# Generating various airfoil shapes with required lift coefficient using conditional variational autoencoders

arXiv: https://arxiv.org/abs/2106.09901 · HTML: https://mlsanity.com/paper/2106.09901/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2021.

## Built on by (most cited first, 6 of 6)

- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Inverse airfoil design method for generating varieties of smooth airfoils using conditional WGAN-gp](https://mlsanity.com/paper/2110.00212/) (2021)
- [Implicitly Guided Design with PropEn: Match your Data to Follow the Gradient](https://mlsanity.com/paper/2405.18075/) (2024)
- [Exploring the Potentials and Challenges of Deep Generative Models in Product Design Conception](https://mlsanity.com/paper/2407.11104/) (2024)
- [Physics-guided generative adversarial network to learn physical models](https://mlsanity.com/paper/2304.11488/) (2023)
- [Masked Conditioning for Deep Generative Models](https://mlsanity.com/paper/2505.16725/) (2025)

## Abstract (arXiv)

Multiple shapes must be obtained in the mechanical design process to satisfy the required design specifications. The inverse design problem has been analyzed in previous studies to obtain such shapes. However, finding multiple shapes in a short computation period is difficult while using the conventional methods. This paper proposes the use of the conditional variational autoencoders (CVAE) with normal distribution, denoted by N-CVAE, along with the von Mises-Fischer distribution, denoted by S-CVAE, to find multiple solutions for the inverse design problems. Both the CVAE models embed shapes into a latent space. The S-CVAE enables the separation of data in the latent space, whereas the N-CVAE embeds the data in a narrow space. These different features are used for various tasks in this study. In one of the tasks, the dataset consists of only one type of data and generates similar airfoils. Here, S-CVAE outperforms N-CVAE because it can separate the data. Another task involves combining different types of airfoils and generating new types of data. N-CVAE is useful in this instance since it embeds different shapes in the same latent area, due to which, the model outputs intermediate shapes of different types. The shape-generation capability of S-CVAE and N-CVAE are experimentally compared in this study.