the necessarily limited observational data. Designing such inverse processes to extract maximal information from sparse data remains a central difficulty and an important direction for future research in aerodynamic uncertainty quantification.