Surrogate modeling for probability distribution estimation: Uniform or adaptive design?
系统比较了主动学习与均匀设计在构建替代模型估计完整分布函数时的表现，发现主动学习的优势低于预期，并针对不同问题特征给出了模型选择建议。
The active learning (AL) technique, one of the state-of-the-art methods for constructing surrogate models, has shown high accuracy and efficiency in forward uncertainty quantification (UQ) analysis. This paper provides a comprehensive study on AL-based global surrogates for computing the full distribution function, i.e., the cumulative distribution function (CDF) and the complementary CDF (CCDF). To this end, we investigate the three essential components for building surrogates, i.e., types of surrogate models, enrichment methods for experimental designs, and stopping criteria. For each component, we choose several representative methods and study their desirable configurations. In addition, we use a uniform design based on maximin-distance criteria as a baseline for measuring the improvement of using AL. Combining all the representative methods, a total of 1920 UQ analyses are carried out to solve 16 benchmark examples. The performance of the selected strategies is evaluated based on accuracy and efficiency. In the context of full distribution estimation, this study concludes that ( i ) The benefit of using AL is lower than expected and varies across different surrogate models, with three reasons for this performance variability analyzed in detail. ( ii ) Detailed recommendations are provided for the three surrogate components, depending on the features of the problems (especially the local nonlinearity), target accuracy, and computational budget.