# Towards Deep Learning Surrogate for the Forward Problem in Electrocardiology: A Scalable Alternative to Physics-Based Models

arXiv: https://arxiv.org/abs/2512.13765 · HTML: https://mlsanity.com/paper/2512.13765/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 7 references that are in the map.
- First posted on arXiv 15 Dec 2025.

## Builds on (most cited first, 2 of 2)

- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Solving the Inverse Problem of Electrocardiography for Cardiac Digital Twins: A Survey](https://mlsanity.com/paper/2406.11445/) (2024)

## Abstract (arXiv)

The forward problem in electrocardiology, computing body surface potentials from cardiac electrical activity, is traditionally solved using physics-based models such as the bidomain or monodomain equations. While accurate, these approaches are computationally expensive, limiting their use in real-time and large-scale clinical applications. We propose a proof-of-concept deep learning (DL) framework as an efficient surrogate for forward solvers. The model adopts a time-dependent, attention-based sequence-to-sequence architecture to predict electrocardiogram (ECG) signals from cardiac voltage propagation maps. A hybrid loss combining Huber loss with a spectral entropy term was introduced to preserve both temporal and frequency-domain fidelity. Using 2D tissue simulations incorporating healthy, fibrotic, and gap junction-remodelled conditions, the model achieved high accuracy (mean R2 = 0.99 ± 0.01). Ablation studies confirmed the contributions of convolutional encoders, time-aware attention, and spectral entropy loss. These findings highlight DL as a scalable, cost-effective alternative to physics-based solvers, with potential for clinical and digital twin applications.