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

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.