Learning Airfoil Flow Field Representation via Geometric Attention Neural Field

Numerical simulation in fluid dynamics can be computationally expensive and difficult to achieve. To enhance efficiency, developing high-performance and accurate surrogate models is crucial, where deep learning shows potential. This paper introduces geometric attention (GeoAttention), a method that leverages attention mechanisms to encode geometry represented by point cloud, thereby enhancing the neural network’s generalizability across different geometries. Furthermore, by integrating GeoAttention with neural field, we propose the geometric attention neural field (GeoANF), specifically for learning representations of airfoil flow fields. The GeoANF embeds observational data independently of the specific discretization process into a latent space, constructing a mapping that relates geometric shape to the corresponding flow fields under given initial conditions. We use the public dataset AirfRANS to evaluate our approach, GeoANF significantly surpasses the baseline models on four key performance metrics, particularly in volume flow field and surface pressure measurements, achieving mean squared errors of 0.0038 and 0.0089, respectively.