An extensible Benchmarking Graph-Mesh dataset for studying Steady-State Incompressible Navier-Stokes EquationsDownload PDF

02 Mar 2022, 12:21 (edited 22 Apr 2022)GTRL 2022 PosterReaders: Everyone
  • Keywords: Geometric Deep Learning, Neural Operators, Multi-scale representations, Partial Differential Equations, Computational Fluid Dynamics, Physics Metrics, Meshes, Graphs, Point of Clouds
  • TL;DR: We propose a benchmarking graph-mesh dataset to study Steady-State Incompressible Navier-Stokes's 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: Dataset:
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