Equivariant graph neural networks as surrogate for computational fluid dynamics in 3D artery models

Computational fluid dynamics (CFD) is an invaluable tool in modern physics but the time-intensity and computational complexity limit its applicability to practical problems, e.g. in medicine. Surrogate methods could speed up inference and allow use in such time-critical applications. We consider the problem of estimating hemodynamic quantities (i.e. related to blood flow) on the surface of 3D artery geometries and employ anisotropic graph convolution in an end-to-end SO(3)-equivariant neural network operating directly on the polygonal surface mesh. We show that our network can accurately predict hemodynamic vectors for each vertex on the surface mesh with normalised mean absolute error of 0.6 [%] and approximation accuracy of 90.5 [%], demonstrating its feasibility as surrogate method for CFD.