Uncertainty Propagation in High-Dimensional Fields using Non-Intrusive Reduced Order Modeling and Polynomial Chaos

Abstract

View Video Presentation: https://doi.org/10.2514/6.2023-1686.vid High-fidelity, physics-based modeling and simulation have become integral to the design of aircraft, but can have intractably high computational costs when used for uncertainty quantification. This study presents a non-intrusive, parametric reduced order modeling method to enable the prediction of uncertain high-dimensional outputs with complex, nonlinear features and limited sampling budgets. A Proper Orthogonal Decomposition (POD) procedure is utilized to reduce the dimensionality of the high-dimensional space and identify a low-dimensional latent space. A sparse regression-based polynomial chaos expansion (PCE) is then used to construct a mapping between the uncertain input parameters and the latent space coordinates. The methodology is assessed on three test cases, including two-dimensional transonic flow around the RAE2822 airfoil with geometric uncertainties and several canonical problems with varying input and output space dimensionality. The study focuses on problems with strong nonlinearities and discontinuities, such as shocks, to investigate the effectiveness of the ROM in predicting high-speed aerodynamic fields. The performance is assessed by comparing the uncertain mean, variance, point predictions, and integrated quantities of interest obtained using the ROMs to Monte Carlo simulations.