Gradient and Uncertainty Enhanced Sequential Sampling for Global Fit
This work addresses the challenge of reducing data requirements for surrogate modeling in engineering, offering an incremental improvement over existing adaptive sampling methods.
The paper tackles the problem of efficiently building accurate surrogate models for costly simulations by proposing GUESS, a new adaptive sampling strategy that combines gradient and uncertainty information, and shows it achieves the highest sample efficiency on average compared to nine other strategies across 26 benchmark functions.
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.