A multi-fidelity surrogate model based on moving least squares: fusing different fidelity data for engineering design

In numerical simulations, a high-fidelity (HF) simulation is generally more accurate than a low-fidelity (LF) simulation, while the latter is generally more computationally efficient than the former. To take advantages of both HF and LF simulations, a multi-fidelity surrogate (MFS) model based on moving least squares (MLS), termed as adaptive MFS-MLS, is proposed. The MFS-MLS calculates the LF scaling factors and the unknown coefficients of the discrepancy function simultaneously using an extended MLS model. In the proposed method, HF samples are not regarded as equally important in the process of constructing MFS-MLS models, and adaptive weightings are given to different HF samples. Moreover, both the size of the influence domain and the scaling factors can be determined adaptively according to the training samples. The MFS-MLS model is compared with three state-of-the-art MFS models and three single-fidelity surrogate models in terms of the prediction accuracy through multiple benchmark numerical cases and an engineering problem. In addition, the effects of key factors on the performance of the MFS-MLS model, such as the correlation between HF and LF models, the cost ratio of HF to LF samples, and the combination of HF and LF samples, are also investigated. The results show that MFS-MLS is able to provide competitive performance with high computational efficiency.