# A Flow-rate-conserving CNN-based Domain Decomposition Method for Blood Flow Simulations

arXiv: https://arxiv.org/abs/2509.15900 · HTML: https://mlsanity.com/paper/2509.15900/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 45 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Horovod: fast and easy distributed deep learning in TensorFlow](https://mlsanity.com/paper/1802.05799/) (2018)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations](https://mlsanity.com/paper/2407.07218/) (2024)
- [Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains](https://mlsanity.com/paper/2104.10873/) (2021)
- [Hard-Constrained Deep Learning for Climate Downscaling](https://mlsanity.com/paper/2208.05424/) (2022)
- [Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey](https://mlsanity.com/paper/2408.12171/) (2024)
- [Machine learning and domain decomposition methods -- a survey](https://mlsanity.com/paper/2312.14050/) (2023)
- [Breaking Boundaries: Distributed Domain Decomposition with Scalable Physics-Informed Neural PDE Solvers](https://mlsanity.com/paper/2308.14258/) (2023)
- [A Learning-based Domain Decomposition Method](https://mlsanity.com/paper/2507.17328/) (2025)

## Built on by (most cited first, 1 of 1)

- [An overview of machine learning-enhanced iterative methods for systems of linear and nonlinear equations](https://mlsanity.com/paper/2610.07211/) (2026)

## Abstract (arXiv)

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 that incorporating a physics-aware constraint, as, in our case, flow rate conservation, into the USDS improves the prediction accuracy and convergence behavior of the Schwarz method compared to a purely data-driven USDS. As the USDS is a data-driven, inexact subdomain solver, admissible parameter ranges for the geometry and inflow configurations must be defined and tested.