Adaptive Physics-Informed Neural Networks with Overlapping Domain Decomposition for Vascular Flow Velocity Modeling

Abstract

: Hemodynamic information is crucial for studying cardiovascular pathogenesis and risk assessment. When measurement data are sparse, boundary data are incomplete, and branching geometries are involved, classical computational fluid dynamics (CFD) remains computationally intensive, while standard physics-informed neural networks (PINNs) often suffer from training instability due to poor gradient balance among competing loss terms and inadequate resolution of high-frequency flow features near bifurcations. This paper proposes three innovations to address these challenges. First, a residual-gradient-based adaptive weighting scheme is developed to mitigate gradient competition between boundary terms and data-driven terms, embedded into a meshless PINN for three-dimensional incompressible Navier-Stokes flow. Second, an overlapping subdomain decomposition with zero-to second-order interface conditions is constructed to enhance physical consistency between subdomains and suppress non-physical oscillations near bifurcations. Third, the same strategy is extended to one-dimensional pulse wave propagation, bridging local three-dimensional reconstruction and network-scale analysis. Numerical experiments on porcine abdominal aorta geometries demonstrate that the adaptive weighting yields more uniform gradient contributions and stable optimization paths; the overlapping decomposition improves reconstructed flow and accelerates convergence; and the one-dimensional formulation confirms that partial differential equation (PDE), boundary, and interface terms can be jointly minimized, providing empirical support for multiscale hemodynamic modeling.