# Physics-informed graph neural networks for flow field estimation in carotid arteries

arXiv: https://arxiv.org/abs/2408.07110 · HTML: https://mlsanity.com/paper/2408.07110/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 38 references that are in the map.
- First posted on arXiv 13 Aug 2024.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems](https://mlsanity.com/paper/2107.12146/) (2021)
- [Mesh Neural Networks for SE(3)-Equivariant Hemodynamics Estimation on the Artery Wall](https://mlsanity.com/paper/2212.05023/) (2022)
- [Scalable algorithms for physics-informed neural and graph networks](https://mlsanity.com/paper/2205.08332/) (2022)
- [Deep Learning-Based Carotid Artery Vessel Wall Segmentation in Black-Blood MRI Using Anatomical Priors](https://mlsanity.com/paper/2112.01137/) (2021)
- [SE(3) symmetry lets graph neural networks learn arterial velocity estimation from small datasets](https://mlsanity.com/paper/2302.08780/) (2023)
- [Physics-informed compressed sensing for PC-MRI: an inverse Navier-Stokes problem](https://mlsanity.com/paper/2207.01466/) (2022)
- [Transient Hemodynamics Prediction Using an Efficient Octree-Based Deep Learning Model](https://mlsanity.com/paper/2302.06557/) (2023)

## Built on by (most cited first, 6 of 6)

- [Deep vectorised operators for pulsatile hemodynamics estimation in coronary arteries from a steady-state prior](https://mlsanity.com/paper/2410.11920/) (2024)
- [Active Learning for Deep Learning-Based Hemodynamic Parameter Estimation](https://mlsanity.com/paper/2503.03453/) (2025)
- [Wall Shear Stress Estimation in Abdominal Aortic Aneurysms: Towards Generalisable Neural Surrogate Models](https://mlsanity.com/paper/2507.22817/) (2025)
- [When Does Equivariance Help? Canonical Alignment in Neural Fluid Surrogates](https://mlsanity.com/paper/2605.18816/) (2026)
- [ONE CYLinder: A Benchmark for Graph-Based Surrogate Modeling of Unsteady Bluff-Body Flows](https://mlsanity.com/paper/2609.08947/) (2026)
- [Interactive 4D Volumetric Liquid Forecasting under Moving-Solid Interaction](https://mlsanity.com/paper/2610.16167/) (2026)

## Abstract (arXiv)

Hemodynamic quantities are valuable biomedical risk factors for cardiovascular pathology such as atherosclerosis. Non-invasive, in-vivo measurement of these quantities can only be performed using a select number of modalities that are not widely available, such as 4D flow magnetic resonance imaging (MRI). In this work, we create a surrogate model for hemodynamic flow field estimation, powered by machine learning. We train graph neural networks that include priors about the underlying symmetries and physics, limiting the amount of data required for training. This allows us to train the model using moderately-sized, in-vivo 4D flow MRI datasets, instead of large in-silico datasets obtained by computational fluid dynamics (CFD), as is the current standard. We create an efficient, equivariant neural network by combining the popular PointNet++ architecture with group-steerable layers. To incorporate the physics-informed priors, we derive an efficient discretisation scheme for the involved differential operators. We perform extensive experiments in carotid arteries and show that our model can accurately estimate low-noise hemodynamic flow fields in the carotid artery. Moreover, we show how the learned relation between geometry and hemodynamic quantities transfers to 3D vascular models obtained using a different imaging modality than the training data. This shows that physics-informed graph neural networks can be trained using 4D flow MRI data to estimate blood flow in unseen carotid artery geometries.