A Bifurcation-Based Domain Decomposition Method with Neural Operators for Blood Flow Simulation
Abstract
Fast and accurate simulation of hemodynamic behavior within vascular networks is essential for numerous clinical applications. However, obtaining high-quality and computationally efficient flow measurements across complex vascular networks remains challenging. To address this, we first decompose the vascular network into a set of bifurcation units and then develop an operator network capable of mapping unit-specific parameters to the local solution fields of each bifurcation unit. By lumping the Windkessel-model outlet parameters and incorporating inlet boundary conditions from the solution of parent units, the flow and pressure fields can be rapidly approximated. Subsequently, operator-network-driven Schwarz waveform relaxation is applied across bifurcation units to correct discontinuities and improve numerical accuracy. On 7-segment and 55-segment arterial tree models, the proposed method achieves 13× to 17× wall-clock speedups over conventional 1D numerical simulation, with relative L2 errors of 1% in both pressure and velocity. The resulting pulse wave velocity biomarkers agree with the conventional reference to within 1--2%, and the same trained operator generalizes to different tree-like 1D vascular network topologies.
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BibTeX
@misc{zhao2026bifurcationbased,
title = {{A Bifurcation-Based Domain Decomposition Method with Neural Operators for Blood Flow Simulation}},
author = {Yuzhou Zhao and Han Zhang and J. Matias Di Martino and Jean-Michel Morel and Guillermo Sapiro},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02238},
eprint = {2610.02238},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02238},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Bifurcation-Based Domain Decomposition Method with Neural Operators for Blood Flow Simulation
AU - Yuzhou Zhao
AU - Han Zhang
AU - J. Matias Di Martino
AU - Jean-Michel Morel
AU - Guillermo Sapiro
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.02238
UR - https://arxiv.org/abs/2610.02238
AB - Fast and accurate simulation of hemodynamic behavior within vascular networks is essential for numerous clinical applications. However, obtaining high-quality and computationally efficient flow measurements across complex vascular networks remains challenging. To address this, we first decompose the vascular network into a set of bifurcation units and then develop an operator network capable of mapping unit-specific parameters to the local solution fields of each bifurcation unit. By lumping the Windkessel-model outlet parameters and incorporating inlet boundary conditions from the solution of parent units, the flow and pressure fields can be rapidly approximated. Subsequently, operator-network-driven Schwarz waveform relaxation is applied across bifurcation units to correct discontinuities and improve numerical accuracy. On 7-segment and 55-segment arterial tree models, the proposed method achieves 13× to 17× wall-clock speedups over conventional 1D numerical simulation, with relative L^2 errors of 1% in both pressure and velocity. The resulting pulse wave velocity biomarkers agree with the conventional reference to within 1--2%, and the same trained operator generalizes to different tree-like 1D vascular network topologies.
ER -