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 - <p style="text-align: justify;">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.</p>