NeuralFoil is an open-source Python-based tool for rapid aerodynamics analysis of airfoils, similar in purpose to XFoil. Speedups ranging from 8x to 1,000x over XFoil are demonstrated, after controlling for equivalent accuracy. NeuralFoil computes both global and local quantities (lift, drag, velocity distribution, etc.) over a broad input space, including: an 18-dimensional space of airfoil shapes, possibly including control deflections; a 360 degree range of angles of attack; Reynolds numbers from $10^2$ to $10^{10}$; subsonic flows up to the transonic drag rise; and with varying turbulence parameters. Results match those of XFoil closely: the mean relative error of drag is 0.37% on simple cases, and remains as low as 2.0% on a test dataset with numerous post-stall and transitional cases. NeuralFoil facilitates gradient-based design optimization, due to its $C^\infty$-continuous solutions, automatic-differentiation-compatibility, and bounded computational cost without non-convergence issues. NeuralFoil is a hybrid of physics-informed machine learning techniques and analytical models. Here, physics information includes symmetries that are structurally embedded into the model architecture, feature engineering using domain knowledge, and guaranteed extrapolation to known limit cases. This work also introduces a new approach for surrogate model uncertainty quantification that enables robust design optimization. This work discusses the methodology and performance of NeuralFoil with several case studies, including a practical airfoil design optimization study including both aerodynamic and non-aerodynamic constraints. Here, NeuralFoil optimization is able to produce airfoils nearly identical in performance and shape to expert-designed airfoils within seconds; these computationally-optimized airfoils provide a useful starting point for further expert refinement.

翻译：NeuralFoil 是一款基于 Python 的开源工具，用于快速分析翼型空气动力学特性，其功能定位与 XFoil 类似。在保证同等精度的前提下，该工具相较于 XFoil 可实现 8 倍至 1000 倍的加速效果。NeuralFoil 能够在广阔的参数空间内计算全局与局部气动参数（升力、阻力、速度分布等），其输入空间涵盖：18 维的翼型几何形状空间（可包含操纵面偏转）；360° 攻角范围；雷诺数从 $10^2$ 至 $10^{10}$；亚声速流动直至跨声速阻力发散状态；以及变化的湍流参数。其计算结果与 XFoil 高度吻合：在简单工况下阻力平均相对误差为 0.37%，在包含大量失速后及转捩工况的测试数据集上误差仍可低至 2.0%。NeuralFoil 具备 $C^\infty$ 连续解、自动微分兼容性及无发散问题的稳定计算成本，特别适用于基于梯度的设计优化。该工具融合了物理信息机器学习技术与解析模型方法，其中物理信息的嵌入方式包括：通过模型架构设计内置对称性、基于领域知识的特征工程，以及对已知极限情况的保证外推。本研究还提出了一种新的代理模型不确定性量化方法，以实现鲁棒设计优化。本文通过多个案例研究探讨了 NeuralFoil 的方法学与性能表现，其中包括同时考虑气动与非气动约束的实际翼型设计优化研究。在此案例中，NeuralFoil 优化可在数秒内生成与专家设计翼型在性能和外形上高度接近的翼型方案；这些通过计算优化的翼型为后续专家精细化设计提供了有效的初始解。