# Active Learning for Deep Learning-Based Hemodynamic Parameter Estimation

arXiv: https://arxiv.org/abs/2503.03453 · HTML: https://mlsanity.com/paper/2503.03453/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 5 Mar 2025.

## Builds on (most cited first, 14 of 14)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [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)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems](https://mlsanity.com/paper/1809.08327/) (2018)
- [Mesh Neural Networks for SE(3)-Equivariant Hemodynamics Estimation on the Artery Wall](https://mlsanity.com/paper/2212.05023/) (2022)
- [Active Training of Physics-Informed Neural Networks to Aggregate and Interpolate Parametric Solutions to the Navier-Stokes Equations](https://mlsanity.com/paper/2005.05092/) (2020)
- [LaB-GATr: geometric algebra transformers for large biomedical surface and volume meshes](https://mlsanity.com/paper/2403.07536/) (2024)
- [SE(3) symmetry lets graph neural networks learn arterial velocity estimation from small datasets](https://mlsanity.com/paper/2302.08780/) (2023)
- [Physics-informed graph neural networks for flow field estimation in carotid arteries](https://mlsanity.com/paper/2408.07110/) (2024)
- [Deep vectorised operators for pulsatile hemodynamics estimation in coronary arteries from a steady-state prior](https://mlsanity.com/paper/2410.11920/) (2024)
- [Learning Hemodynamic Scalar Fields on Coronary Artery Meshes: A Benchmark of Geometric Deep Learning Models](https://mlsanity.com/paper/2501.09046/) (2025)

## Built on by (most cited first, 2 of 2)

- [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)

## Abstract (arXiv)

Hemodynamic parameters such as pressure and wall shear stress play an important role in diagnosis, prognosis, and treatment planning in cardiovascular diseases. These parameters can be accurately computed using computational fluid dynamics (CFD), but CFD is computationally intensive. Hence, deep learning methods have been adopted as a surrogate to rapidly estimate CFD outcomes. A drawback of such data-driven models is the need for time-consuming reference CFD simulations for training. In this work, we introduce an active learning framework to reduce the number of CFD simulations required for the training of surrogate models, lowering the barriers to their deployment in new applications. We propose three distinct querying strategies to determine for which unlabeled samples CFD simulations should be obtained. These querying strategies are based on geometrical variance, ensemble uncertainty, and adherence to the physics governing fluid dynamics. We benchmark these methods on velocity field estimation in synthetic coronary artery bifurcations and find that they allow for substantial reductions in annotation cost. Notably, we find that our strategies reduce the number of samples required by up to 50% and make the trained models more robust to difficult cases. Our results show that active learning is a feasible strategy to increase the potential of deep learning-based CFD surrogates.