Multi-output Gaussian process prediction for computationally expensive problems with multiple levels of fidelity

Abstract The multi-output Gaussian process (MOGP) modeling approach is a promising way to deal with multiple correlated outputs since it can capture useful information across outputs to provide more accurate predictions than simply modeling these outputs separately. While the existing MOGP models are considered as single-fidelity models and need a large number of high-fidelity samples to construct a relatively accurate surrogate model. The computational cost is often prohibitive, especially for computationally expensive problems. In this paper, a multi-fidelity multi-output Gaussian process (MMGP) model is proposed to deal with multi-fidelity (MF) data with multiple correlated outputs. It aims to approximate multiple correlated high-fidelity (HF) functions enhanced by the low-fidelity (LF) data. The MMGP model can make a trade-off between high prediction accuracy and low computational cost to relieve the computational burden. The performance of the MMGP model is demonstrated with two analytical examples with different data structures and an aerodynamic prediction example for a NACA 0012 airfoil. Another four well-known surrogate modeling methods are also tested to compare with the proposed approach. Results show that the proposed model is capable of dealing with diverse data structures, heterotopic data, or HF samples generated in different regions. The proposed model provides more accurate predictions than the other approaches for most test cases, especially when using the heterotopic training data. In the NACA0012 airfoil case, the root-mean-square error (RMSE) for the drag coefficient can be reduced by 30%–40% using the MMGP model compared with that of the other MF modeling methods.