Uncertainty Propagation in CFD Simulations using Non-Intrusive Polynomial Chaos Expansion and Reduced Order Modeling

Uncertainty propagation in expensive simulations, such as computational fluid dynamics, with high-dimensional outputs is challenging due to limited training data and prohibitive computational evaluation costs. Proper Orthogonal Decomposition (POD) is a popular linear dimension reduction method used in reduced order modeling (ROM) to enable the rapid prediction of uncertain outputs. However, achieving parametric robustness is particularly challenging in problems that exhibit strong non-linearities, discontinuities, and gradients. This study presents a non-intrusive, nonlinear ROM which combines manifold learning with sparse polynomial chaos expansions to enable uncertainty propagation in high-dimensional fields with nonlinear features. The study evaluates the performance of both global and local manifold learning methods, such as Isometric Mapping and Locally Linear Embedding, against the POD on two numerical examples, including two-dimensional supersonic flow around the RAE2822 airfoil with uncertainties in geometry and flow conditions. These methods are benchmarked against Monte Carlo simulations to quantify the impact of polynomial order and sample count on the predicted mean, standard deviation, and uncertainty distributions for both linear and nonlinear ROMs.