Tailoring Generative Adversarial Networks for Smooth Airfoil Design

TL;DR

This work tackles the non-smoothness problem in GAN-based airfoil design by replacing post-processing smoothing with a generator-side regularization. It introduces a moving-average-based smoothing loss $L_S$ into a conditional GAN, yielding a total generator loss $L^{(G)} = L_{CE} + L_S$ and achieving smooth curves without post-processing. Using a UIUC airfoil dataset of 1399 shapes discretized to $38$ Y-coordinates and eight class conditions defined by medians of $\tau$, $\alpha$, and $\frac{c_l}{c_d}$, the authors demonstrate that the proposed smoothGAN maintains 100% $ACC^{(\tau)}$ while delivering 2–10x higher $\sigma^{(\tau)}$ and 2–6x higher $S$ diversity than a baseline GAN augmented with a Savitzky–Golay filter. The results show the approach can produce smooth, diverse airfoil designs and may extend to 3D surfaces and other engineering design problems.

Abstract

In the realm of aerospace design, achieving smooth curves is paramount, particularly when crafting objects such as airfoils. Generative Adversarial Network (GAN), a widely employed generative AI technique, has proven instrumental in synthesizing airfoil designs. However, a common limitation of GAN is the inherent lack of smoothness in the generated airfoil surfaces. To address this issue, we present a GAN model featuring a customized loss function built to produce seamlessly contoured airfoil designs. Additionally, our model demonstrates a substantial increase in design diversity compared to a conventional GAN augmented with a post-processing smoothing filter.

Figures (6)

• Figure 1: (a) The generator (G) of a trained conditional-GAN takes a noise vector and a label vector as inputs and the generator outputs a 2D airfoil curve. The generator is trained with a loss function $L^{(\text{G})}$ which includes a binary cross entropy loss ($L_{\text{CE}}$) and a mean square error loss $L_{\text{S}}$ to impose curve smoothing. (b) The generator outputs non-smooth curves if $L^{(\text{G})}$ only includes $L_{\text{CE}}$, i.e., without $L_{\text{S}}$. (c) The generator outputs desired smooth curves when $L_{\text{S}}$ is included in the generator loss in addition to $L_{\text{CE}}$.
• Figure 2: An original airfoil (solid line) after reducing the number of points to 38 (symbols).
• Figure 3: The architecture of conditional-GAN consists of a generator (G) and a discriminator (D). Both G and D are fully connected deep neural networks.
• Figure 4: Generated airfoil samples from the GAN trained without the smoothing loss and augmented with a post-processing smoothing filter. Each panel represents a class defined by low/high (0/1) $c_l/c_d$, $\alpha$, and $\tau$. It displays 600 airfoil samples and their mean shape (dashed curve).
• Figure 5: Generated airfoil samples from the GAN model trained with the smoothing loss. Each panel represents a class defined by low/high (0/1) $c_l/c_d$, $\alpha$, and $\tau$. It displays 600 airfoil samples and their mean shape (dashed curve).