In this work, we perform a systematic comparison of the effectiveness and efficiency of generative and non-generative models in constructing design spaces for novel and efficient design exploration and shape optimization. We apply these models in the case of airfoil/hydrofoil design and conduct the comparison on the resulting design spaces. A conventional Generative Adversarial Network (GAN) and a state-of-the-art generative model, the Performance-Augmented Diverse Generative Adversarial Network (PaDGAN), are juxtaposed with a linear non-generative model based on the coupling of the Karhunen-Lo\`eve Expansion and a physics-informed Shape Signature Vector (SSV-KLE). The comparison demonstrates that, with an appropriate shape encoding and a physics-augmented design space, non-generative models have the potential to cost-effectively generate high-performing valid designs with enhanced coverage of the design space. In this work, both approaches are applied to two large foil profile datasets comprising real-world and artificial designs generated through either a profile-generating parametric model or deep-learning approach. These datasets are further enriched with integral properties of their members' shapes as well as physics-informed parameters. Our results illustrate that the design spaces constructed by the non-generative model outperform the generative model in terms of design validity, generating robust latent spaces with none or significantly fewer invalid designs when compared to generative models. We aspire that these findings will aid the engineering design community in making informed decisions when constructing designs spaces for shape optimization, as we have show that under certain conditions computationally inexpensive approaches can closely match or even outperform state-of-the art generative models.

翻译：本文系统比较了生成式与非生成式模型在构建设计空间以进行新颖高效的设计探索与形状优化中的有效性和效率。我们将这些模型应用于翼型/水翼设计案例，并对生成的设计空间进行比较。传统的生成对抗网络（GAN）和最先进的生成模型——性能增强多样生成对抗网络（PaDGAN），与基于Karhunen-Loève展开与物理信息形状特征向量耦合的线性非生成模型（SSV-KLE）进行了对比。比较表明，在合适的形状编码和物理增强设计空间下，非生成模型有潜力以较低成本生成高性能的有效设计，并增强设计空间的覆盖范围。本文将两种方法应用于两个大型翼型剖面数据集，这些数据集包含通过剖面生成参数模型或深度学习方法生成的真实与人工设计。这些数据集进一步通过其成员形状的积分特性以及物理信息参数得到丰富。结果表明，非生成模型构建的设计空间在设计有效性方面优于生成模型，能够生成鲁棒的潜在空间，且相比生成模型，无效设计数量为零或显著更少。我们期望这些发现将帮助工程设计社区在构建形状优化设计空间时做出明智决策，因为我们已证明在特定条件下，计算成本较低的方法能够紧密匹配甚至超越最先进的生成模型。