arrow
Volume 13, Issue 2
An Adaptive Non-Intrusive Multi-Fidelity Reduced Basis Method for Parameterized Partial Differential Equations

Yuanhong Chen, Xiang Sun, Yifan Lin & Zhen Gao

East Asian J. Appl. Math., 13 (2023), pp. 398-419.

Published online: 2023-04

Export citation
  • Abstract

An adaptive non-intrusive multi-fidelity reduced basis method for parameterized partial differential equations is developed. Based on snapshots with different fidelity, the method reduces the number of high-fidelity snapshots in the regression model training and improves the accuracy of reduced-order model. One can employ the reduced-order model built on the low-fidelity data to adaptively identify the important parameter values for the high-fidelity evaluations under a given tolerance. The multi-fidelity reduced basis is constructed based on the high-fidelity snapshot matrix and the singular value decomposition of the low-fidelity snapshot matrix. Coefficients of such multi-fidelity reduced basis are determined by projecting low-fidelity snapshots on the low-fidelity reduced basis and using the Gaussian process regression. The projection method is more accurate than the regression method, but it requires low-fidelity snapshots. The regression method trains the Gaussian process regression only once but with slightly lower accuracy. Numerical tests show that the proposed multi-fidelity method can improve the accuracy and efficiency of reduced-order models.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{EAJAM-13-398, author = {Chen , YuanhongSun , XiangLin , Yifan and Gao , Zhen}, title = {An Adaptive Non-Intrusive Multi-Fidelity Reduced Basis Method for Parameterized Partial Differential Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2023}, volume = {13}, number = {2}, pages = {398--419}, abstract = {

An adaptive non-intrusive multi-fidelity reduced basis method for parameterized partial differential equations is developed. Based on snapshots with different fidelity, the method reduces the number of high-fidelity snapshots in the regression model training and improves the accuracy of reduced-order model. One can employ the reduced-order model built on the low-fidelity data to adaptively identify the important parameter values for the high-fidelity evaluations under a given tolerance. The multi-fidelity reduced basis is constructed based on the high-fidelity snapshot matrix and the singular value decomposition of the low-fidelity snapshot matrix. Coefficients of such multi-fidelity reduced basis are determined by projecting low-fidelity snapshots on the low-fidelity reduced basis and using the Gaussian process regression. The projection method is more accurate than the regression method, but it requires low-fidelity snapshots. The regression method trains the Gaussian process regression only once but with slightly lower accuracy. Numerical tests show that the proposed multi-fidelity method can improve the accuracy and efficiency of reduced-order models.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2022-244.241022}, url = {http://global-sci.org/intro/article_detail/eajam/21654.html} }
TY - JOUR T1 - An Adaptive Non-Intrusive Multi-Fidelity Reduced Basis Method for Parameterized Partial Differential Equations AU - Chen , Yuanhong AU - Sun , Xiang AU - Lin , Yifan AU - Gao , Zhen JO - East Asian Journal on Applied Mathematics VL - 2 SP - 398 EP - 419 PY - 2023 DA - 2023/04 SN - 13 DO - http://doi.org/10.4208/eajam.2022-244.241022 UR - https://global-sci.org/intro/article_detail/eajam/21654.html KW - Multi-fidelity method, non-intrusive, reduced-order model, Gaussian process regression, adaptive sampling. AB -

An adaptive non-intrusive multi-fidelity reduced basis method for parameterized partial differential equations is developed. Based on snapshots with different fidelity, the method reduces the number of high-fidelity snapshots in the regression model training and improves the accuracy of reduced-order model. One can employ the reduced-order model built on the low-fidelity data to adaptively identify the important parameter values for the high-fidelity evaluations under a given tolerance. The multi-fidelity reduced basis is constructed based on the high-fidelity snapshot matrix and the singular value decomposition of the low-fidelity snapshot matrix. Coefficients of such multi-fidelity reduced basis are determined by projecting low-fidelity snapshots on the low-fidelity reduced basis and using the Gaussian process regression. The projection method is more accurate than the regression method, but it requires low-fidelity snapshots. The regression method trains the Gaussian process regression only once but with slightly lower accuracy. Numerical tests show that the proposed multi-fidelity method can improve the accuracy and efficiency of reduced-order models.

Yuanhong Chen, Xiang Sun, Yifan Lin & Zhen Gao. (2023). An Adaptive Non-Intrusive Multi-Fidelity Reduced Basis Method for Parameterized Partial Differential Equations. East Asian Journal on Applied Mathematics. 13 (2). 398-419. doi:10.4208/eajam.2022-244.241022
Copy to clipboard
The citation has been copied to your clipboard