  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.
