A sequential multi-fidelity metamodeling approach for data regression

Multi-fidelity (MF) metamodeling approaches have attracted significant attention recently for data regression because they can make a trade-off between high accuracy and low computational expense by integrating the information from high-fidelity (HF) and low-fidelity (LF) models. To facilitate the usage of the MF metamodeling approaches, there are still challenging issues on the sample size ratio between HF and LF models and the locations of samples since these two components have profound effects on the prediction accuracy of the MF metamodels. In this study, a sequential multi-fidelity (SMF) metamodeling approach is proposed to address the issues of 1) where to allocate the LF and HF sample points, and 2) how to obtain an optimal combination of the high and low-fidelity sample sizes for a given computational budget and a high-to-low simulation cost ratio. Firstly, sequential objective formulations, with the objective to reduce the estimation of prediction error of MF metamodel, are constructed to update the LF and HF sampling data. Secondly, a decision criterion is proposed to determine whether one HF experiment or several LF experiments with the equivalent computational cost should be selected to update the MF metamodel. The proposed criterion is developed according to which selection will have a greater potential value to improve the prediction accuracy of the MF metamodel. To demonstrate the effectiveness and merits of the proposed SMF metamodeling approach, two numerical examples and a practical aerospace application example are used. Results show that the proposed approach can generate more accurate MF metamodels by providing the optimal high-to-low sample size ratio and sample locations.