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Computer simulations (a.k.a. white-box models) are more indispensable thanever to model intricate engineering systems. However, computational modelsalone often fail to fully capture the complexities of reality. When physicalexperiments are accessible though, it is of interest to enhance the incompleteinformation offered by computational models. Gray-box modeling is concernedwith the problem of merging information from data-driven (a.k.a. black-box)models and white-box (i.e., physics-based) models. In this paper, we propose toperform this task by using multi-fidelity surrogate models (MFSMs). A MFSMintegrates information from models with varying computational fidelity into anew surrogate model. The multi-fidelity surrogate modeling framework we proposehandles noise-contaminated data and is able to estimate the underlyingnoise-free high-fidelity function. Our methodology emphasizes on deliveringprecise estimates of the uncertainty in its predictions in the form ofconfidence and prediction intervals, by quantitatively incorporating thedifferent types of uncertainty that affect the problem, arising frommeasurement noise and from lack of knowledge due to the limited experimentaldesign budget on both the high- and low-fidelity models. Applied to gray-boxmodeling, our MFSM framework treats noisy experimental data as thehigh-fidelity and the white-box computational models as their low-fidelitycounterparts. The effectiveness of our methodology is showcased throughsynthetic examples and a wind turbine application.

A comprehensive framework for multi-fidelity surrogate modeling with noisy data: a gray-box perspective