# Learning cardiac activation and repolarization times with operator learning

## TL;DR

This paper shows how machine learning can speed up heart simulations by predicting electrical signal timing, making them more practical for clinical use.

## Contribution

The study introduces efficient data-driven models for predicting cardiac activation and repolarization times using operator learning.

## Key findings

- FNO and KOL models accurately predict activation and repolarization times with high efficiency.
- The learned models are robust to hyperparameter choices and significantly faster than traditional PDE-based methods.
- Operator learning methods show potential for clinical integration due to reduced computation time and maintained accuracy.

## Abstract

Solving partial or ordinary differential equation models in cardiac electrophysiology is a computationally demanding task, particularly when high-resolution meshes are required to capture the complex dynamics of the heart. Moreover, in clinical applications, it is essential to employ computational tools that provide only relevant information, ensuring clarity and ease of interpretation. In this work, we exploit two recently proposed operator learning approaches, namely Fourier Neural Operators (FNO) and Kernel Operator Learning (KOL), to learn the operator mapping the applied stimulus in the physical domain into the activation and repolarization time distributions. These data-driven methods are evaluated on synthetic 2D and 3D domains, as well as on a physiologically realistic left ventricle geometry. Notably, while the learned map between the applied current and activation time has its modeling counterpart in the Eikonal model, no equivalent partial differential equation (PDE) model is known for the map between the applied current and repolarization time. Our results demonstrate that both FNO and KOL approaches are robust to hyperparameter choices and computationally efficient compared to traditional PDE-based Monodomain models. These findings highlight the potential use of these surrogate operators to accelerate cardiac simulations and facilitate their clinical integration.

Cardiac electrophysiology simulations are crucial for understanding how electrical signals propagate through the heart. However, solving the underlying mathematical models—typically partial differential equations—requires significant computational resources, especially when high-resolution anatomical detail is involved. This limits their real-time use in clinical settings. In this study, we explore two operator learning techniques, Fourier Neural Operators (FNO) and Kernel Operator Learning (KOL), as efficient alternatives to traditional solvers. These machine learning models learn how to predict activation and repolarization times —the key quantities that describe the electrical behavior of the heart— directly from the input electrical stimulus. We test these models on idealized 2D and 3D domains, as well as on a realistic human left ventricle geometry. Remarkably, our learned models achieve high accuracy while being orders of magnitude faster than traditional solvers. While activation times can be related to well-established mathematical models, repolarization times lack such a direct modeling framework—making our data-driven approach especially valuable. Our findings suggest that operator learning methods can make high-fidelity cardiac simulations more accessible for clinical applications by drastically reducing computation time while maintaining accuracy.