# Learning Reduced-Order Models for Cardiovascular Simulations with Graph Neural Networks

arXiv: https://arxiv.org/abs/2303.07310 · HTML: https://mlsanity.com/paper/2303.07310/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 66 references that are in the map.
- First posted on arXiv 13 Mar 2023.

## Builds on (most cited first, 15 of 15)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks](https://mlsanity.com/paper/1905.04817/) (2019)
- [A Deep-Learning Approach For Direct Whole-Heart Mesh Reconstruction](https://mlsanity.com/paper/2102.07899/) (2021)
- [Automated generation of 0D and 1D reduced-order models of patient-specific blood flow](https://mlsanity.com/paper/2111.04878/) (2021)
- [Learning Large-scale Subsurface Simulations with a Hybrid Graph Network Simulator](https://mlsanity.com/paper/2206.07680/) (2022)
- [Whole Heart Mesh Generation For Image-Based Computational Simulations By Learning Free-From Deformations](https://mlsanity.com/paper/2107.10839/) (2021)
- [SE(3) symmetry lets graph neural networks learn arterial velocity estimation from small datasets](https://mlsanity.com/paper/2302.08780/) (2023)
- [PCE-PINNs: Physics-Informed Neural Networks for Uncertainty Propagation in Ocean Modeling](https://mlsanity.com/paper/2105.02939/) (2021)
- [On the periodicity of cardiovascular fluid dynamics simulations](https://mlsanity.com/paper/2102.00107/) (2021)
- [Comparison of 1D and 3D Models for the Estimation of Fractional Flow Reserve](https://mlsanity.com/paper/1805.11472/) (2018)

## Built on by (most cited first, 20 of 20)

- [A graph convolutional autoencoder approach to model order reduction for parametrized PDEs](https://mlsanity.com/paper/2305.08573/) (2023)
- [Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networks](https://mlsanity.com/paper/2308.01602/) (2023)
- [Simulation-based Inference for Cardiovascular Models](https://mlsanity.com/paper/2307.13918/) (2023)
- [Shape-informed surrogate models based on signed distance function domain encoding](https://mlsanity.com/paper/2409.12400/) (2024)
- [Deep vectorised operators for pulsatile hemodynamics estimation in coronary arteries from a steady-state prior](https://mlsanity.com/paper/2410.11920/) (2024)
- [Branched Latent Neural Maps](https://mlsanity.com/paper/2308.02599/) (2023)
- [Liquid Fourier Latent Dynamics Networks for fast GPU-based numerical simulations in computational cardiology](https://mlsanity.com/paper/2408.09818/) (2024)
- [Full-field surrogate modeling of cardiac function encoding geometric variability](https://mlsanity.com/paper/2504.20479/) (2025)
- [Learning Hemodynamic Scalar Fields on Coronary Artery Meshes: A Benchmark of Geometric Deep Learning Models](https://mlsanity.com/paper/2501.09046/) (2025)
- [Time Extrapolation with Graph Convolutional Autoencoder and Tensor Train Decomposition](https://mlsanity.com/paper/2511.23037/) (2025)
- [Image2Flow: A hybrid image and graph convolutional neural network for rapid patient-specific pulmonary artery segmentation and CFD flow field calculation from 3D cardiac MRI data](https://mlsanity.com/paper/2402.18236/) (2024)
- [Thermodynamics-informed graph neural networks for real-time simulation of digital human twins](https://mlsanity.com/paper/2412.12034/) (2024)
- [Discovery of Probabilistic Dirichlet-to-Neumann Maps on Graphs](https://mlsanity.com/paper/2506.02337/) (2025)
- [GReAT: leveraging geometric artery data to improve wall shear stress assessment](https://mlsanity.com/paper/2508.19030/) (2025)
- [Data-Driven Bifurcation Handling in Physics-Based Reduced-Order Vascular Hemodynamic Models](https://mlsanity.com/paper/2508.21165/) (2025)
- [Mesh-Informed Reduced Order Models for Aneurysm Rupture Risk Prediction](https://mlsanity.com/paper/2410.03802/) (2024)
- [Graph Neural Network for Cerebral Blood Flow Prediction With Clinical Datasets](https://mlsanity.com/paper/2411.17971/) (2024)
- [Physics-informed self-supervised learning for predictive modeling of coronary artery digital twins](https://mlsanity.com/paper/2512.03055/) (2025)
- [Multi-fidelity graph-based neural networks architectures to learn Navier-Stokes solutions on non-parametrized 2D domains](https://mlsanity.com/paper/2601.02157/) (2026)
- [Real-Time Surrogate Modeling for Personalized Blood Flow Prediction and Hemodynamic Analysis](https://mlsanity.com/paper/2604.03197/) (2026)

## Abstract (arXiv)

Reduced-order models based on physics are a popular choice in cardiovascular modeling due to their efficiency, but they may experience reduced accuracy when working with anatomies that contain numerous junctions or pathological conditions. We develop one-dimensional reduced-order models that simulate blood flow dynamics using a graph neural network trained on three-dimensional hemodynamic simulation data. Given the initial condition of the system, the network iteratively predicts the pressure and flow rate at the vessel centerline nodes. Our numerical results demonstrate the accuracy and generalizability of our method in physiological geometries comprising a variety of anatomies and boundary conditions. Our findings demonstrate that our approach can achieve errors below 2% and 3% for pressure and flow rate, respectively, provided there is adequate training data. As a result, our method exhibits superior performance compared to physics-based one-dimensional models, while maintaining high efficiency at inference time.