Airfoil Design Parameterization and Optimization using Bézier Generative Adversarial Networks

Abstract

Global optimization of aerodynamic shapes usually requires a large number of expensive computational fluid dynamics simulations because of the high dimensionality of the design space. One approach to combat this problem is to reduce the design space dimension by obtaining a new representation. This requires a parametric function that compactly and sufficiently describes useful variation in shapes. We propose a deep generative model, Bézier-GAN, to parameterize aerodynamic designs by learning from shape variations in an existing database. The resulted new parameterization can accelerate design optimization convergence by improving the representation compactness while maintaining sufficient representation capacity. We use the airfoil design as an example to demonstrate the idea and analyze Bézier-GAN's representation capacity and compactness. Results show that Bézier-GAN both (1) learns smooth

MO-PaDGAN: Reparameterizing Engineering Designs for augmented multi-objective optimization

“…It provides the geometries of nearly 1,600 real-world airfoil designs. We preprocessed and augmented the dataset similar to [9], which led to a dataset of 38,802 airfoils, each of which is represented by 192 surface points (i.e., x i ∈ R 192×2 ). Figure 6(a) shows airfoil shapes randomly drawn from the training data.…”

“…We use a residual neural network (ResNet) [17] as the surrogate model to predict the performance indicators and a BézierGAN [9,18,19] to parameterize airfoils. Please refer to the appendix and the code for details on their network architectures.…”

“…Instead of generating airfoil surface points freely in a 2D space, it uses a Bézier layer to constrain generated points to be on a rational Bézier curve. We follow [9] to setup the model architecture. We use the same training data as for the neural network surrogate model.…”

“…While one can use both inputs as design parameters, we only use the latent codes as variable design parameters in our optimization experiments. How either input affects optimization performance is not central to this work (please refer to [9] for related details).…”

“…Variational autoencoders (VAEs) [5] and Generative Adversarial Networks (GANs) [6] are the two most commonly used deep generative models for these tasks. These models are applied in design optimization over domains including microstructural design [7], 3D modeling [8], and aerodynamic shape design [9]. However, existing generative models, whose goal is learning the distribution of existing designs, face three challenges when being used for parameterizing designs: 1) generated designs may have limited design space coverage (e.g., when mode collapse happens with GANs), 2) the generator ignores design performance, and 3) the new parameterization is unable to represent designs outside the training data.…”