Bi-fidelity adaptive sparse reconstruction of polynomial chaos using Bayesian compressive sensing

In recent years, non-intrusive polynomial chaos expansion (NIPCE) has been recognized as a practical method for uncertainty quantification (UQ) of stochastic problems. However, this method suffers from the curse of dimensionality, where the computational cost of constructing the expansion increases dramatically with the dimension of the stochastic space. Due to this issue, the application of classical NIPCE in real-world industrial problems with a large number of uncertainty sources becomes unaffordable. To manage the computational cost of UQ in high-dimensional stochastic problems, this paper introduces a novel, efficient method for multi-fidelity sparse reconstruction of NIPCE. The developed framework incorporates a multi-task adaptive Bayesian compressive sensing (MTABCS) method into the regression-based NIPCE. Firstly, a set of inexpensive deterministic computations is used to compress the chaos expansion by recovering the basis that strongly affect the response. Subsequently, the sparsely constructed expansion is refined using a limited number of high-fidelity computations. Two challenging CFD test cases, namely the transonic RAE2822 airfoil and the NASA Rotor 37, are considered to assess the performance of the developed method in realistic, large-scale engineering problems. The investigations indicate that, in addition to a considerable reduction in computational cost, the present method accurately reproduces the results of the classic NIPCE. It is observed that the MTABCS approach reduces the computational workload of UQ analysis in the test cases by an order of magnitude compared to the standard chaos expansion method.