论文标题
一个可扩展的基准图形网格数据集，用于研究稳态不可压缩的Navier-Stokes方程
An extensible Benchmarking Graph-Mesh dataset for studying Steady-State Incompressible Navier-Stokes Equations
论文作者
论文摘要
\ emph {几何深度学习}（GDL）的最新进展显示了其提供强大数据驱动模型的潜力。这提供了探索从图形数据中\ emph {部分微分方程}（PDES）控制的物理系统的新方法的动力。然而，尽管努力和最近的成就，但几个研究方向仍未开发，进步仍然远远不令人满足现实现象的物理要求。主要障碍之一是缺乏基准数据集和常见的物理评估协议。在本文中，我们提出了一个2-D Graph-Mesh数据集，以研究High Reynolds制度的机翼上的气流（从$ 10^6 $及以后）。我们还引入了有关翼型上应力力的指标，以评估重要的物理量的GDL模型。此外，我们提供广泛的GDL基准。
Recent progress in \emph{Geometric Deep Learning} (GDL) has shown its potential to provide powerful data-driven models. This gives momentum to explore new methods for learning physical systems governed by \emph{Partial Differential Equations} (PDEs) from Graph-Mesh data. However, despite the efforts and recent achievements, several research directions remain unexplored and progress is still far from satisfying the physical requirements of real-world phenomena. One of the major impediments is the absence of benchmarking datasets and common physics evaluation protocols. In this paper, we propose a 2-D graph-mesh dataset to study the airflow over airfoils at high Reynolds regime (from $10^6$ and beyond). We also introduce metrics on the stress forces over the airfoil in order to evaluate GDL models on important physical quantities. Moreover, we provide extensive GDL baselines.
