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）高效计算动脉血流的数值方法，重点采用区域分解技术求解不可压缩Navier-Stokes方程。与传统计算流体力学方法不同，PINNs无需离散化网格即可直接求解偏微分方程（PDEs），具有显著优势。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），该方法基于广义时空域分解技术，专为精细化血流动力学模拟而设计。多神经网络结构增强了加权PINN方法的表征能力。此外，通过为每个子域分配独立神经网络，加权PINN可在并行计算框架下高效训练。研究表明，PINNs模拟结果能避免回流不稳定性，这凸显了相较于传统数值方法在求解此类复杂血流模型时的显著优势，且这些问题可直接在其数学框架中得到解决。数值实验表明，本文提出的加权PINNs优于传统将子PINN分别应用于各子域的标准配置。本研究推动了深度学习与流体力学的融合，为生物医学应用尤其是动脉血流建模中实现精准高效的高保真模拟开辟了新途径。