Non-intrusive framework of reduced-order modeling based on proper orthogonal decomposition and polynomial chaos expansion

Xiang Sun, Xiaomin Pan, Jung Il Choi

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1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Article number113372
JournalJournal of Computational and Applied Mathematics
Volume390
DOIs
Publication statusPublished - 2021 Jul

Bibliographical note

Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science and ICT) (NRF-2017R1E1A1A0-3070161 and NRF-20151009350). Xiaomin Pan was in part supported by Shanghai Sailing Program, China (20YF1413500).

Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science and ICT) ( NRF-2017R1E1A1A0-3070161 and NRF-20151009350 ). Xiaomin Pan was in part supported by Shanghai Sailing Program, China ( 20YF1413500 ).

Publisher Copyright:
© 2020 Elsevier B.V.

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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