IG-GAN：一种基于内在几何的空气动力学数据生成生成对抗网络
IG-GAN: A Generative Adversarial Network for Aerodynamic Data Generation Based on Intrinsic Geometry
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中文总结 AI 辅助
针对现实世界多数数据是嵌入高维欧几里得空间流形的情况，提出基于内在几何的生成对抗网络IG-GAN用于空气动力学数据生成。其生成器用贝塞尔曲面构建流形，判别器为RBF-D。实验显示该方法相比基线能显著降低预测均方误差。
中文摘要 AI 辅助
现有生成模型在平坦欧几里得空间学习数据分布，而现实世界多数数据是嵌入高维欧几里得空间的流形。为此提出基于内在几何的生成对抗网络IG-GAN用于空气动力学数据生成。其生成器将空气动力学数据表示为由贝塞尔曲面构成的分段光滑流形，学习各贝塞尔曲面系数并自动组合成光滑流形，判别器是基于径向基函数的判别器（RBF-D）。实验表明IG-GAN预测均方误差低于三个基线。如在伯格斯方程数据集上，相比SSL-Transformer，IG-GAN使速度u的预测MSE降低97.41%；在ONERA M6飞机数据集上，相比SSL-Transformer，IG-GAN使九个空气动力学系数的总体MSE降低82.95%。
英文摘要
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.
发表机构
- School of Information Science and Engineering, Hebei University of Science and Technology（信息科学与工程学院，河北科技大学）
机构由 AI 辅助整理，请以论文原文为准。
