Comparison of intrusive and nonintrusive polynomial chaos expansion-based approaches for high dimensional parametric uncertainty quantification and propagation

Abstract

We present an uncertainty quantification (UQ) algorithm using the intrusive generalized polynomial chaos (gPC) expansion in combination with dimension reduction techniques and compare the UQ accuracy and computational efficiency of the intrusive gPC-based UQ algorithm to other sampling-based nonintrusive methods. The successful application of intrusive gPC-based UQ is associated with the stochastic Galerkin (SG) projection, which yields a family of models described by several coupled equations of gPC coefficients. Using these coefficients, the evolution of uncertainty in a dynamic system can be quickly determined when there is probabilistic uncertainty in the system. While elegant, when dealing with models that involve complex functions (e.g., nonpolynomial terms) and larger numbers of uncertainties, SG projection becomes computationally intractable and cannot be applied directly to solve gPC coefficients in real-time. To address this issue, the generalized dimension reduction method (gDRM) is used to convert a high-dimensional integral involved in the SG projection into several lower-dimensional integrals that can be easily solved. To show the accuracy of UQ, the algorithm in this work is compared to sampling-based approaches such as the nonintrusive stochastic collocation (SC) and Monte Carlo (MC) simulations using three cases: a nonlinear algebraic benchmark, a penicillin manufacturing process, and autocrine signalling networks of living cells.