The effects of scale factor and correction on the multi-fidelity model

Many researchers have studied Multi-fidelity (MF) models to obtain the optimum solution efficiently when the time of analysis and evaluation is long. The MF model is a meta-model that combines High fidelity (HF) data, which requires large computational cost for evaluation; and Low fidelity (LF) data, which needs small computation cost but has low accuracy. Therefore, integrating HF and LF data with a scale factor and correction model is highly important in MF modeling. This study investigates the performance of the MF model in terms of definition and estimation. First, three different MF models are built: An LF model multiplied by the scale factor, an LF model combined with a correction model, and an LF model with both scale factor and correction model. Second, the effects of scale factor on the MF model are analyzed in terms of constant vs. linear and maximum likelihood estimation vs. least squares estimation. Finally, a correction model is built using two methods, namely, interpolation and regression, to assess the influence of the correction model on the MF model. To evaluate the MF model performance, several test problems are applied, and the root mean square error of each model is estimated as the accuracy measure. In conclusion, the characteristics of different types of MF models are summarized and guidelines for the generation of MF models are proposed to approximate closely the precise models.