A Bifurcation-Based Domain Decomposition Method with Neural Operators for Blood Flow Simulation

2026-09-28

AI Summary

This study addresses the challenge of balancing computational efficiency and accuracy in blood flow simulations within complex vascular networks by proposing a novel framework that integrates bifurcation-based domain decomposition with neural operators. The method decomposes vascular networks into individual bifurcation units, employing neural operators to rapidly approximate local solutions. Boundary discontinuities are corrected via the Schwarz waveform relaxation algorithm, while distal impedance is handled through an integrated Windkessel model. This framework exhibits strong topological generalization, effectively overcoming the speed limitations of conventional one-dimensional simulations. Experimental results demonstrate a 13- to 17-fold acceleration over traditional methods, with relative L2 errors for pressure and velocity at approximately 1%. Furthermore, errors in key biomarkers such as pulse wave velocity remain within 1–2%, achieving highly efficient and accurate hemodynamic simulations.

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 $13\times$ to $17\times$ 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.

Problem

• hemodynamic simulation
• vascular networks
• blood flow
• computational efficiency
• domain decomposition

Innovation

• Neural Operators
• Domain Decomposition
• Schwarz Waveform Relaxation
• Hemodynamics Simulation
• Vascular Networks