Generative vs. Non-Generative Models in Engineering Shape Optimization

Generative models offer design diversity but tend to be computationally expensive, while non-generative models are computationally cost-effective but produce less diverse and often invalid designs. However, the limitations of non-generative models can be overcome with the introduction of augmented shape signature vectors (SSVs) to represent both geometric and physical information. This recent advancement has inspired 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, which is demonstrated in this work. These models are showcased in airfoil/hydrofoil design, and a comparison of the resulting design spaces is conducted in this work. 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 were applied to two large foil profile datasets comprising real-world and artificial designs generated through either a profile-generating parametric model or a deep-learning approach. These datasets were further enriched with integral properties of their members’ shapes, as well as physics-informed parameters. The obtained 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 no or significantly fewer invalid designs when compared to generative models. The performance and diversity of the generated designs were compared to provide further insights about the quality of the resulting spaces. These findings can aid the engineering design community in making informed decisions when constructing design spaces for shape optimization, as it has been demonstrated that, under certain conditions, computationally inexpensive approaches can closely match or even outperform state-of-the art generative models.