Keywords: multi-fidelity, surrogate model, optimization, kriging, metaheuristic, leave one out cross validation, correlation coefficient.

Multi-fidelity surrogate modelling methods have gained significant attention in engineering optimization, as they can achieve high accuracy at a reduced computational cost. However, to construct a high-performing multi-fidelity surrogate model, it is essential to accurately capture the correlation between the high-fidelity and low-fidelity models. In this paper, we propose a novel Kriging-based multi-fidelity surrogate model. The proposed method tunes the low-fidelity Kriging model to capture both the linear and nonlinear correlations with the high-fidelity data, enabling a close approximation to the high-fidelity model. Then, a suitable surrogate model for the discrepancy data is selected from among the Kriging model and the polynomial regression model. The basis functions for the Kriging model and the discrepancy Kriging model are included as part of the hyperparameter optimization. All hyperparameters are optimized simultaneously using a metaheuristic algorithm to ensure that all complex relationships between hyperparameters are considered. The proposed method demonstrates superior performance and robustness in analytical problems.

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