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

2026-07-13

AI Summary

Traditional generative models struggle to effectively capture the non-Euclidean manifold structure inherent in aerodynamic data within Euclidean space. To address this limitation, this work proposes the Intrinsic Geometry Generative Adversarial Network (IG-GAN), which uniquely integrates Bézier surfaces with intrinsic geometry. IG-GAN explicitly constructs a globally smooth manifold by learning the coefficients of piecewise-smooth Bézier surfaces and introduces a radial basis function–based discriminator (RBF-D) for optimization. Evaluated on the Burgers’ equation dataset, the method reduces the mean squared error (MSE) of velocity field prediction by 97.41% compared to SSL-Transformer. On the ONERA M6 aircraft dataset, it achieves an 82.95% reduction in overall MSE across nine aerodynamic coefficients, demonstrating substantially improved generation accuracy for data residing on non-Euclidean manifolds.

Abstract

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 Bézier surfaces, and the generator tries to learn the coefficients of each Bézier surface to further combine multiple Bézier 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.

Problem

• generative adversarial network
• intrinsic geometry
• aerodynamic data generation
• manifold learning
• Bézier surfaces

Innovation

• Intrinsic Geometry
• Generative Adversarial Network
• Bézier Surfaces
• Manifold Learning
• Radial Basis Function Discriminator