Volume 28, Issue 5
High-Dimensional Nonlinear Multi-Fidelity Model with Gradient-Free Active Subspace Method

Bangde LiuGuang Lin

Commun. Comput. Phys., 28 (2020), pp. 1937-1969.

Published online: 2020-11

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  • Abstract

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.

  • Keywords

Gaussian process regression, dimension reduction, multi-fidelity model, active subspace, machine learning.

  • AMS Subject Headings

60G15, 60A99, 62A99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-28-1937, author = {Liu , Bangde and Lin , Guang}, title = {High-Dimensional Nonlinear Multi-Fidelity Model with Gradient-Free Active Subspace Method}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {5}, pages = {1937--1969}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0195}, url = {http://global-sci.org/intro/article_detail/cicp/18401.html} }
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 -

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.

Bangde Liu & Guang Lin. (2020). High-Dimensional Nonlinear Multi-Fidelity Model with Gradient-Free Active Subspace Method. Communications in Computational Physics. 28 (5). 1937-1969. doi:10.4208/cicp.OA-2020-0195
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