# Airfoil GAN: Encoding and Synthesizing Airfoils for Aerodynamic Shape Optimization

arXiv: https://arxiv.org/abs/2101.04757 · HTML: https://mlsanity.com/paper/2101.04757/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 89 references that are in the map.
- First posted on arXiv 12 Jan 2021.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Fully Convolutional Instance-aware Semantic Segmentation](https://mlsanity.com/paper/1611.07709/) (2016)
- [TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain](https://mlsanity.com/paper/2003.04685/) (2020)
- [Deep Learning in Robotics: A Review of Recent Research](https://mlsanity.com/paper/1707.07217/) (2017)
- [Airfoil Design Parameterization and Optimization using B'ezier Generative Adversarial Networks](https://mlsanity.com/paper/2006.12496/) (2020)
- [SurfNet: Generating 3D shape surfaces using deep residual networks](https://mlsanity.com/paper/1703.04079/) (2017)
- [Application of Convolutional Neural Network to Predict Airfoil Lift Coefficient](https://mlsanity.com/paper/1712.10082/) (2017)
- [Multi-Stage Variational Auto-Encoders for Coarse-to-Fine Image Generation](https://mlsanity.com/paper/1705.07202/) (2017)
- [B'ezierGAN: Automatic Generation of Smooth Curves from Interpretable Low-Dimensional Parameters](https://mlsanity.com/paper/1808.08871/) (2018)

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

- [Inverse airfoil design method for generating varieties of smooth airfoils using conditional WGAN-gp](https://mlsanity.com/paper/2110.00212/) (2021)
- [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)
- [A Manifold-based Airfoil Geometric-feature Extraction and Discrepant Data Fusion Learning Method](https://mlsanity.com/paper/2206.12254/) (2022)
- [Full Domain Analysis in Fluid Dynamics](https://mlsanity.com/paper/2505.22275/) (2025)
- [Learning with Geometry: Including Riemannian Geometric Features in Coefficient of Pressure Prediction on Aircraft Wings](https://mlsanity.com/paper/2401.09452/) (2023)
- [IG-GAN: A Generative Adversarial Network for Aerodynamic Data Generation Based on Intrinsic Geometry](https://mlsanity.com/paper/2607.11497/) (2026)

## Abstract (arXiv)

The current design of aerodynamic shapes, like airfoils, involves computationally intensive simulations to explore the possible design space. Usually, such design relies on the prior definition of design parameters and places restrictions on synthesizing novel shapes. In this work, we propose a data-driven shape encoding and generating method, which automatically learns representations from existing airfoils and uses the learned representations to generate new airfoils. The representations are then used in the optimization of synthesized airfoil shapes based on their aerodynamic performance. Our model is built upon VAEGAN, a neural network that combines Variational Autoencoder with Generative Adversarial Network and is trained by the gradient-based technique. Our model can (1) encode the existing airfoil into a latent vector and reconstruct the airfoil from that, (2) generate novel airfoils by randomly sampling the latent vectors and mapping the vectors to the airfoil coordinate domain, and (3) synthesize airfoils with desired aerodynamic properties by optimizing learned features via a genetic algorithm. Our experiments show that the learned features encode shape information thoroughly and comprehensively without predefined design parameters. By interpolating/extrapolating feature vectors or sampling from Gaussian noises, the model can automatically synthesize novel airfoil shapes, some of which possess competitive or even better aerodynamic properties comparing to airfoils used for model training purposes. By optimizing shapes on the learned latent domain via a genetic algorithm, synthesized airfoils can evolve to target aerodynamic properties. This demonstrates an efficient learning-based airfoil design framework, which encodes and optimizes the airfoil on the latent domain and synthesizes promising airfoil candidates for required aerodynamic performance.