用几何结构生成气动数据，精度远超传统方法
IG-GAN: A Generative Adversarial Network for Aerodynamic Data Generation Based on Intrinsic Geometry
- 将气动数据建模为贝塞尔曲面拼接的流形，学习其几何结构
- 在伯格斯方程和ONERA M6机翼数据上，预测误差降低超97%和83%
- 适合需要高精度物理数据生成的航空航天研究者
现有生成模型在平坦的欧氏空间中学习数据分布，但现实中多数数据是高维欧氏空间中的流形。为此，我们提出基于内在几何的生成对抗网络（IG-GAN）用于气动数据生成。IG-GAN的生成器将气动数据表示为由贝塞尔曲面构成的分片光滑流形，并学习各贝塞尔曲面的系数，自动组合成光滑整体。判别器采用基于径向基函数的判别器（RBF-D）。实验表明，IG-GAN的预测均方误差（MSE）显著低于三种基线模型。具体而言，在伯格斯方程数据集上，速度u的预测MSE相比最先进的SSL-Transformer降低97.41%；在ONERA M6飞机数据集上，九个气动系数的整体MSE相比SSL-Transformer降低82.95%。
原文摘要 · Abstract (English)
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.
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