# Deep Generative Model for Efficient 3D Airfoil Parameterization and Generation

arXiv: https://arxiv.org/abs/2101.02744 · HTML: https://mlsanity.com/paper/2101.02744/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 51 references that are in the map.
- First posted on arXiv 7 Jan 2021.

## Builds on (most cited first, 17 of 17)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [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)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [Octree Generating Networks: Efficient Convolutional Architectures for High-resolution 3D Outputs](https://mlsanity.com/paper/1703.09438/) (2017)
- [Meta-Sim: Learning to Generate Synthetic Datasets](https://mlsanity.com/paper/1904.11621/) (2019)
- [Airfoil Design Parameterization and Optimization using B'ezier Generative Adversarial Networks](https://mlsanity.com/paper/2006.12496/) (2020)
- [Matryoshka Networks: Predicting 3D Geometry via Nested Shape Layers](https://mlsanity.com/paper/1804.10975/) (2018)
- [SurfNet: Generating 3D shape surfaces using deep residual networks](https://mlsanity.com/paper/1703.04079/) (2017)
- [Multi-chart Generative Surface Modeling](https://mlsanity.com/paper/1806.02143/) (2018)
- [DeformNet: Free-Form Deformation Network for 3D Shape Reconstruction from a Single Image](https://mlsanity.com/paper/1708.04672/) (2017)
- [MO-PaDGAN: Reparameterizing Engineering Designs for Augmented Multi-objective Optimization](https://mlsanity.com/paper/2009.07110/) (2020)
- [Learning Free-Form Deformations for 3D Object Reconstruction](https://mlsanity.com/paper/1803.10932/) (2018)

## Built on by (most cited first, 10 of 10)

- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Inverse design optimization framework via a two-step deep learning approach: application to a wind turbine airfoil](https://mlsanity.com/paper/2108.08500/) (2021)
- [GAN-DUF: Hierarchical Deep Generative Models for Design Under Free-Form Geometric Uncertainty](https://mlsanity.com/paper/2202.10558/) (2022)
- [Inverse airfoil design method for generating varieties of smooth airfoils using conditional WGAN-gp](https://mlsanity.com/paper/2110.00212/) (2021)
- [Airfoil Diffusion: Denoising Diffusion Model For Conditional Airfoil Generation](https://mlsanity.com/paper/2408.15898/) (2024)
- [Range-GAN: Range-Constrained Generative Adversarial Network for Conditioned Design Synthesis](https://mlsanity.com/paper/2103.06230/) (2021)
- [Deep Generative Models for Geometric Design Under Uncertainty](https://mlsanity.com/paper/2112.08919/) (2021)
- [A Generative Neural Network Approach for 3D Multi-Criteria Design Generation and Optimization of an Engine Mount for an Unmanned Air Vehicle](https://mlsanity.com/paper/2311.03414/) (2023)
- [Deep convolutional surrogates and degrees of freedom in thermal design](https://mlsanity.com/paper/2208.07482/) (2022)
- [Surrogate Assisted Pedestrian Protection Design via a Foundation Model Orchestrated Workflow](https://mlsanity.com/paper/2606.17577/) (2026)

## Abstract (arXiv)

In aerodynamic shape optimization, the convergence and computational cost are greatly affected by the representation capacity and compactness of the design space. Previous research has demonstrated that using a deep generative model to parameterize two-dimensional (2D) airfoils achieves high representation capacity/compactness, which significantly benefits shape optimization. In this paper, we propose a deep generative model, Free-Form Deformation Generative Adversarial Networks (FFD-GAN), that provides an efficient parameterization for three-dimensional (3D) aerodynamic/hydrodynamic shapes like aircraft wings, turbine blades, car bodies, and hulls. The learned model maps a compact set of design variables to 3D surface points representing the shape. We ensure the surface smoothness and continuity of generated geometries by incorporating an FFD layer into the generative model. We demonstrate FFD-GAN's performance using a wing shape design example. The results show that FFD-GAN can generate realistic designs and form a reasonable parameterization. We further demonstrate FFD-GAN's high representation compactness and capacity by testing its design space coverage, the feasibility ratio of the design space, and its performance in design optimization. We demonstrate that over 94% feasibility ratio is achieved among wings randomly generated by the FFD-GAN, while FFD and B-spline only achieve less than 31%. We also show that the FFD-GAN leads to an order of magnitude faster convergence in a wing shape optimization problem, compared to the FFD and the B-spline parameterizations.