  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 devise a uniform design (i.e., space-filling design) as a
baseline for measuring the improvement of using AL. Combining all the
representative methods, a total of 1,920 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) AL techniques cannot provide a
systematic improvement compared with uniform designs, (ii) the recommended
surrogate modeling methods depend on the features of the problems (especially
the local nonlinearity), target accuracy, and computational budget.
