A radial basis function-based multi-fidelity surrogate model: exploring correlation between high-fidelity and low-fidelity models

  • Xueguan Song
  • Liye LvEmail author
  • Wei Sun
  • Jie Zhang
Research Paper


In computational simulation, a high-fidelity (HF) model is generally more accurate than a low-fidelity (LF) model, while the latter is generally more computationally efficient than the former. To take advantages of both HF and LF models, a multi-fidelity surrogate model based on radial basis function (MFS-RBF) is developed in this paper by combining HF and LF models. To determine the scaling factor between HF and LF models, a correlation matrix is augmented by further integrating LF responses. The scaling factor and relevant basis function weights are then calculated by employing corresponding HF responses. MFS-RBF is compared with Co-Kriging model, multi-fidelity surrogate based on linear regression (LR-MFS) model, CoRBF model, and three single-fidelity surrogates. The impact of key factors, such as the cost ratio of LF to HF models and different combinations of HF and LF samples, is also investigated. The results show that (i) MFS-RBF presents a better accuracy and robustness than the three benchmark MFS models and single-fidelity surrogates in about 90% cases of this paper; (ii) MFS-RBF is less sensitive to the correlation between HF and LF models than the three MFS models; (iii) by fixing the total computational cost, the cost ratio of LF to HF models is suggested to be less than 0.2, and 10–80% of the total cost should be used for LF samples; (iv) the MFS-RBF model is able to save an average of 50 to 70% computational cost if HF and LF models are highly correlated.


Multi-fidelity surrogate Radial basis function Correlation Scaling factor Robustness 


Funding information

The research is supported by the National Natural Science Foundation of China (Grant No. 51505061 and Grant U1608256).

Compliance with ethical standards

Conflict of interest statement

The authors declare that they have no conflict of interest.

Replication of results

The main codes and raw data corresponding to each figure are submitted as supplementary materials.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringDalian University of TechnologyDalianChina
  2. 2.Department of Mechanical EngineeringThe University of Texas at DallasRichardsonUSA

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