Hybrid Entropy–Uncertainty Data Acquisition for Global Metamodeling

Abstract An adaptive sampling acquisition criterion is developed to improve global surrogate model accuracy under data-limited engineering simulations using Gaussian process (GP) regression. The approach combines Integrated Mutual Information (IMI), which quantifies expected global information gain over a reference set, with GP predictive uncertainty that reflects local uncertainty of surrogate model. These two complementary quantities are normalized over the candidate set and blended through a single weighting parameter, resulting in a Hybrid Entropy–Uncertainty (HEU) acquisition for adaptive sampling. HEU leverages information-theoretic global informativeness while retaining robust uncertainty-driven exploration, making it suitable for global-fit surrogate construction under constrained budgets. Its performance is evaluated using one mathematical benchmark problem and an engineering case study on steady-state temperature-field prediction based upon spatial surrogate reconstruction. The case study results demonstrated that the HEU criterion yields a more stable and effective reduction of global prediction error than representative acquisition functions from major adaptive sampling families.