Non-intrusive framework of reduced-order modeling based on proper orthogonal decomposition and 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 sparse PCE in predicting statistical quantities. Furthermore, the proposed method reasonably predicts the outputs of the full order model using only a few snapshots. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

The proposed method utilizes POD and PCE to construct an efficient stochastic representation model through non-intrusive methods, significantly reducing computational costs and storage requirements for high-dimensional physical and random spaces, while demonstrating similar accuracy in predicting statistical quantities as classical sparse PCE.