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-Loève 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 additionally compare the performance and diversity of generated designs to provide further insights about the quality of the resulting spaces. 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 demonstrated that under certain conditions computationally inexpensive approaches can closely match or even outperform state-of-the art generative models.

Deep generative models are proven to be a useful tool for automatic design synthesis and design space exploration. When applied in engineering design, existing generative models face two challenges: 1) generated designs lack diversity and do not cover all areas of the design space and 2) it is difficult to explicitly improve the overall performance or quality of generated designs without excluding low-quality designs from the dataset, which may impair the performance of the trained model due to reduced training sample size. In this paper, we simultaneously address these challenges by proposing a new Determinantal Point Processes based loss function for probabilistic modeling of diversity and quality. With this new loss function, we develop a variant of the Generative Adversarial Network, named "Performance Augmented Diverse Generative Adversarial Network" or PaDGAN, which can generate novel high-quality designs with good coverage of the design space. We demonstrate that PaDGAN can generate diverse and high-quality designs on both synthetic and real-world examples and compare PaDGAN against other models such as the vanilla GAN and the BezierGAN. Unlike typical generative models that usually generate new designs by interpolating within the boundary of training data, we show that PaDGAN expands the design space boundary towards high-quality regions. The proposed method is broadly applicable to many tasks including design space exploration, design optimization, and creative solution recommendation.