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 phenomena 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.

Details regarding the datasets are provided in Appendix A. Morphing strategies and dimensionality Regarding the AirfRANS dataset, the reader is referred to [14]. Examples of input geometries are shown in Figure 6 together with the associated output pressure fields. The output scalars of the problem are obtained by post-processing the three-dimensional velocity. Examples of input geometries are shown in Figure 7. Figure 8: ( Tensile2d) Illustration of the Tutte's barycentric mapping used in the morphing stage. Notice that although these morphing techniques are called "mesh A zoom of the RBF morphing close to the airfoil for test sample 787 is illustrated in Figure 10.

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 phenomena 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.