With the growing demand for hypersonic vehicle design, efficient aerodynamic optimization is increasingly important. Surrogate-based optimization offers a promising means for low-cost and rapid design, yet its accuracy is often sensitive to sample size, and the high computational cost of generating sufficient high-fidelity data limits practical efficiency. Although wall-quantity-based models can reduce reliance on training samples, they frequently suffer from low predictive accuracy under small-sample conditions and lack effective synergy with aerodynamic coefficient models, restricting their predictive capability. To address these challenges, this study proposes a variable-fidelity modeling method that integrates wall-quantity information. The framework combines a ConvNeXt-based wall-quantity prediction model with transfer learning to provide low-fidelity data, together with an improved Gaussian process regression algorithm incorporating automatic kernel construction to capture correlations across fidelity levels. Validation results demonstrate that the proposed method approximates optimal reference values using only 24 low-fidelity and ten high-fidelity samples, with a computational cost of 355.56 central processing unit (CPU) core-hours. Compared with a conventional high-fidelity-only approach requiring 20 samples and 497.78 CPU core-hours, the proposed method reduces computational cost by 28.57% while maintaining accuracy. These findings highlight its effectiveness in achieving efficient and high-precision aerodynamic optimization under small-sample conditions.
Weng et al. (2026) studied this question.