  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.
