A Flow-rate-conserving CNN-based Domain Decomposition Method for Blood Flow Simulations
Abstract
This work aims to predict blood flow with non-Newtonian viscosity in stenosed arteries using convolutional neural network (CNN) surrogate models. An alternating Schwarz domain decomposition method is proposed which uses CNN-based subdomain solvers. A universal subdomain solver (USDS) is trained on a single, fixed geometry and then applied for each subdomain solve in the Schwarz method. Results for two-dimensional stenotic arteries of varying shape and length for different inflow conditions are presented and statistically evaluated. One key finding, when using a limited amount of training data, is the need to implement a USDS which preserves some of the physics, as, in our case, flow rate conservation. A physics-aware approach outperforms purely data-driven USDS, delivering improved subdomain solutions and preventing overshooting or undershooting of the global solution during the Schwarz iterations, thereby leading to more reliable convergence.
Keywords
Cite
@article{arxiv.2509.15900,
title = {A Flow-rate-conserving CNN-based Domain Decomposition Method for Blood Flow Simulations},
author = {Simon Klaes and Axel Klawonn and Natalie Kubicki and Martin Lanser and Kengo Nakajima and Takashi Shimokawabe and Janine Weber},
journal= {arXiv preprint arXiv:2509.15900},
year = {2025}
}