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

Traditional generative models, such as standard GANs and Transformers, typically operate in flat Euclidean spaces. However, aerodynamic data often exists as low-dimensional manifolds embedded within high-dimensional spaces. This paper investigates whether explicitly incorporating intrinsic geometric properties—specifically by representing aerodynamic data as piecewise smooth Bézier surfaces—can improve the accuracy of generative models in fluid mechanics.

To address this, the authors propose the Intrinsic Geometry-based Generative Adversarial Network (IG-GAN). The model architecture consists of two primary components:

1. Bézier-based Generator: Instead of generating raw data points directly, the generator learns to predict the coefficient matrices of Bézier surfaces. These coefficients are then combined analytically with power-basis vectors to reconstruct the aerodynamic manifold. This approach forces the generator to respect the underlying geometric structure of the data.
2. RBF-based Discriminator: The discriminator utilizes a Radial Basis Function (RBF) network. By measuring the Euclidean distance between input samples and learnable RBF centers, the discriminator gains enhanced local approximation capabilities, which helps stabilize the adversarial training process.

The model was evaluated on two challenging tasks: reconstructing flow fields governed by the Burgers' equation and predicting aerodynamic coefficients for the ONERA M6 aircraft wing.

IG-GAN consistently outperformed baseline models, including RBF-GAN, RGFiL, and the state-of-the-art SSL-Transformer. On the Burgers' equation dataset, IG-GAN reduced the Mean Squared Error (MSE) of velocity predictions by 97.41% compared to the SSL-Transformer. Similarly, for the ONERA M6 aircraft dataset, the model achieved an 82.95% reduction in overall MSE across nine aerodynamic coefficients. These results suggest that embedding intrinsic geometric constraints into the generative process allows neural networks to capture complex aerodynamic phenomena more effectively than purely data-driven, Euclidean-based methods.