Multifidelity Surrogate Based on Single Linear Regression

Multifidelity surrogates (MFS) combine low-fidelity models with few high-fidelity samples to infer the response of the high-fidelity model for design optimization or uncertainty quantification. Most publications in MFS focus on Bayesian frameworks based on Gaussian process. Other types of surrogates might be preferred for some applications. In this paper, a simple and yet powerful MFS based on single linear regression is proposed, termed as linear regression multifulelity surrogate (LR-MFS), especially for fitting high-fidelity data with noise. The LR-MFS considers the low-fidelity model as a basis function and identifies unknown coefficients of both the low-fidelity model and the discrepancy function using a single linear regression. Because the proposed LR-MFS is obtained from standard linear regression, it can take advantage of established regression techniques such as prediction variance, D-optimal design, and inference. The LR-MFS is first compared with three Bayesian frameworks using a benchmark dataset from the simulations of a fluidized-bed process. The LR-MFS showed a comparable accuracy with the best Bayesian frameworks. The effect of combining multiple low-fidelity models was also discussed. Then the LR-MFS is evaluated using an algebraic function with different sampling plans. The LR-MFS bested co-kriging for 55 similar to 63% cases with an increasing number of high-fidelity (HF) samples. The sources of uncertainty with an increasing number of samples were also discussed. For both examples, the LR-MFS proved to be better than fitting only HF samples and robust with noisy data.