Hybrid Entropy–Uncertainty Data Acquisition for Global Metamodeling

Abstract

Abstract. An adaptive sampling acquisition criterion is developed to improve global surrogate model accuracy for computationally expensive engineering simulations using Gaussian process (GP) regression. The proposed approach combines integrated mutual information (IMI), which quantifies expected global information gain over a reference set, with GP predictive uncertainty that characterizes local model uncertainty. These complementary quantities are normalized over the candidate set and integrated through a dynamically updated weighting mechanism to form a hybrid entropy–uncertainty (HEU) acquisition criterion, in which the blending weight is sequentially adjusted based on feedback from newly observed samples to adaptively balance global information gain and local uncertainty during sampling. The performance of HEU is evaluated under constrained evaluation budgets using several analytical benchmark function of varying dimensionality together with a two-dimensional steady-state temperature-field reconstruction problem, with identical initial designs and fixed sampling budgets across methods. Statistical reliability is assessed through repeated independent runs. To characterize convergence behavior under prescribed accuracy requirements, a dual-threshold samples-to-threshold metric based on two global performance measures is introduced. Samples to threshold is defined as the first iteration at which the accuracy criteria are both satisfied within a fixed sampling budget. Results indicate that HEU achieves competitive and stable global error reduction relative to representative adaptive sampling strategies, demonstrating consistent sample efficiency under constrained budgets.