Multi-Fidelity Surrogate Model Based on Canonical Correlation Analysis and Least Squares

Abstract

Abstract The multi-fidelity surrogate (MFS) model is designed to make use of a small amount of expensive but accurate high-fidelity (HF) information and a lot of inaccurate but cheap low-fidelity (LF) information. In this paper, a canonical correlation analysis (CCA)-based MFS model in which the least squares (LS) method is used to determine optimal parameters, named CCA-LS-MFS, is proposed. The CCA-LS-MFS model consists of three stages. The first stage is to construct two transition matrices of HF and LF samples using the CCA method. Then, the discrepancy function between HF and LF models is constructed. In the third stage, parameters are determined by using the LS method. The correlation between HF and LF models, the cost ratio of HF to LF models, and the combination of HF and LF samples are explored. It is observed that the increase of the correlation between HF and LF models can highly improve the performance of the CCA-LS-MFS model. CCA-LS-MFS is capable of providing more robust performance than the other two baseline MFS models, especially when the HF and LF models are highly or weakly correlated, and is promising for being applied into the engineering problems with unclear correlation between HF and LF models. In addition, it has been found that in case of given total budget and HF information, the cost ratio of HF to LF models plays an important role in prediction performance, which requires more research in the future work.