Bi-fidelity surrogate modeling via scaled correlation construction and penalty minimization

Bi-fidelity surrogate (BFS) modeling is a powerful technique to mitigate the constraints of computational time and resources in high-fidelity (HF) models. However, obtaining sufficient HF samples in real-world scenarios remains challenging. This issue drives the creation of dependable surrogates capable of performing effectively on limited datasets. In this research, an innovative method is devised for constructing a BFS model based on scaled correlation construction and penalty minimization, with the goal of improving the performance of surrogate models when data are limited. This method starts by establishing a tuning factor that measures the contribution of different features to the response, thereby reducing the impact of redundant features on model construction. This factor is integrated into the construction of the discrepancy function to represent the variations between low-fidelity (LF) and HF samples. Additionally, a regularization constraint is imposed on the model parameter to prevent overfitting, which in turn increases the model’s robustness and interpretability. To validate the superiority of the developed BFS model, five leading surrogate models are selected for comparison. Experiments are conducted across various dimensions and nonlinearities of numerical problems, showcasing the competitiveness of the developed BFS model. Furthermore, a case study in engineering illustrates the practical application of the developed BFS model in the real-world scenarios.