关键词: 主动学习, 贝叶斯深度神经网络, 高维不确定性, 多输出问题

Abstract: An uncertainty propagation method was proposed based on active learning and BDNN for solving the high dimensional multioutput problems existed in practical engineering. Since the multiple output responses corresponded to the same input variables, the efficient one-step sampling was implemented and the initial training dataset was established. BDNN was utilized for initially establishing the surrogate model for high dimensional multioutput problem. Because BDNN might provide the uncertainty estimation for multiple predictive output responses simultaneously, an active sampling strategy was proposed for high dimensional multioutput problem. Then, Monte Carlo sampling(MCS) method and Gaussian mixture model were combined for computing the joint probability density function of multiple output responses. The results show that proposed method may avoid the repeated computing processes for different output responses individually, and make full use of the internal relationship among multiple output responses for implementing active learning. Therefore, the efficiency for solving high-dimensional multioutput problems may be improved to some extent. Finally, several numerical examples were utilized to validate the efficiency of the proposed method. 

Key words: active learning, Bayesian deep neural network(BDNN), high dimensional uncertainty, multioutput problem