Deep learning for high-dimensional reliability analysis

Abstract High-dimensional reliability analysis remains a grand challenge since most of the existing methods suffer from the curse of dimensionality. This paper introduces a novel high-dimensional data abstraction (HDDA) framework for dimension reduction in reliability analysis. It first involves training of a failure-informed autoencoder network to reduce the dimensionality of the high-dimensional input space, aiming at creating a distinguishable failure surface in a low-dimensional latent space. Then a deep feedforward neural network is constructed to connect the high-dimensional input parameters with the low-dimensional latent variables. With the HDDA framework, the high-dimensional reliability can be estimated by capturing the limit state function in the latent space using Gaussian process regression. To manage the uncertainty due to lack of training data, a distance-based sampling strategy is developed for iteratively identifying critical training samples, which improves the accuracy of the high-dimensional reliability estimations. Three high-dimensional examples are used to demonstrate the effectiveness of the proposed approach.