Polynomial Chaos Kriging Models for Uncertainty Quantification in High-Speed Flow Applications

Polynomial chaos expansions (PCEs) are a popular method for performing uncertainty quantification (UQ) in computationally expensive simulations. However, given their linear formulation, PCE models perform inadequately in problems with large nonlinearities and sharp gradients. These challenges are exacerbated in high-dimensional problems with thousands of correlated random variables, such as UQ in computational fluid dynamics simulations. This study relies on dimensionality reduction (DR) and a nonintrusive method that combines polynomial chaos with kriging to construct a mapping between the uncertain input parameters and the low-dimensional latent space. By combining global approximations with local refinements along with DR, the proposed method is compared to Monte Carlo and PCE on a series of high-speed aerodynamic problems. Even in the most complex test cases, the results demonstrate that the proposed method reaches a normalized root mean square error of 0.1 with a fourfold reduction in the required training data compared to the benchmark, while maintaining a 50% lower maximum absolute error near shockwaves. Furthermore, the method’s robustness is evident not only in its global and local performance near discontinuities but also in its ability to accurately reconstruct the mean, variance, and integrated quantities, even as the amount of training data decreases.