mlsanityData to 14 Oct 2026

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

arXiv 2303.07310 ↗First posted 13 Mar 2023cs.LG cs.CEcited by 20

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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.

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.

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15 of 66 references.

References · 15

  1. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 7,005
  2. 2020Learning to Simulate Complex Physics with Graph Networkscited by 880
  3. 2020Learning Mesh-Based Simulation with Graph Networkscited by 868
  4. 2019Machine Learning for Fluid Mechanicscited by 385
  5. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 373
  6. 2017Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equationscited by 161
  7. 2019Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networkscited by 76
  8. 2021A Deep-Learning Approach For Direct Whole-Heart Mesh Reconstructioncited by 47
  9. 2021Automated generation of 0D and 1D reduced-order models of patient-specific blood flowcited by 15
  10. 2022Learning Large-scale Subsurface Simulations with a Hybrid Graph Network Simulatorcited by 15
  11. 2021Whole Heart Mesh Generation For Image-Based Computational Simulations By Learning Free-From Deformationscited by 12
  12. 2023SE(3) symmetry lets graph neural networks learn arterial velocity estimation from small datasetscited by 11
3 more
  1. 2021PCE-PINNs: Physics-Informed Neural Networks for Uncertainty Propagation in Ocean Modelingcited by 9
  2. 2021On the periodicity of cardiovascular fluid dynamics simulationscited by 5
  3. 2018Comparison of 1D and 3D Models for the Estimation of Fractional Flow Reservecited by 2

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Citing papers per year: 2023: 4; 2024: 7; 2025: 7; 2026: 2.

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  1. 2023A graph convolutional autoencoder approach to model order reduction for parametrized PDEscited by 44
  2. 2023Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networkscited by 17
  3. 2023Simulation-based Inference for Cardiovascular Modelscited by 11
  4. 2024Shape-informed surrogate models based on signed distance function domain encodingcited by 6
  5. 2024Deep vectorised operators for pulsatile hemodynamics estimation in coronary arteries from a steady-state priorcited by 6
  6. 2023Branched Latent Neural Mapscited by 3
  7. 2024Liquid Fourier Latent Dynamics Networks for fast GPU-based numerical simulations in computational cardiologycited by 3
  8. 2025Full-field surrogate modeling of cardiac function encoding geometric variabilitycited by 3
  9. 2025Learning Hemodynamic Scalar Fields on Coronary Artery Meshes: A Benchmark of Geometric Deep Learning Modelscited by 2
  10. 2025Time Extrapolation with Graph Convolutional Autoencoder and Tensor Train Decompositioncited by 2
  11. 2024Image2Flow: A hybrid image and graph convolutional neural network for rapid patient-specific pulmonary artery segmentation and CFD flow field calculation from 3D cardiac MRI datacited by 1
  12. 2024Thermodynamics-informed graph neural networks for real-time simulation of digital human twinscited by 1
8 more
  1. 2025Discovery of Probabilistic Dirichlet-to-Neumann Maps on Graphscited by 1
  2. 2025GReAT: leveraging geometric artery data to improve wall shear stress assessmentcited by 1
  3. 2025Data-Driven Bifurcation Handling in Physics-Based Reduced-Order Vascular Hemodynamic Modelscited by 1
  4. 2024Mesh-Informed Reduced Order Models for Aneurysm Rupture Risk Predictioncited by 0
  5. 2024Graph Neural Network for Cerebral Blood Flow Prediction With Clinical Datasetscited by 0
  6. 2025Physics-informed self-supervised learning for predictive modeling of coronary artery digital twinscited by 0
  7. 2026Multi-fidelity graph-based neural networks architectures to learn Navier-Stokes solutions on non-parametrized 2D domainscited by 0
  8. 2026Real-Time Surrogate Modeling for Personalized Blood Flow Prediction and Hemodynamic Analysiscited by 0