# Airfoil Design Parameterization and Optimization using B'ezier Generative Adversarial Networks

arXiv: https://arxiv.org/abs/2006.12496 · HTML: https://mlsanity.com/paper/2006.12496/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2020.

## Built on by (most cited first, 30 of 35)

- [Engineering Sketch Generation for Computer-Aided Design](https://mlsanity.com/paper/2104.09621/) (2021)
- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [Inverse design optimization framework via a two-step deep learning approach: application to a wind turbine airfoil](https://mlsanity.com/paper/2108.08500/) (2021)
- [ShipHullGAN: A generic parametric modeller for ship hull design using deep convolutional generative model](https://mlsanity.com/paper/2305.00210/) (2023)
- [Deep Generative Model for Efficient 3D Airfoil Parameterization and Generation](https://mlsanity.com/paper/2101.02744/) (2021)
- [GAN-DUF: Hierarchical Deep Generative Models for Design Under Free-Form Geometric Uncertainty](https://mlsanity.com/paper/2202.10558/) (2022)
- [Aligning Constraint Generation with Design Intent in Parametric CAD](https://mlsanity.com/paper/2504.13178/) (2025)
- [Airfoil GAN: Encoding and Synthesizing Airfoils for Aerodynamic Shape Optimization](https://mlsanity.com/paper/2101.04757/) (2021)
- [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)
- [On the Noise Scheduling for Generating Plausible Designs with Diffusion Models](https://mlsanity.com/paper/2311.11207/) (2023)
- [EngiBench: A Framework for Data-Driven Engineering Design Research](https://mlsanity.com/paper/2508.00831/) (2025)
- [Range-GAN: Range-Constrained Generative Adversarial Network for Conditioned Design Synthesis](https://mlsanity.com/paper/2103.06230/) (2021)
- [Physics-guided training of GAN to improve accuracy in airfoil design synthesis](https://mlsanity.com/paper/2308.10038/) (2023)
- [Generative VS non-Generative Models in Engineering Shape Optimization](https://mlsanity.com/paper/2402.08540/) (2024)
- [Generative Aerodynamic Design with Diffusion Probabilistic Models](https://mlsanity.com/paper/2409.13328/) (2024)
- [3DID: Direct 3D Inverse Design for Aerodynamics with Physics-Aware Optimization](https://mlsanity.com/paper/2512.08987/) (2025)
- [Tailoring Generative Adversarial Networks for Smooth Airfoil Design](https://mlsanity.com/paper/2404.11816/) (2024)
- [Co-Learning Bayesian Optimization](https://mlsanity.com/paper/2501.13332/) (2025)
- [Three-dimensional Deep Shape Optimization with a Limited Dataset](https://mlsanity.com/paper/2506.12326/) (2025)
- [Deep Generative Models for Geometric Design Under Uncertainty](https://mlsanity.com/paper/2112.08919/) (2021)
- [PPI-NET: End-to-End Parametric Primitive Inference](https://mlsanity.com/paper/2308.01521/) (2023)
- [Generative Models for Anomaly Detection and Design-Space Dimensionality Reduction in Shape Optimization](https://mlsanity.com/paper/2308.04051/) (2023)
- [Generative method for aerodynamic optimization based on classifier-free guided denoising diffusion probabilistic model](https://mlsanity.com/paper/2503.07056/) (2025)
- [Predicting Onflow Parameters Using Transfer Learning for Domain and Task Adaptation](https://mlsanity.com/paper/2506.14784/) (2025)
- [Generative Inverse Design with Abstention via Diagonal Flow Matching](https://mlsanity.com/paper/2603.15925/) (2026)
- [Compact and Intuitive Airfoil Parameterization Method through Physics-aware Variational Autoencoder](https://mlsanity.com/paper/2311.10921/) (2023)
- [A mechanism-driven reinforcement learning framework for shape optimization of airfoils](https://mlsanity.com/paper/2403.04329/) (2024)
- [Physics-Informed Geometric Operators to Support Surrogate, Dimension Reduction and Generative Models for Engineering Design](https://mlsanity.com/paper/2407.07611/) (2024)
- [Flow Battery Manifold Design with Heterogeneous Inputs Through Generative Adversarial Neural Networks](https://mlsanity.com/paper/2508.08863/) (2025)

## Abstract (arXiv)

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, B'ezier-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 B'ezier-GAN's representation capacity and compactness. Results show that B'ezier-GAN both (1) learns smooth and realistic shape representations for a wide range of airfoils and (2) empirically accelerates optimization convergence by at least two times compared to state-of-the-art parameterization methods.