# Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps

arXiv: https://arxiv.org/abs/2201.12362 · HTML: https://mlsanity.com/paper/2201.12362/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 53 references that are in the map.
- First posted on arXiv 28 Jan 2022.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [Fast Tetrahedral Meshing in the Wild](https://mlsanity.com/paper/1908.03581/) (2019)
- [The Vector Heat Method](https://mlsanity.com/paper/1805.09170/) (2018)
- [Gaussian Process Manifold Interpolation for Probabilistic Atrial Activation Maps and Uncertain Conduction Velocity](https://mlsanity.com/paper/2004.10586/) (2020)
- [Exploring the potential of transfer learning for metamodels of heterogeneous material deformation](https://mlsanity.com/paper/2010.16260/) (2020)
- [Learning atrial fiber orientations and conductivity tensors from intracardiac maps using physics-informed neural networks](https://mlsanity.com/paper/2102.10863/) (2021)
- [Modeling cardiac muscle fibers in ventricular and atrial electrophysiology simulations](https://mlsanity.com/paper/2101.10960/) (2021)
- [PIEMAP: Personalized Inverse Eikonal Model from cardiac Electro-Anatomical Maps](https://mlsanity.com/paper/2008.10724/) (2020)

## Built on by (most cited first, 14 of 14)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Delta-PINNs: physics-informed neural networks on complex geometries](https://mlsanity.com/paper/2209.03984/) (2022)
- [Towards Enabling Cardiac Digital Twins of Myocardial Infarction Using Deep Computational Models for Inverse Inference](https://mlsanity.com/paper/2307.04421/) (2023)
- [Physics-informed Neural Network Estimation of Material Properties in Soft Tissue Nonlinear Biomechanical Models](https://mlsanity.com/paper/2312.09787/) (2023)
- [Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunities](https://mlsanity.com/paper/2501.06572/) (2025)
- [Shape of my heart: Cardiac models through learned signed distance functions](https://mlsanity.com/paper/2308.16568/) (2023)
- [Digital twinning of cardiac electrophysiology models from the surface ECG: a geodesic backpropagation approach](https://mlsanity.com/paper/2308.08410/) (2023)
- [Physics-Informed Machine Learning in Biomedical Science and Engineering](https://mlsanity.com/paper/2510.05433/) (2025)
- [Utilising physics-guided deep learning to overcome data scarcity](https://mlsanity.com/paper/2211.15664/) (2022)
- [Estimation of fibre architecture and scar in myocardial tissue using electrograms: an in-silico study](https://mlsanity.com/paper/2212.03012/) (2022)
- [Physics-informed neural networks for blood flow inverse problems](https://mlsanity.com/paper/2308.00927/) (2023)
- [Going Deeper with Five-point Stencil Convolutions for Reaction-Diffusion Equations](https://mlsanity.com/paper/2308.04735/) (2023)
- [WarpPINN-fibers: improved cardiac strain estimation from cine-MR with physics-informed neural networks](https://mlsanity.com/paper/2509.08872/) (2025)
- [HAPI-EP: Towards Hybrid, Adaptive, and Predictive Digital Twins of Cardiac Electrophysiology](https://mlsanity.com/paper/2606.15637/) (2026)

## Abstract (arXiv)

We propose FiberNet, a method to estimate in-vivo the cardiac fiber architecture of the human atria from multiple catheter recordings of the electrical activation. Cardiac fibers play a central role in the electro-mechanical function of the heart, yet they are difficult to determine in-vivo, and hence rarely truly patient-specific in existing cardiac models. FiberNet learns the fiber arrangement by solving an inverse problem with physics-informed neural networks. The inverse problem amounts to identifying the conduction velocity tensor of a cardiac propagation model from a set of sparse activation maps. The use of multiple maps enables the simultaneous identification of all the components of the conduction velocity tensor, including the local fiber angle. We extensively test FiberNet on synthetic 2-D and 3-D examples, diffusion tensor fibers, and a patient-specific case. We show that 3 maps are sufficient to accurately capture the fibers, also in the presence of noise. With fewer maps, the role of regularization becomes prominent. Moreover, we show that the fitted model can robustly reproduce unseen activation maps. We envision that FiberNet will help the creation of patient-specific models for personalized medicine. The full code is available at http://github.com/fsahli/FiberNet.