Fluid–structure interaction training of integral conservation physics-informed neural networks for blood flow in elastic vessels

Physics-informed neural networks (PINNs) have recently emerged as a promising paradigm for simulating three-dimensional fluid-structure interaction (FSI) in cardiovascular systems. Building on our Integral Conservation Physics-Informed Neural Networks (ICPINNs) framework for patient-specific hemodynamics [Liu Y, et al., Comput. Phys. Commun., 2025, 109569], this study develops an extended framework for elastic vessels, termed E-ICPINNs. E-ICPINNs adopts a dual-subnetwork design, in which separate subnetworks learn the fluid variables and structural variables, respectively. The incompressible Navier-Stokes equations in an arbitrary Lagrangian-Eulerian formulation and vessel wall mechanics are embedded as meshless physics-informed constraints, thereby enforcing FSI coupling in deformable vascular domains. The coupled problem is further formulated as a multi-objective optimization task, and a sequential-alternative training algorithm is developed by combining regularization-based pretraining with alternating optimization over subsets of physics-informed loss terms, which improves training stability and convergence under strong coupling. In addition, an adaptive SiLU activation function is incorporated to preserve smooth differentiability across coupled fields and to mitigate vanishing-gradient effects in deep networks. Comprehensive numerical experiments, together with systematic comparisons of network depth/width, activation functions, and representative architectures, demonstrate that E-ICPINNs achieves accurate and robust predictions with favorable accuracy-efficiency trade-offs. The proposed framework provides an effective meshless computational approach for clinically relevant vascular FSI simulations.