# IG-GAN: A Generative Adversarial Network for Aerodynamic Data Generation Based on Intrinsic Geometry

arXiv: https://arxiv.org/abs/2607.11497 · HTML: https://mlsanity.com/paper/2607.11497/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 22 references that are in the map.
- First posted on arXiv 13 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Manifold learning: what, how, and why](https://mlsanity.com/paper/2311.03757/) (2023)
- [The Euclidean Space is Evil: Hyperbolic Attribute Editing for Few-shot Image Generation](https://mlsanity.com/paper/2211.12347/) (2022)
- [Transformer models: an introduction and catalog](https://mlsanity.com/paper/2302.07730/) (2023)
- [Intrinsic Neural Fields: Learning Functions on Manifolds](https://mlsanity.com/paper/2203.07967/) (2022)
- [Flow Field Reconstructions with GANs based on Radial Basis Functions](https://mlsanity.com/paper/2009.02285/) (2020)
- [Airfoil GAN: Encoding and Synthesizing Airfoils for Aerodynamic Shape Optimization](https://mlsanity.com/paper/2101.04757/) (2021)
- [Intrinsic and extrinsic deep learning on manifolds](https://mlsanity.com/paper/2302.08606/) (2023)
- [A Manifold-based Airfoil Geometric-feature Extraction and Discrepant Data Fusion Learning Method](https://mlsanity.com/paper/2206.12254/) (2022)
- [A novel approach to data generation in generative model](https://mlsanity.com/paper/2502.10092/) (2025)
- [Geodesic Gradient Descent: A Generic and Learning-rate-free Optimizer on Objective Function-induced Manifolds](https://mlsanity.com/paper/2603.06651/) (2026)

## Abstract (arXiv)

Existing generative models learn data distributions in flat Euclidean space. However, most data in our real world are manifolds embedded in high dimensional Euclidean space. Therefore, we propose an intrinsic-geometry-based generative adversarial network (IG-GAN) for data generation in the field of aerodynamics. The generator of the IG-GAN represents aerodynamic data as a piecewise smooth manifold constructed by B'ezier surfaces, and the generator tries to learn the coefficients of each B'ezier surface to further combine multiple B'ezier surfaces into a smooth manifold automatically. The discriminator in the IG-GAN is a radial-basis-function based discriminator (RBF-D). Experimental results show that IG-GAN achieves lower predicted Mean Squared Errors (MSEs) than those of three baselines. Specifically, on the Burgers' equation dataset, IG-GAN reduces the predicted MSE of velocity u by 97.41% compared with state of the art SSL-Transformer. Additionally, on the ONERA M6 aircraft dataset, IG-GAN reduces the overall MSE of nine aerodynamic coefficients by 82.95% compared with SSL-Transformer.