# Physics-guided training of GAN to improve accuracy in airfoil design synthesis

arXiv: https://arxiv.org/abs/2308.10038 · HTML: https://mlsanity.com/paper/2308.10038/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 48 references that are in the map.
- First posted on arXiv 19 Aug 2023.

## Builds on (most cited first, 16 of 16)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [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)
- [Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations](https://mlsanity.com/paper/1811.02033/) (2018)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Physics informed neural networks for continuum micromechanics](https://mlsanity.com/paper/2110.07374/) (2021)
- [Airfoil Design Parameterization and Optimization using B'ezier Generative Adversarial Networks](https://mlsanity.com/paper/2006.12496/) (2020)
- [PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physics](https://mlsanity.com/paper/2106.02993/) (2021)
- [Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equations](https://mlsanity.com/paper/2203.08501/) (2022)
- [Loss Landscape Engineering via Data Regulation on PINNs](https://mlsanity.com/paper/2205.07843/) (2022)
- [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)
- [Physics-guided generative adversarial network to learn physical models](https://mlsanity.com/paper/2304.11488/) (2023)

## Built on by (most cited first, 4 of 4)

- [VehicleSDF: A 3D generative model for constrained engineering design via surrogate modeling](https://mlsanity.com/paper/2410.18986/) (2024)
- [Flow marching for a generative PDE foundation model](https://mlsanity.com/paper/2509.18611/) (2025)
- [Tailoring Generative Adversarial Networks for Smooth Airfoil Design](https://mlsanity.com/paper/2404.11816/) (2024)
- [Compact and Intuitive Airfoil Parameterization Method through Physics-aware Variational Autoencoder](https://mlsanity.com/paper/2311.10921/) (2023)

## Abstract (arXiv)

Generative adversarial networks (GAN) have recently been used for a design synthesis of mechanical shapes. A GAN sometimes outputs physically unreasonable shapes. For example, when a GAN model is trained to output airfoil shapes that indicate required aerodynamic performance, significant errors occur in the performance values. This is because the GAN model only considers data but does not consider the aerodynamic equations that lie under the data. This paper proposes the physics-guided training of the GAN model to guide the model to learn physical validity. Physical validity is computed using general-purpose software located outside the neural network model. Such general-purpose software cannot be used in physics-informed neural network frameworks, because physical equations must be implemented inside the neural network models. Additionally, a limitation of generative models is that the output data are similar to the training data and cannot generate completely new shapes. However, because the proposed model is guided by a physical model and does not use a training dataset, it can generate completely new shapes. Numerical experiments show that the proposed model drastically improves the accuracy. Moreover, the output shapes differ from those of the training dataset but still satisfy the physical validity, overcoming the limitations of existing GAN models.