Gradient-enhanced least-square polynomial chaos expansions for uncertainty quantification and robust optimization

Regression-based Polynomial Chaos expansions offer several advantages over projection-based approaches, including their lower computation cost and greater flexibility. In the presence of expensive function evaluations, such as with computational fluid dynamics and finite element analysis, the availability of gradient information, coming from adjoint solvers, can be used to reduce the cost of least-square estimation. Particular attention needs to be payed to the accuracy of gradient information, as adjoint solvers are often more noisy than their primal counterparts. This paper compares different approaches for gradient-enhanced least-square Polynomial Chaos expansion, both for algebraic test cases, and for real-world test cases, i.e. a transonic compressor and a modern jet engine fan.