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

Florent Bonnet, Jocelyn Ahmed Mazari, Thibaut Munzer, Pierre Yser, Patrick Gallinari

International Conference on Learning Representations (ICLR) 2022 Workshop on Geometrical and Topological Representation Learning

April 29, 2022
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 106 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.

Affiliations

1/ Sorbonne Universite, CNRS, ISIR, F-75005 Paris, France

2/ Ecole Normale Superieure Paris Saclay, France

3/ Extrality, 75002 Paris, France

4/ Criteo AI Lab, Paris, France

Links

/ Other published papers

Multi-scale Physical Representations for Approximating PDE Solutions with Graph Neural Operators
Léon Migus, Yuan Yin, Jocelyn Ahmed Mazari, Patrick Gallinari
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