1 research outputs found
A non-intrusive reduced-order modeling method using polynomial chaos expansion
We propose a non-intrusive reduced-order modeling method based on proper
orthogonal decomposition (POD) and polynomial chaos expansion (PCE) for
stochastic representations in uncertainty quantification (UQ) analysis.
Firstly, POD provides an optimally ordered basis from a set of selected
full-order snapshots. Truncating this optimal basis, we construct a
reduced-order model with undetermined coefficients. Then, PCE is utilized to
approximate the coefficients of the truncated basis. In the proposed method, we
construct a PCE using a non-intrusive regression-based method. Combined with
the model reduction ability of POD, the proposed method efficiently provides
stochastic representations in UQ analysis. To investigate the performance of
the proposed method, we provide three numerical examples, i.e., a highly
nonlinear analytical function with three uncertain parameters, two-dimensional
(2D) heat-driven cavity flow with a stochastic boundary temperature, and 2D
heat diffusion with stochastic conductivity. The results demonstrate that the
proposed method significantly reduces the computational costs and storage
requirements that arise due to high-dimensional physical and random spaces.
While demonstrating a similar accuracy with that of the classical full-PCE in
predicting statistical quantities. Furthermore, the proposed method reasonably
predict the outputs of the full order model using only a few snapshots.Comment: 30 pages, 15 figures, research pape