# Learning geometry-dependent lead-field operators for forward ECG modeling

arXiv: https://arxiv.org/abs/2602.22367 · HTML: https://mlsanity.com/paper/2602.22367/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 51 references that are in the map.
- First posted on arXiv 25 Feb 2026.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
- [Building Statistical Shape Spaces for 3D Human Modeling](https://mlsanity.com/paper/1503.05860/) (2015)
- [AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fields](https://mlsanity.com/paper/2406.02176/) (2024)
- [Solving the Inverse Problem of Electrocardiography for Cardiac Digital Twins: A Survey](https://mlsanity.com/paper/2406.11445/) (2024)
- [Shape of my heart: Cardiac models through learned signed distance functions](https://mlsanity.com/paper/2308.16568/) (2023)
- [Towards scalable surrogate models based on Neural Fields for large scale aerodynamic simulations](https://mlsanity.com/paper/2505.14704/) (2025)
- [A bi-atrial statistical shape model for large-scale in silico studies of human atria: model development and application to ECG simulations](https://mlsanity.com/paper/2102.10838/) (2021)
- [Probabilistic learning of the Purkinje network from the electrocardiogram](https://mlsanity.com/paper/2312.09887/) (2023)
- [Personalized Topology-Informed Localization of Standard 12-Lead ECG Electrode Placement from Incomplete Cardiac MRIs for Efficient Cardiac Digital Twins](https://mlsanity.com/paper/2408.13945/) (2024)
- [Accurate and Efficient Cardiac Digital Twin from surface ECGs: Insights into Identifiability of Ventricular Conduction System](https://mlsanity.com/paper/2411.00165/) (2024)
- [Shape-informed cardiac mechanics surrogates in data-scarce regimes via geometric encoding and generative augmentation](https://mlsanity.com/paper/2602.20306/) (2026)
- [Volumetric Non-Invasive Cardiac Mapping for Accessible Global Arrhythmia Characterization](https://mlsanity.com/paper/2510.17539/) (2025)

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

- [Geometry-physics confounding impairs PDE learning across varying domains](https://mlsanity.com/paper/2609.38623/) (2026)

## Abstract (arXiv)

Modern forward electrocardiogram (ECG) computational models rely on an accurate representation of the torso domain. The lead-field method enables fast ECG simulations while preserving full geometric fidelity. Achieving high anatomical accuracy in torso representation is, however, challenging in clinical practice, as imaging protocols are typically focused on the heart and often do not include the entire torso. In addition, the computational cost of the lead-field method scales linearly with the number of electrodes, limiting its applicability in high-density recording settings. To date, no existing approach simultaneously achieves high anatomical fidelity, low data requirements and computational efficiency. In this work, we propose a shape-informed surrogate model of the lead-field operator that serves as a drop-in replacement for the full-order model in forward ECG simulations. The proposed framework consists of two components: a geometry-encoding module that maps anatomical shapes into a low-dimensional latent space, and a geometry-conditioned neural surrogate that predicts lead-field gradients from spatial coordinates, electrode positions and latent codes. The proposed method achieves high accuracy in approximating lead fields both within the torso (mean angular error 5deg) and inside the heart, resulting in highly accurate ECG simulations (relative mean squared error <2.5%. The surrogate consistently outperforms the widely used pseudo lead-field approximation while preserving negligible inference cost. Owing to its compact latent representation, the method does not require a fully detailed torso segmentation and can therefore be deployed in data-limited settings while preserving high-fidelity ECG simulations.