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