A novel active learning-based Gaussian process metamodelling strategy for estimating the full probability distribution in forward UQ analysis

TL;DR

This paper introduces an active learning-based Gaussian process metamodelling approach that efficiently estimates the full probability distribution in forward uncertainty quantification, overcoming discretization trade-offs and improving accuracy in low-probability regions.

Contribution

It develops a specialized error measure and learning function enabling accurate CDF/CCDF estimation over a range without discretization dependence.

Findings

Accurately estimates CDF and CCDF in low-probability regions.

Avoids discretization trade-offs between accuracy and efficiency.

Validated with three numerical examples.

Abstract

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.