This study introduces a computational approach leveraging Physics-Informed Neural Networks (PINNs) for the efficient computation of arterial blood flows, particularly focusing on solving the incompressible Navier-Stokes equations by using the domain decomposition technique. Unlike conventional computational fluid dynamics methods, PINNs offer advantages by eliminating the need for discretized meshes and enabling the direct solution of partial differential equations (PDEs). In this paper, we propose the weighted Extended Physics-Informed Neural Networks (WXPINNs) and weighted Conservative Physics-Informed Neural Networks (WCPINNs), tailored for detailed hemodynamic simulations based on generalized space-time domain decomposition techniques. The inclusion of multiple neural networks enhances the representation capacity of the weighted PINN methods. Furthermore, the weighted PINNs can be efficiently trained in parallel computing frameworks by employing separate neural networks for each sub-domain. We show that PINNs simulation results circumvent backflow instabilities, underscoring a notable advantage of employing PINNs over traditional numerical methods to solve such complex blood flow models. They naturally address such challenges within their formulations. The presented numerical results demonstrate that the proposed weighted PINNs outperform traditional PINNs settings, where sub-PINNs are applied to each subdomain separately. This study contributes to the integration of deep learning methodologies with fluid mechanics, paving the way for accurate and efficient high-fidelity simulations in biomedical applications, particularly in modeling arterial blood flow.

翻译：本研究提出了一种利用物理信息神经网络（PINNs）的计算方法，用于高效计算动脉血流，特别是通过区域分解技术求解不可压缩纳维-斯托克斯方程。与传统计算流体动力学方法不同，PINNs的优势在于无需离散化网格，可直接求解偏微分方程。本文提出了加权扩展物理信息神经网络（WXPINNs）和加权守恒物理信息神经网络（WCPINNs），它们基于广义时空区域分解技术，专为详细的血流动力学模拟而设计。多个神经网络的引入增强了加权PINNs方法的表示能力。此外，通过为每个子域使用独立的神经网络，加权PINNs可以在并行计算框架中高效训练。我们表明，PINNs模拟结果避免了回流不稳定性，这突显了使用PINNs而非传统数值方法求解此类复杂血流模型的一个显著优势——它们能自然地在其公式中应对这些挑战。给出的数值结果表明，所提出的加权PINNs优于传统的PINNs设置（即对每个子域分别应用子PINNs）。本研究推动了深度学习方法与流体力学的融合，为生物医学应用中（尤其是动脉血流建模）实现准确高效的高保真模拟铺平了道路。