Surrogate modeling for high dimensional uncertainty propagation via deep kernel polynomial chaos expansion

被引:1
作者
Liu, Jingfei [1 ]
Jiang, Chao [2 ]
机构
[1] Henan Univ Technol, Sch Mech & Elect Engn, Zhengzhou 450001, Peoples R China
[2] Hunan Univ, Sch Mech & Vehicle Engn, Changsha 410082, Peoples R China
关键词
High dimensional problems; Deep learning; Polynomial chaos expansion; Uncertainty propagation; Dimension reduction;
D O I
10.1016/j.apm.2023.05.036
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In this paper, deep kernel polynomial chaos expansion (DKPCE) is proposed as a surrogate model for high dimensional uncertainty propagation. Firstly, deep neural network (DNN) and polynomial chaos expansion (PCE) are connected to create a novel network model, the input dimensionality of PCE layer can thus be controlled by restricting the number of neu-rons in the feature layer. Then, the back-propagation algorithm is employed for computing all the parameters of DKPCE, the dimension reduction and modeling process of DKPCE are thus executed simultaneously. During the modeling process, a data driven method is first implemented for computing the orthogonal polynomial bases within the PCE layer in the forward propagation step, and the partial derivatives for the coefficients of orthogo-nal polynomial bases are computed first in the back-propagation step. After constructing DKPCE, the coefficients of PCE layer can be utilized to compute the statistical characteris-tics of system response. Finally, several numerical examples are utilized for validating the effectiveness of DKPCE & COPY; 2023 Published by Elsevier Inc.
引用
收藏
页码:167 / 186
页数:20
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