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

2025-09-19

AI Summary

This work addresses the challenge of high-fidelity, computationally efficient prediction of non-Newtonian blood flow in stenosed arteries. Methodologically, we propose a physics-informed CNN surrogate model built upon an alternating Schwarz domain decomposition framework. We introduce a novel universal subdomain solver enforcing mass conservation, seamlessly integrating physical constraints with data-driven learning to achieve rapid convergence and global stability—even under limited training data. Crucially, the CNN surrogate requires training on only a single arterial geometry yet generalizes robustly to diverse two-dimensional stenosed configurations (varying shapes and lengths). Experimental results demonstrate high predictive accuracy and strong robustness; notably, the approach effectively suppresses numerical oscillations commonly observed in conventional iterative solvers. By enabling personalized hemodynamic simulation at significantly reduced computational cost, our method establishes a scalable, physics-aware paradigm for clinical and biomedical applications.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Hardware-aware ML
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

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.

Problem

• Predicting non-Newtonian blood flow in stenosed arteries
• Developing CNN-based domain decomposition method
• Ensuring flow rate conservation in simulations

Innovation

• CNN-based domain decomposition method
• Physics-aware universal subdomain solver
• Flow-rate conserving Schwarz iterations