The current design of aerodynamic shapes, like airfoils, involves computationally intensive simulations to explore the possible design space. Usually, such design relies on the prior definition of design parameters and places restrictions on synthesizing novel shapes. In this work, we propose a data-driven shape encoding and generating method, which automatically learns representations from existing airfoils and uses the learned representations to generate new airfoils. The representations are then used in the optimization of synthesized airfoil shapes based on their aerodynamic performance. Our model is built upon VAEGAN, a neural network that combines Variational Autoencoder with Generative Adversarial Network and is trained by the gradient-based technique. Our model can (1) encode the existing airfoil into a latent vector and reconstruct the airfoil from that, (2) generate novel airfoils by randomly sampling the latent vectors and mapping the vectors to the airfoil coordinate domain, and (3) synthesize airfoils with desired aerodynamic properties by optimizing learned features via a genetic algorithm. Our experiments show that the learned features encode shape information thoroughly and comprehensively without predefined design parameters. By interpolating/extrapolating feature vectors or sampling from Gaussian noises, the model can automatically synthesize novel airfoil shapes, some of which possess competitive or even better aerodynamic properties comparing to airfoils used for model training purposes. By optimizing shapes on the learned latent domain via a genetic algorithm, synthesized airfoils can evolve to target aerodynamic properties. This demonstrates an efficient learning-based airfoil design framework, which encodes and optimizes the airfoil on the latent domain and synthesizes promising airfoil candidates for required aerodynamic performance.

翻译：当前气动外形（如翼型）的设计依赖于计算密集型的仿真来探索可能的设计空间。此类设计通常需要预先定义设计参数，并对合成新型形状施加限制。本文提出一种数据驱动的形状编码与生成方法，该方法从现有翼型中自动学习表示，并利用学习到的表示生成新翼型。随后，基于合成翼型的气动性能，将这些表示用于优化翼型形状。我们的模型基于VAEGAN——一种结合变分自编码器与生成对抗网络，并通过梯度方法训练的神经网络。该模型能够：(1) 将现有翼型编码为潜在向量，并据此重建翼型；(2) 通过随机采样潜在向量并将其映射至翼型坐标域，生成新型翼型；(3) 通过遗传算法优化学习到的特征，合成具有所需气动特性的翼型。实验表明，学习到的特征无需预定义设计参数即可全面彻底地编码形状信息。通过插值/外推特征向量或从高斯噪声中采样，模型可自动合成新型翼型形状，其中部分翼型的气动性能甚至优于训练所用翼型。通过遗传算法在学习的潜在域上优化形状，合成翼型可演变至目标气动特性。这展示了一种高效的基于学习的翼型设计框架，该框架在潜在域上编码与优化翼型，并为所需气动性能合成有前景的翼型候选方案。