Gaussian process regression based on deep neural network for reliability analysis in high dimensions

An efficient method is proposed to deal with high-dimensional reliability problems. The critical contribution lies in developing an advanced DGPR model, which effectively combines deep neural network (DNN)-based dimension reduction and Gaussian process regression (GPR) model. Specifically, the parameters of both the DNN and the GPR are calibrated through a joint-training scheme, and the network architecture of the DGPR is optimally selected via a grid-search scheme coupled with five-fold cross validation. In this regard, both the supervised extraction of low-dimensional latent space and the training of GPR in the latent space are intrinsically achieved by the DGPR. Then, an active learning strategy is adopted to combine the DGPR and the subset simulation for reliability analysis. To verify the efficacy of the proposed approach, three numerical examples are investigated and comparisons are made against other reliability methods. Numerical results demonstrate that the proposed approach gains reasonable computational cost savings whilst maintaining satisfactory accuracy of reliability results.