A novel active learning-based Gaussian process metamodelling strategy for estimating the full probability distribution in forward UQ analysis
This work addresses a computational efficiency and accuracy trade-off in uncertainty quantification for expensive black-box solvers, representing an incremental improvement over existing methods.
The paper tackles the problem of estimating full probability distributions in forward uncertainty quantification by proposing an active learning-based Gaussian process metamodelling method that efficiently estimates cumulative and complementary cumulative distribution functions without discretization dependency, achieving accurate results in median-low probability regions as demonstrated in three numerical examples.
This paper proposes an active learning-based Gaussian process (AL-GP) metamodelling method to estimate the cumulative as well as complementary cumulative distribution function (CDF/CCDF) for forward uncertainty quantification (UQ) problems. Within the field of UQ, previous studies focused on developing AL-GP approaches for reliability (rare event probability) analysis of expensive black-box solvers. A naive iteration of these algorithms with respect to different CDF/CCDF threshold values would yield a discretized CDF/CCDF. However, this approach inevitably leads to a trade-off between accuracy and computational efficiency since both depend (in opposite way) on the selected discretization. In this study, a specialized error measure and a learning function are developed such that the resulting AL-GP method is able to efficiently estimate the CDF/CCDF for a specified range of interest without an explicit dependency on discretization. Particularly, the proposed AL-GP method is able to simultaneously provide accurate CDF and CCDF estimation in their median-low probability regions. Three numerical examples are introduced to test and verify the proposed method.