{"ID":2868796,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.15900","arxiv_id":"2509.15900","title":"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.","short_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 geome...","url_abs":"https://arxiv.org/abs/2509.15900","url_pdf":"https://arxiv.org/pdf/2509.15900v1","authors":"[\"Simon Klaes\",\"Axel Klawonn\",\"Natalie Kubicki\",\"Martin Lanser\",\"Kengo Nakajima\",\"Takashi Shimokawabe\",\"Janine Weber\"]","published":"2025-09-19T11:56:54Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"cs.LG\"]","methods":"[\"Convolutional Neural Network\"]","has_code":false}