ICPINN: Integral conservation physics-informed neural networks based on adaptive activation functions for 3D blood flow simulations

Blood flow modeling can improve our understanding of vascular pathologies, assist in designing more effective drug delivery systems, and aid in developing safe and effective medical devices. Physics-informed neural networks (PINN) have been used to simulate blood flow by encoding the nonlinear Navier–Stokes equations and training data into the neural network. However, noninvasive, real-time and accurate acquisition of hemodynamics data remains a challenge for current invasive detection and simulation algorithms. In this paper, we propose an integral conservation physics-informed neural networks (ICPINN) with adaptive activation functions to accurately predict the velocity, pressure, and wall shear stress (WSS) based on patient-specific vessel geometries without relying on any simulation data. To achieve unsupervised learning, loss function incorporates mass flow rate residuals derived from the mass conservation law, significantly enhancing the precision and effectiveness of the predictions. Moreover, a detailed comparative analysis of various weighting coefficient selection strategies and activation functions is performed, which ultimately identifies the optimal configuration for 3D blood flow simulations that achieves the lowest relative error. Numerical results demonstrate that the proposed ICPINN framework enables accurate prediction of blood flow in realistic cardiovascular geometry, and that mass flow rate is essential for complex structures, such as bifurcations, U-bend, stenosis, and aneurysms, offering potential applications in medical diagnostics and treatment planning.