#4th place - (Best student solution) :A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils

Computational modeling of aerodynamics is a key problem in aerospace engineering, often involving fluids interacting with solid objects such as airfoils. Deep surrogate models have emerged as purely data-driven approaches that learn direct mappings from simulation conditions to solutions based on either simulation or experimental data. Here, we consider modeling of incompressible flows over solid objects, wherein geometric structures are a key factor in determining aerodynamics. To effectively incorporate geometries, we propose a message passing scheme that efficiently and expressively integrates the airfoil shape with the mesh representation. Under this framework, we first obtain a representation of the geometry in the form of a latent graph on the airfoil surface. We subsequently propagate this representation to all collocation points through message passing on a directed, bipartite graph. Additionally, we augment the base coordinate system of the mesh such that our model can distinguish between distinct spatial regimes of dynamics relative to the airfoil. To further enhance the expressiveness of our coordinate system representations, we embed our hybrid Polar-Cartesian coordinates using sinusoidal and spherical harmonics bases. We additionally find that a change of basis to canonicalize input representations with respect to inlet velocity substantially improves generalization. Altogether, these design choices lead to a purely data-driven machine learning framework known as GeoMPNN, which won the Best Student Submission award at the NeurIPS 2024 ML4CFD Competition, placing fourth overall. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).