# Inverse airfoil design method for generating varieties of smooth airfoils using conditional WGAN-gp

arXiv: https://arxiv.org/abs/2110.00212 · HTML: https://mlsanity.com/paper/2110.00212/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 42 references that are in the map.
- First posted on arXiv 1 Oct 2021.

## Builds on (most cited first, 10 of 10)

- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [NIPS 2016 Tutorial: Generative Adversarial Networks](https://mlsanity.com/paper/1701.00160/) (2016)
- [Airfoil Design Parameterization and Optimization using B'ezier Generative Adversarial Networks](https://mlsanity.com/paper/2006.12496/) (2020)
- [B'ezierGAN: Automatic Generation of Smooth Curves from Interpretable Low-Dimensional Parameters](https://mlsanity.com/paper/1808.08871/) (2018)
- [Deep Generative Model for Efficient 3D Airfoil Parameterization and Generation](https://mlsanity.com/paper/2101.02744/) (2021)
- [Airfoil GAN: Encoding and Synthesizing Airfoils for Aerodynamic Shape Optimization](https://mlsanity.com/paper/2101.04757/) (2021)
- [Generating various airfoil shapes with required lift coefficient using conditional variational autoencoders](https://mlsanity.com/paper/2106.09901/) (2021)
- [DeepCloud. The Application of a Data-driven, Generative Model in Design](https://mlsanity.com/paper/1904.01083/) (2019)

## Built on by (most cited first, 7 of 7)

- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Parametric Generative Schemes with Geometric Constraints for Encoding and Synthesizing Airfoils](https://mlsanity.com/paper/2205.02458/) (2022)
- [Physics-guided training of GAN to improve accuracy in airfoil design synthesis](https://mlsanity.com/paper/2308.10038/) (2023)
- [Mode-Aware Continual Learning for Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2305.11400/) (2023)
- [Tailoring Generative Adversarial Networks for Smooth Airfoil Design](https://mlsanity.com/paper/2404.11816/) (2024)
- [Generative method for aerodynamic optimization based on classifier-free guided denoising diffusion probabilistic model](https://mlsanity.com/paper/2503.07056/) (2025)
- [A generative adversarial network optimization method for damage detection and digital twinning by deep AI fault learning: Z24 Bridge structural health monitoring benchmark validation](https://mlsanity.com/paper/2511.00099/) (2025)

## Abstract (arXiv)

Machine learning models are recently utilized for airfoil shape generation methods. It is desired to obtain airfoil shapes that satisfies required lift coefficient. Generative adversarial networks (GAN) output reasonable airfoil shapes. However, shapes obtained from ordinal GAN models are not smooth, and they need smoothing before flow analysis. Therefore, the models need to be coupled with Bezier curves or other smoothing methods to obtain smooth shapes. Generating shapes without any smoothing methods is challenging. In this study, we employed conditional Wasserstein GAN with gradient penalty (CWGAN-GP) to generate airfoil shapes, and the obtained shapes are as smooth as those obtained using smoothing methods. With the proposed method, no additional smoothing method is needed to generate airfoils. Moreover, the proposed model outputs shapes that satisfy the lift coefficient requirements.