Computer simulations are increasingly used to complement clinical decision making in the diagnosis and treatment of cardiovascular disease. High-fidelity cardiovascular models are traditionally deterministic and solved using implicit time integration, without directly accounting for uncertainty and variability in the underlying input processes, for example boundary conditions, material properties or segmented model anatomy. I will discuss an alternative simulation paradigm based on the explicit integration in time of an ensemble of model realizations, running on multiple GPUs. Additionally, I will present some results on the acceleration of traditional numerical solvers through data-driven methods based on deep neural networks, focusing on synchronization-avoiding algorithms for distributed finite element solvers.