  Computational fluid dynamics (CFD) is a valuable asset for patient-specific
cardiovascular-disease diagnosis and prognosis, but its high computational
demands hamper its adoption in practice. Machine-learning methods that estimate
blood flow in individual patients could accelerate or replace CFD simulation to
overcome these limitations. In this work, we consider the estimation of
vector-valued quantities on the wall of three-dimensional geometric artery
models. We employ group equivariant graph convolution in an end-to-end
SE(3)-equivariant neural network that operates directly on triangular surface
meshes and makes efficient use of training data. We run experiments on a large
dataset of synthetic coronary arteries and find that our method estimates
directional wall shear stress (WSS) with an approximation error of 7.6% and
normalised mean absolute error (NMAE) of 0.4% while up to two orders of
magnitude faster than CFD. Furthermore, we show that our method is powerful
enough to accurately predict transient, vector-valued WSS over the cardiac
cycle while conditioned on a range of different inflow boundary conditions.
These results demonstrate the potential of our proposed method as a plugin
replacement for CFD in the personalised prediction of hemodynamic vector and
scalar fields.
