Surrogate models are necessary to optimize meaningful quantities in physical dynamics as their recursive numerical resolutions are often prohibitively expensive. It is mainly the case for fluid dynamics and the resolution of Navier-Stokes equations. However, despite the fast-growing field of data-driven models for physical systems, reference datasets representing real-world phenomenons are lacking. In this work, we develop \textsc{AirfRANS}, a dataset for studying the two-dimensional incompressible steady-state Reynolds-Averaged-Navier-Stokes equations over airfoils at a subsonic regime and for different angles of attacks. We also introduce metrics on the stress forces at the surface of geometries and visualization of boundary layers to assess the capabilities of models to accurately predict the meaningful information of the problem. Finally, we propose deep learning baselines on four machine learning tasks to study \textsc{AirfRANS} under different constraints for generalization considerations: big and scarce data regime, Reynolds number and angle of attack extrapolation.

1/Sorbonne Université, CNRS, ISIR, F-75005 Paris, France
2/ Sorbonne Université, Institut Jean Le Rond d’Alembert, 4 Place Jussieu, 75005 Paris, France
3/ Extrality, 75002 Paris, France4/ Criteo AI Lab, Paris, France