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

TL;DR

This paper introduces a new 2-D graph-mesh dataset for studying airflow over airfoils at high Reynolds numbers, along with evaluation metrics and baseline models to advance physics-informed geometric deep learning.

Contribution

It provides the first extensible benchmark dataset and evaluation protocols for GDL models on steady-state incompressible Navier-Stokes equations.

Findings

The dataset enables standardized evaluation of GDL models.

Baseline models demonstrate the current capabilities and limitations.

Metrics for stress forces facilitate physical accuracy assessment.

Abstract

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.