Graph-Based Domain Decomposition for Scalable Cardiovascular Flow Super-Resolution

Cardiovascular flow simulations require high-fidelity computational fluid dynamics modeling to accurately capture complex hemodynamic phenomena. However, this can impose an enormous computational burden, hindering computational translations of computational tools. Data-driven up-sampling methods like physics-informed neural networks (PINNs) help reduce the computational resources required. However, the capacity of machine learning models and hardware limitations still pose challenges when evaluating large-scale cardiovascular simulations with complex blood flow dynamics. Recently, we proposed a method that applies the principle of locality in physical systems to neural network layers, allowing for concurrent inference on smaller subdomains with improved efficiency and accuracy. Based on such an idea, we extend the theory of domain decomposition to complex three-dimensional vascular geometries using graph neural networks (GNNs). We developed a graph decomposition method to improve the training and inference efficiency of machine learning models for cardiovascular applications. Super-resolution GNNs are then trained on individual subdomains distributed across GPU nodes, and during the inference phase, their predictions are combined to achieve a near-linear time reduction as the number of parallel GPUs increases. This approach significantly reduces computational overhead while maintaining the accuracy of hemodynamic metrics. We demonstrate the method's capability in super-resolving the flow field at a coronary artery bifurcation and recovering detailed wall shear stress distributions from low-resolution simulations. The approach shows broad generalizability across varying bifurcation angles. These results suggest that our approach can effectively bridge the gap between computational efficiency and simulation fidelity in cardiovascular modeling, enabling more accessible, high-quality hemodynamic analysis for research and clinical applications.