To improve robustness and efficiency of automatic transition prediction in aerodynamic design, a reduced model of linear stability analysis is usually adopted, such as $e^N$-envelope or $e^N$-database method. Nevertheless, building such a model is challenging when it comes to compressible flows, as the transition mechanism is more complex and multiple flow parameters should be taken into consideration. To address this problem, this paper proposes an efficient surrogate-based $e^N$ method for compressible boundary layers that uses pretrained surrogate models to substitute linear stability analysis, concerning stability analysis of both Tollmien–Schlichting and Mack modes, as well as transition prediction of flow over arbitrary-shaped airfoils. The proposed method is demonstrated by stability analysis of compressible flat-plate boundary layers at a wide range of Mach numbers of $M_{\infty }=0\sim 6$. It is also validated by transition prediction of flow over a low-speed natural-laminar-flow (NLF) airfoil NLF-0416 and a transonic NLF airfoil NPU-LSC-72613. Besides, a sample partitioning method is presented to accelerate surrogate-model training with large samples. Results show that the predicted growth rates of perturbations, $N$ factors, and corresponding transition locations by our method of using surrogate-based stability analysis agree well with those by a standard $e^N$ method of solving full linear stability equations.

为了提高气动设计中自动过渡预测的鲁棒性和效率，通常采用线性稳定性分析的简化模型，例如 ${\mathrm{电子}}^N$-信封或 ${\mathrm{电子}}^N$- 数据库方法。然而，当涉及可压缩流时，构建这样的模型具有挑战性，因为转换机制更加复杂，并且应该考虑多个流动参数。为了解决这个问题，本文提出了一种有效的基于代理的${\mathrm{电子}}^N$一种用于可压缩边界层的方法，使用预训练的替代模型来替代线性稳定性分析，涉及 Tollmien-Schlichting 和 Mack 模式的稳定性分析，以及任意形状翼型上流动的过渡预测。所提出的方法通过可压缩平板边界层在很宽的马赫数范围内的稳定性分析得到证明。${米}_{\infty }=0～6$. 它还通过低速自然层流 (NLF) 翼型 NLF-0416 和跨音速 NLF 翼型 NPU-LSC-72613 上的流动过渡预测进行了验证。此外，提出了一种样本划分方法来加速大样本的代理模型训练。结果表明，预测的扰动增长率，$N$ 我们使用基于代理的稳定性分析的方法确定的因素和相应的过渡位置与标准的一致 ${\mathrm{电子}}^N$ 求解完全线性稳定性方程的方法。