An active learning multi-fidelity metamodeling method based on the bootstrap estimator

Abstract Multi-fidelity (MF) metamodel has attracted significant attention recently in simulation-based design and optimization. It can achieve a desirable modeling accuracy with relatively lower simulation cost by making use of the data from both low-fidelity (LF) and high-fidelity (HF) simulations. To facilitate the usage of MF metamodel, there are still challenging issues on (1) how to determine the location of sample points, and (2) how to allocate the limited computational budget to HF and LF simulations. In this study, a bootstrap-based sequential multi-fidelity (BB-SMF) metamodeling method is proposed for data regression of computationally expensive black-box problems. First, constrained optimization problems with the goal of reducing the global predicted error of the MF metamodel are constructed to obtain the candidates for HF and LF simulations, respectively. Specifically, the predicted error of the MF metamodel is evaluated by a developed MF bootstrap estimator. Second, a criterion based on the uncertainty of pseudo-updated MF metamodel is developed to determine whether one HF sample or several LF sample points with the equivalent computational budget are selected to update the MF metamodel. To demonstrate the performance of the proposed method, two analytical functions and a maximum stress prediction problem of the micro-aerial vehicle (MAV) fuselage are adopted. Different test conditions are also discussed, such as different correlation level, initial sample sizes, and cost ratios. Results show that the proposed BB-SMF metamodel is more accurate and robust than the compared methods.