  Neural network (NN) ensembles can reduce large prediction variance of NN and
improve prediction accuracy. For highly nonlinear problems with insufficient
data set, the prediction accuracy of NN models becomes unstable, resulting in a
decrease in the accuracy of ensembles. Therefore, this study proposes a
frequency distribution-based ensemble that identifies core prediction values,
which are expected to be concentrated near the true prediction value. The
frequency distribution-based ensemble classifies core prediction values
supported by multiple prediction values by conducting statistical analysis with
a frequency distribution, which is based on various prediction values obtained
from a given prediction point. The frequency distribution-based ensemble can
improve predictive performance by excluding prediction values with low accuracy
and coping with the uncertainty of the most frequent value. An adaptive
sampling strategy that sequentially adds samples based on the core prediction
variance calculated as the variance of the core prediction values is proposed
to improve the predictive performance of the frequency distribution-based
ensemble efficiently. Results of various case studies show that the prediction
accuracy of the frequency distribution-based ensemble is higher than that of
Kriging and other existing ensemble methods. In addition, the proposed adaptive
sampling strategy effectively improves the predictive performance of the
frequency distribution-based ensemble compared with the previously developed
space-filling and prediction variance-based strategies.
