A Review of Equation-Based and Data-Driven Reduced Order Models featuring a Hybrid cardiovascular application

TL;DR

This paper reviews equation-based and data-driven reduced order models for cardiovascular blood flow simulation, introducing a hybrid approach that combines projection techniques with neural networks to improve efficiency and accuracy.

Contribution

It presents a novel hybrid ROM integrating projection methods with neural networks and a lifting function for physiologically realistic blood flow modeling.

Findings

Significant reduction in computational cost.

High fidelity in velocity and pressure field reconstruction.

Effective integration of data-driven and projection-based techniques.

Abstract

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.