Physics-Informed Learning of Microvascular Flow Models using Graph Neural Networks

Abstract: The simulation of microcirculatory blood flow in realistic vascular architectures poses significant challenges due to the multiscale nature of the problem and the topological complexity of capillary networks. In this work, we propose a novel deep learning-based reduced-order modeling strategy, leveraging Graph Neural Networks (GNNs) trained on synthetic microvascular graphs to approximate hemodynamic quantities on anatomically realistic domains. Our method combines algorithms for synthetic vascular generation with a physics-informed training procedure that integrates graph topological information and local flow dynamics. To ensure the physical reliability of the learned surrogates, we incorporate a physics-informed loss functional derived from the governing equations, allowing enforcement of mass conservation and rheological constraints. The resulting GNN architecture demonstrates robust generalization capabilities across diverse network configurations. The GNN formulation is validated on benchmark problems with linear and nonlinear rheology, showing accurate pressure and velocity field reconstruction with substantial computational gains over full-order solvers. The methodology showcases significant generalization capabilities with respect to vascular complexity, as highlighted by tests on data from the mouse cerebral cortex. This work establishes a new class of graph-based surrogate models for microvascular flow, grounded in physical laws and equipped with inductive biases that mirror mass conservation and rheological models, opening new directions for real-time inference in vascular modeling and biomedical applications.