TY - JOUR
T1 - High-Dimensional Nonlinear Multi-Fidelity Model with Gradient-Free Active Subspace Method
AU - Liu , Bangde
AU - Lin , Guang
JO - Communications in Computational Physics
VL - 5
SP - 1937
EP - 1969
PY - 2020
DA - 2020/11
SN - 28
DO - http://doi.org/10.4208/cicp.OA-2020-0195
UR - https://global-sci.org/intro/article_detail/cicp/18401.html
KW - Gaussian process regression, dimension reduction, multi-fidelity model, active subspace, machine learning.
AB - <p style="text-align: justify;">In scientific and engineering applications, often sufficient low-cost low-fidelity data is available while only a small fractional of high-fidelity data is accessible. The multi-fidelity model integrates a large set of low-cost but biased low-fidelity
datasets with a small set of precise but high-cost high-fidelity data to make an accurate
inference of quantities of interest. Under many circumstances, the number of model
input dimensions is often high in real applications. To simplify the model, dimension
reduction is often used. The gradient-free active subspace is employed in this research
for dimension reduction. In this work, a novel predictive model for high-dimensional
nonlinear problems by integrating the nonlinear multi-fidelity Gaussian progress regression and the gradient-free active subspace method is put forward. Numerical results demonstrated that the proposed approach can not only perform effective dimension reduction on the original data but also obtain accurate prediction results thanks
to the effective dimension reduction procedure.</p>