Active Learning for Efficient Rare Event Probability Estimation and Sensitivity Analyses in Highly Nonlinear Systems

This paper presents a robust method for rare event probability estimation in highly nonlinear systems. Utilizing a nearest-neighbor approximation of the true performance function and an adaptively extended experimental design, we introduce a simple yet effective active learning function. This function dynamically balances global exploration and local exploitation through sequential adaptive selection of points from the input domain. The resulting surrogate model, refined based on distances, serves the dual purpose of estimating failure probability and selecting optimal candidates for further model evaluations. Our adaptive design supports accurate real-time estimation of failure probability and failure probability sensitivity to individual variables, especially in cases of non-smooth or highly nonlinear functions. Even in scenarios with smooth functions, our method outperforms existing approaches utilizing the function gradients in estimation accuracy for a given computational budget. The adaptively constructed surrogate model excels in handling intricate failure surfaces, multiple design points, and systems with bifurcations. This approach is particularly suitable for random vectors with small to moderate dimensions.