Multi-fidelity surrogate modeling, by integrating high-fidelity (HF) and low-fidelity (LF) data, provides an efficient approximation framework for complex fluid dynamics problems, particularly those driven by numerical resolution discrepancies. However, under limited computational budgets, efficiently selecting HF samples remains a critical challenge. This study proposes a Nonlinear-Guided Active Learning Multi-Fidelity Surrogate (NG-AL-MFS) modeling method. The proposed framework employs a recursive Co-Kriging model combined with an adaptive sampling strategy to achieve hierarchical data fusion. In this approach, the adaptive sampling strategy introduces a local nonlinearity indicator derived from LF responses to identify complex regions and integrates a distance-based exploration criterion to balance exploitation and exploration during potential HF sampling. Throughout the process, NG-AL-MFS quantitatively extracts local nonlinear features from LF responses to iteratively and adaptively update HF samples, thereby constructing a multi-fidelity surrogate that achieves a superior trade-off between modeling accuracy and computational cost. The proposed framework is validated using three benchmark functions and two fluid engineering applications. Results demonstrate that NG-AL-MFS outperforms existing approaches in terms of prediction accuracy, convergence efficiency, and statistical robustness, offering notable advantages in multivariate nonlinear scenarios. Overall, NG-AL-MFS provides a data-efficient and reliable solution for budget-constrained surrogate modeling in fluid dynamics and other computation-intensive domains.
Yang et al. (Sun,) studied this question.