Statistical and spatial analysis in the generation of aerodynamic profiles using generative adversarial networks

Аuthors

Snazin A. A.^*, Sevchenko V. I.

Mlitary spaсe Aсademy named after A.F. Mozhaisky, St. Petersburg, Russia

*e-mail: alexandersnzn@mail.ru

Abstract

The generation of aerodynamic airfoils using generative models is of interest as a means of accelerating the design process; however, its practical value is determined not only by the visual plausibility of the synthesized shapes, but also by the model’s ability to reproduce the distributional structure of real airfoils. The aim of this study was to assess the extent to which a generative adversarial network can synthesize airfoils while preserving the key geometric characteristics of the training set and the diversity of admissible shapes. To this end, a GAN was trained on a dataset of four-digit NACA airfoils represented as discretized coordinate vectors. The quality of generation was evaluated using the distributions of maximum thickness, the chordwise position of maximum thickness, and airfoil area, as well as diversity metrics, the Wasserstein distance, and data projections in the PCA and t-SNE spaces. The results indicate that the quality of generation is nonuniform across the shape space. The model reproduces the central region of the distribution and the principal ranges of geometric parameters with acceptable fidelity; however, it is less successful in describing the extreme regions of the shape space, smooths characteristic peaks in the distributions, and produces a small number of invalid samples. This pattern suggests that the generator primarily concentrates on the most typical averaged shapes and does not fully capture the geometric variability of the latent space. These findings show that the evaluation of generative models for aerodynamic design must take into account not only the realism of individual airfoils, but also the completeness of coverage of the space of admissible configurations.

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