Development of an Efficient Multifidelity Non-intrusive Uncertainty Quantification Method

Most engineering problems contain a large number of input random variables, and thus their polynomial chaos expansion (PCE) suffers from the curse of dimensionality. This issue can be tackled if the polynomial chaos representation is sparse. In the present paper a novel methodology is presented based on combination of \(\ell _1\)-minimization and multifidelity methods. The proposed method employ the \(\ell _1\)-minimization method to recover important coefficients of PCE using low-fidelity computations. The developed method is applied on a stochastic CFD problem and the results are presented. The transonic RAE2822 airfoil with combined operational and geometrical uncertainties is considered as a test case to examine the performance of the proposed methodology. It is shown that the new method can reproduce accurate results with much lower computational cost than the classical full Polynomial Choas (PC), and \(\ell _1\)-minimization methods. It is observed that the present method is almost 15–20 times faster than the full PC method and 3–4 times faster than the classical \(\ell _1\)-minimization method.