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

Researchers have proposed a convolutional neural network method to simulate non-Newtonian blood flow in narrowed arteries, using a domain decomposition approach with a universal subdomain solver trained on a single fixed geometry [1]. The work, posted on the arXiv preprint server, targets blood flow prediction in stenosed arteries through CNN surrogate models [1]. An alternating Schwarz domain decomposition method applies the CNN-based subdomain solvers. A universal subdomain solver, or USDS, is trained on one fixed geometry and then reused for each subdomain solve within the Schwarz method [1]. The study tests the approach on two-dimensional stenotic arteries with varying shape and length under different inflow conditions [1]. A central finding is that incorporating a physics-aware constraint — specifically flow rate conservation — into the USDS improves prediction accuracy and convergence behavior compared to a purely data-driven USDS, particularly when training data is limited [1]. The authors note that because the USDS is a data-driven, inexact subdomain solver, admissible parameter ranges for geometry and inflow configurations must be defined and tested [1]. The paper was submitted by Axel Klawonn and first appeared on arXiv on 19 September 2025, with a revised version posted on 24 June 2026 [1]. The initial submission file was 6,301 KB; the revision was 2,861 KB [1]. arXiv, which began on 14 August 1991, hosts e-prints in fields including mathematics and computer science and passed two million articles by the end of 2021 [7]. The repository now receives roughly 24,000 articles per month as of November 2024 [7]. The article’s abstract page on arXiv also links to community-developed tools through the arXivLabs framework, which allows third-party collaborators to build features such as citation explorers and code finders [5][6]. arXivLabs projects operate under guidelines that require partners to share arXiv’s values of openness, community, excellence, and user data privacy [5].