Uncertainty Quantification via Latent Gaussian Process Surrogates for the Second AIAA Fluid Dynamics UQ Challenge Problem

Uncertainty quantification (UQ) is critical in computational aerodynamics to ensure credible predictions for design and analysis. The AIAA Fluid Dynamics UQ Challenge Problem 2 addresses this need by tasking participants to predict aerodynamic coefficients (lift ���� , drag ���� , and pitching moment ����) under epistemic input uncertainty using the XFOIL panel solver, with synthetic “truth” data provided for validation. Crucially, this truth data includes epistemic uncertainty intervals on both the inputs and outputs. To efficiently quantify uncertainty in this setting, we present a Bayesian latent Gaussian Process (GP) surrogate model that integrates multiple sources of uncertainty—input variability and model form discrepancy—into a single framework. GP regression provides a flexible surrogate with built-in uncertainty estimates, and we augment it with a latent discrepancy term following the Kennedy and O’Hagan calibration approach. This allows the true aerodynamic response to be modeled as the sum of the XFOIL prediction and an unknown bias field, enabling principled calibration to sparse truth data and improved predictive accuracy over standard surrogate-bias correction methods.