An Extensible Benchmarking Graph-Mesh Dataset for Studying Steady-State Incompressible Navier-Stokes Equations

Abstract

Recent progress in 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 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. Code: https://github.com/Extrality/ICLR_NACA_Dataset_V0 Dataset: https://data.isir.upmc.fr/extrality/