An Adaptive Non-Intrusive Multi-Fidelity Reduced Basis Method for Parameterized Partial Differential Equations

An Adaptive Non-Intrusive Multi-Fidelity Reduced Basis Method for Parameterized Partial Differential Equations

Year:    2023

Author:    Yuanhong Chen, Xiang Sun, Yifan Lin, Zhen Gao

East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.2022-244.241022

East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 2 : pp. 398–419

Published online:    2023-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Multi-fidelity method non-intrusive reduced-order model Gaussian process regression adaptive sampling.

Author Details

Yuanhong Chen

Xiang Sun

Yifan Lin

Zhen Gao