A multi-fidelity surrogate model based on support vector regression

Computational simulations with different fidelities have been widely used in engineering design and optimization. A high-fidelity (HF) model is generally more accurate but also more time-consuming than the corresponding low-fidelity (LF) model. To take advantage of both HF and LF models, a number of multi-fidelity surrogate (MFS) models based on different surrogate models (e.g., Kriging, response surface, and radial basis function) have been developed, but MFS models based on support vector regression are rarely reported. In this paper, a new MFS model based on support vector regression, which is named Co_SVR, is developed. In the proposed method, the HF and LF samples are mapped into a high-dimensional feature space through a kernel function, and then, a linear model is utilized to evaluate the relationship between inputs and outputs. The root mean square error (RMSE) of HF responses of interest is used to express the training error of Co_SVR, and a heuristic algorithm, grey wolf optimizer, is used to obtain the optimal parameters. For verification, the Co_SVR model is compared with four popular multi-fidelity surrogate models and four single-fidelity surrogate models through a number of numerical cases and a pressure relief valve design problem. The results show that Co_SVR provides competitive performance in both numerical cases and the practical case. Moreover, the effects of key factors (i.e., the correlation between HF and LF models, the cost ratio of HF to LF models, and the combination of HF and LF samples) on the performance of Co_SVR are also explored.