用物理约束的CNN模型加速狭窄血管血流模拟，提升精度与收敛性。
A Flow-rate-conserving CNN-based Domain Decomposition Method for Blood Flow Simulations
- 基于物理守恒的CNN子域求解器，结合交替施瓦茨分解法
- 有限训练数据下，流量守恒约束使误差降低、收敛更快
- 适合需要快速高精度血流仿真的医学计算场景
本文利用卷积神经网络（CNN）代理模型预测狭窄动脉中非牛顿粘度下的血流。提出一种交替施瓦茨域分解方法，使用基于CNN的子域求解器。通用子域求解器（USDS）在单一固定几何上训练后，应用于每次施瓦茨方法中的子域求解。针对不同形状和长度的二维狭窄动脉，在多种流入条件下进行结果展示并统计评估。关键发现：在训练数据有限的情况下，将流量守恒等物理感知约束融入USDS，相比纯数据驱动的USDS，显著提升了施瓦茨方法的预测精度和收敛性能。由于USDS为数据驱动的近似子域求解器，需定义并验证几何与流入配置的可接受参数范围。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。