mlsanityData to 7 Oct 2026

Mesh Neural Networks for SE(3)-Equivariant Hemodynamics Estimation on the Artery Wall

arXiv 2212.05023 ↗First posted 9 Dec 2022cs.LG cs.CV math.GRcited by 29

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Abstract (arXiv)

Computational fluid dynamics (CFD) is a valuable asset for patient-specific cardiovascular-disease diagnosis and prognosis, but its high computational demands hamper its adoption in practice. Machine-learning methods that estimate blood flow in individual patients could accelerate or replace CFD simulation to overcome these limitations. In this work, we consider the estimation of vector-valued quantities on the wall of three-dimensional geometric artery models. We employ group equivariant graph convolution in an end-to-end SE(3)-equivariant neural network that operates directly on triangular surface meshes and makes efficient use of training data. We run experiments on a large dataset of synthetic coronary arteries and find that our method estimates directional wall shear stress (WSS) with an approximation error of 7.6% and normalised mean absolute error (NMAE) of 0.4% while up to two orders of magnitude faster than CFD. Furthermore, we show that our method is powerful enough to accurately predict transient, vector-valued WSS over the cardiac cycle while conditioned on a range of different inflow boundary conditions. These results demonstrate the potential of our proposed method as a plugin replacement for CFD in the personalised prediction of hemodynamic vector and scalar fields.

Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). Builds on 14 of its 59 references that are in the map. First posted on arXiv 9 Dec 2022.

Builds on

14 of 59 references.

References · 14

  1. 2017Graph Attention Networkscited by 8,854
  2. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,384
  3. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  4. 2019Deep Learning for 3D Point Clouds: A Surveycited by 557
  5. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 304
  6. 2020DiffusionNet: Discretization Agnostic Learning on Surfacescited by 163
  7. 2021Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problemscited by 100
  8. 2020Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphscited by 90
  9. 2018MeshCNN: A Network with an Edgecited by 69
  10. 2020CNNs on Surfaces using Rotation-Equivariant Featurescited by 42
  11. 2018The Vector Heat Methodcited by 31
  12. 2022Scalable algorithms for physics-informed neural and graph networkscited by 21
2 more
  1. 2019Graph Convolutional Networks for Coronary Artery Segmentation in Cardiac CT Angiographycited by 18
  2. 2021Mesh convolutional neural networks for wall shear stress estimation in 3D artery modelscited by 9

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 5; 2025: 12; 2026: 7.

29 papers.

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  1. 2024Does equivariance matter at scale?cited by 49
  2. 2023Geometric Algebra Transformercited by 46
  3. 2023A graph convolutional autoencoder approach to model order reduction for parametrized PDEscited by 44
  4. 2023Euclidean, Projective, Conformal: Choosing a Geometric Algebra for Equivariant Transformerscited by 12
  5. 2024LaB-GATr: geometric algebra transformers for large biomedical surface and volume meshescited by 12
  6. 2025Machine learning for modelling unstructured grid data in computational physics: a reviewcited by 12
  7. 2024Deep vectorised operators for pulsatile hemodynamics estimation in coronary arteries from a steady-state priorcited by 6
  8. 2024Physics-informed graph neural networks for flow field estimation in carotid arteriescited by 4
  9. 2025Training Transformers for Mesh-Based Simulationscited by 4
  10. 2023Modeling Dynamics over Meshes with Gauge Equivariant Nonlinear Message Passingcited by 3
  11. 2025Learning Hemodynamic Scalar Fields on Coronary Artery Meshes: A Benchmark of Geometric Deep Learning Modelscited by 2
  12. 2025Active Learning for Deep Learning-Based Hemodynamic Parameter Estimationcited by 2
17 more
  1. 2023SIRE: scale-invariant, rotation-equivariant estimation of artery orientations using graph neural networkscited by 1
  2. 2025Universal Collection of Euclidean Invariants between Pairs of Position-Orientationscited by 1
  3. 2025Wall Shear Stress Estimation in Abdominal Aortic Aneurysms: Towards Generalisable Neural Surrogate Modelscited by 1
  4. 2025GReAT: leveraging geometric artery data to improve wall shear stress assessmentcited by 1
  5. 2025TRELLIS-Enhanced Surface Features for Comprehensive Intracranial Aneurysm Analysiscited by 1
  6. 2025Graph Deep Learning for Intracranial Aneurysm Blood Flow Simulation and Risk Assessmentcited by 1
  7. 2024Mesh-Informed Reduced Order Models for Aneurysm Rupture Risk Predictioncited by 0
  8. 2025Permutation Equivariant Neural Networks for Symmetric Tensorscited by 0
  9. 2025Implicit Augmentation from Distributional Symmetry in Turbulence Super-Resolutioncited by 0
  10. 2025Physics-informed self-supervised learning for predictive modeling of coronary artery digital twinscited by 0
  11. 2026Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEscited by 0
  12. 2026Smoothness Errors in Dynamics Models and How to Avoid Themcited by 0
  13. 2026Stable Long-Horizon Spatiotemporal Prediction on Meshes Using Latent Multiscale Recurrent Graph Neural Networkscited by 0
  14. 2026Mesh Based Simulations with Spatial and Temporal awarenesscited by 0
  15. 2026When Does Equivariance Help? Canonical Alignment in Neural Fluid Surrogatescited by 0
  16. 2026Anatomy-Informed Neural Networks: Encoding Anatomic Priors in Loss and Architecture, with an SE(3) Formulation of Guidewire-Induced Aortoiliac Deformationcited by 0
  17. 2026Learning PDE Dynamics between Submanifolds Using Green's Observation Operatorscited by 0