基于方程与数据驱动的降阶模型综述：以一个混合心血管应用为特色
A Review of Equation-Based and Data-Driven Reduced Order Models featuring a Hybrid cardiovascular application
AI总结：
该研究综述基于投影和数据驱动的ROM，并提出融合神经网络与提升函数的混合ROM，用于患者特异性主动脉血流仿真，实现计算成本显著降低且保持速度与压力场高保真。
摘要：
心血管疾病是世界范围内导致死亡的主要原因之一，这推动了用于血流分析的患者特异性模型和基准模型的发展。本章对降阶模型（Reduced Order Models，ROMs）的主要类别进行了理论概述，重点介绍经典框架下基于投影的方法和数据驱动方法。随后，我们提出了一种混合ROM，专为模拟患者特异性主动脉几何结构中的血流而设计。所提出的方法将基于投影的技术与神经网络增强的数据驱动组件相结合，并引入提升函数策略，以施加上符合生理现实的出口压力条件。这种混合方法能够显著降低计算成本，同时在重建速度场和压力场时保持高保真度。我们详细比较了全阶解与降阶解，并批判性地评估了ROMs在患者特异性心血管建模中的优势与局限。
英文摘要：
Cardiovascular diseases are a leading cause of death in the world, driving the development of patient-specific and benchmark models for blood flow analysis. This chapter provides a theoretical overview of the main categories of Reduced Order Models (ROMs), focusing on both projection-based and data-driven approaches within a classical setup. We then present a hybrid ROM tailored for simulating blood flow in a patient-specific aortic geometry. The proposed methodology integrates projection-based techniques with neural network-enhanced data-driven components, incorporating a lifting function strategy to enforce physiologically realistic outflow pressure conditions. This hybrid methodology enables a substantial reduction in computational cost while mantaining high fidelity in reconstructing both velocity and pressure fields. We compare the full- and reduced-order solutions in details and critically assess the advantages and limitations of ROMs in patient-specific cardiovascular modeling.
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