The optimization of geometries for aerodynamic design often relies on a large number of expensive simulations to evaluate and iteratively improve the geometries. It is possible to reduce the number of simulations by providing a starting geometry that has properties close to the desired requirements, often in terms of lift and drag, aerodynamic moments and surface areas. We show that generative models have the potential to provide such starting geometries by generalizing geometries over a large dataset of simulations. In particular, we leverage diffusion probabilistic models trained on XFOIL simulations to synthesize two-dimensional airfoil geometries conditioned on given aerodynamic features and constraints. The airfoils are parameterized with Bernstein polynomials, ensuring smoothness of the generated designs. We show that the models are able to generate diverse candidate designs for identical requirements and constraints, effectively exploring the design space to provide multiple starting points to optimization procedures. However, the quality of the candidate designs depends on the distribution of the simulated designs in the dataset. Importantly, the geometries in this dataset must satisfy other requirements and constraints that are not used in conditioning of the diffusion model, to ensure that the generated geometries are physical.

翻译：气动设计中的几何优化通常依赖于大量昂贵的仿真来评估并迭代改进几何形状。通过提供一个在特性上接近所需要求的起始几何形状（通常涉及升力与阻力、气动力矩及表面积等指标），可以减少仿真次数。我们证明，生成模型具备通过在大规模仿真数据集上泛化几何形状来提供此类起始几何的潜力。具体而言，我们利用在XFOIL仿真数据上训练的扩散概率模型，合成了以给定气动特性与约束为条件的二维翼型几何。翼型采用伯恩斯坦多项式进行参数化，确保生成设计的平滑性。研究表明，该模型能够针对相同的需求与约束生成多样化的候选设计，有效探索设计空间以提供多个优化起始点。然而，候选设计的质量取决于数据集中仿真设计的分布特性。关键在于，数据集中几何形状必须满足扩散模型条件设定中未使用的其他要求与约束，以确保生成几何的物理合理性。