  Surrogate models based on machine learning methods have become an important
part of modern engineering to replace costly computer simulations. The data
used for creating a surrogate model are essential for the model accuracy and
often restricted due to cost and time constraints. Adaptive sampling strategies
have been shown to reduce the number of samples needed to create an accurate
model. This paper proposes a new sampling strategy for global fit called
Gradient and Uncertainty Enhanced Sequential Sampling (GUESS). The acquisition
function uses two terms: the predictive posterior uncertainty of the surrogate
model for exploration of unseen regions and a weighted approximation of the
second and higher-order Taylor expansion values for exploitation. Although
various sampling strategies have been proposed so far, the selection of a
suitable method is not trivial. Therefore, we compared our proposed strategy to
9 adaptive sampling strategies for global surrogate modeling, based on 26
different 1 to 8-dimensional deterministic benchmarks functions. Results show
that GUESS achieved on average the highest sample efficiency compared to other
surrogate-based strategies on the tested examples. An ablation study
considering the behavior of GUESS in higher dimensions and the importance of
surrogate choice is also presented.
