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.

翻译：心血管疾病是全球主要致死原因之一，这推动了面向患者特异性与基准血流分析模型的发展。本章从理论层面综述了降阶模型（ROMs）的主要类别，重点探讨了经典框架下的基于投影的方法与数据驱动方法。随后，我们提出了一种专为患者特异性主动脉几何中血流模拟设计的混合ROM。该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，并采用提升函数策略以强制符合生理现实的外流压力条件。这种混合方法在显著降低计算成本的同时，保持了重建速度场与压力场的高保真度。我们详细比较了全阶与降阶解，并对ROMs在患者特异性心血管建模中的优势与局限进行了批判性评估。