Computational hemodynamics play an increasingly important role in medicine. Based on clinical data, such methods provide complementary insights non-invasively, immensely useful for in-depth analysis, medical device design, and more. Major obstacles are i) large inter-patient variability and uncertainties, and ii) long processing times adopting standard techniques. This work addresses the efficient handling of global variability in aortic geometries, where we distinguish between local and global shape variations. Local shape variations can be used to describe uncertainty from medical imaging and the algorithm chain that leads to a simulation-ready discrete representation. Global shape variations capture the inter-patient variability (see, e.g., the SynthAorta dataset [1]). Our investigations are based on a parametrization of healthy aortas capturing the geometrical variation and subsequent mesh generation, followed by computational fluid dynamics simulation. Variability across shapes is handled using an automated registration based on ResNet-LDDMM. This approach allows to use the simulation data to train shape-informed graph neural network models [2] to create efficient surrogates. The approach can be further extended towards quantifying the effect of shape variability on relevant biomarkers associated with clinical outcomes in numerous vascular pathologies, reducing the computational costs associated with numerical simulations. [1] D. Bosnjak, G.M. Melito, R. Schussnig, K. Ellermann and T.-P. Fries, SynthAorta: A 3D Mesh Dataset of Parametrized Physiological Healthy Aortas, IEEE Trans. Med. Imag., 45(1):421-430, 2025. doi: 10.1109/tmi.2025.3599937. [2] F. Romor, F. Galarce, J. Br¨uning, L. Goubergrits and Alfonso Caiazzo, Data assimilation performed with robust shape registration and graph neural networks: application to aortic coarctation, arXiv preprint, 2025. doi: 10.48550/arXiv.2502.12097