Generative VS non-Generative Models in Engineering Shape Optimization

TL;DR

This paper tackles the challenge of constructing efficient design spaces for shape optimization by comparing generative models (GAN and PaDGAN) with a non-generative Shape-Supervised Dimension Reduction (SSDR) approach that couples Karhunen-Loève Expansion with an augmented Shape Signature Vector. It evaluates these methods on two large airfoil/hydrofoil datasets enriched with geometry and physics-informed features, employing multiple discretization schemes and performance metrics. The results show that, with an appropriate encoding and physics augmentation, the non-generative SSDR method yields higher design validity and robust latent spaces while remaining computationally cheaper, though generative models offer greater design diversity. The findings provide practical guidance for engineers selecting design-space construction strategies and point to promising extensions into 3D surface optimization and CAD-integrated design tools.

Abstract

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 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.

Figures (5)

• Figure 1: Profile instance generated by the parametric model introduced in KostasEtAl2020. The 17 parameters $(p_1, \ldots , p_{17})$ are used to define the coordinates of the 13 control points $\mathbf{b}_i,\,i=0,\ldots,12$ depicted in the same figure; figure adapted from masood2023shape.
• Figure 2: NACA 2410 foil discretized using 4 different point distribution schemes.
• Figure 3: Plots for each Quality Analysis Metric as discussed in §\ref{['sec:QAM']} with cosine spacing and SSVs with $4^{th}$ geometric moments when augmented SSVs are required. The horizontal line within boxes represents the average value, which is also marked at the top of each box.
• Figure 4: Effect of each discretization scheme on the three Quality Analysis Metrics. The horizontal line in boxes represents the average value, which is also marked at the top of each box.
• Figure 5: Probability Density Distribution for each discretization in $\mathcal{D}_1$.