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

Abstract

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 neurons 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 orthogonal 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 characteristics of system response. Finally, several numerical examples are utilized for validating the effectiveness of DKPCE.