# Ensemble learning of the atrial fiber orientation with physics-informed neural networks

arXiv: https://arxiv.org/abs/2410.23388 · HTML: https://mlsanity.com/paper/2410.23388/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 38 references that are in the map.
- First posted on arXiv 30 Oct 2024.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Theory of the Frequency Principle for General Deep Neural Networks](https://mlsanity.com/paper/1906.09235/) (2019)
- [Delta-PINNs: physics-informed neural networks on complex geometries](https://mlsanity.com/paper/2209.03984/) (2022)
- [GEASI: Geodesic-based Earliest Activation Sites Identification in cardiac models](https://mlsanity.com/paper/2102.09962/) (2021)
- [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)
- [Digital twinning of cardiac electrophysiology models from the surface ECG: a geodesic backpropagation approach](https://mlsanity.com/paper/2308.08410/) (2023)
- [Understanding the dynamics of the frequency bias in neural networks](https://mlsanity.com/paper/2405.14957/) (2024)
- [Probabilistic learning of the Purkinje network from the electrocardiogram](https://mlsanity.com/paper/2312.09887/) (2023)

## Built on by (most cited first, 1 of 1)

- [Atrial constitutive neural networks](https://mlsanity.com/paper/2504.02748/) (2025)

## Abstract (arXiv)

The anisotropic structure of the myocardium is a key determinant of the cardiac function. To date, there is no imaging modality to assess in-vivo the cardiac fiber structure. We recently proposed Fibernet, a method for the automatic identification of the anisotropic conduction -- and thus fibers -- in the atria from local electrical recordings. Fibernet uses cardiac activation as recorded during electroanatomical mappings to infer local conduction properties using physics-informed neural networks. In this work, we extend Fibernet to cope with the uncertainty in the estimated fiber field. Specifically, we use an ensemble of neural networks to produce multiple samples, all fitting the observed data, and compute posterior statistics. We also introduce a methodology to select the best fiber orientation members and define the input of the neural networks directly on the atrial surface. With these improvements, we outperform the previous methodology in terms of fiber orientation error in 8 different atrial anatomies. Currently, our approach can estimate the fiber orientation and conduction velocities in under 7 minutes with quantified uncertainty, which opens the door to its application in clinical practice. We hope the proposed methodology will enable further personalization of cardiac digital twins for precision medicine.