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Workshop: Geometrical and Topological Representation Learning

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

Florent Bonnet · Ahmed Mazari · Thibaut Munzer · Pierre Yser · patrick gallinari

Keywords: [ partial differential equations ] [ Neural operators ] [ geometric deep learning ] [ graphs ] [ Multi-scale representations ] [ Point of Clouds ] [ Meshes ] [ Physics Metrics ] [ Computational Fluid Dynamics ]

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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