# Full-field surrogate modeling of cardiac function encoding geometric variability

arXiv: https://arxiv.org/abs/2504.20479 · HTML: https://mlsanity.com/paper/2504.20479/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 72 references that are in the map.
- First posted on arXiv 29 Apr 2025.

## Builds on (most cited first, 15 of 15)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [A Tutorial on Kernel Density Estimation and Recent Advances](https://mlsanity.com/paper/1704.03924/) (2017)
- [Deep learning-based reduced order models in cardiac electrophysiology](https://mlsanity.com/paper/2006.03040/) (2020)
- [Learning Reduced-Order Models for Cardiovascular Simulations with Graph Neural Networks](https://mlsanity.com/paper/2303.07310/) (2023)
- [SDF4CHD: Generative Modeling of Cardiac Anatomies with Congenital Heart Defects](https://mlsanity.com/paper/2311.00332/) (2023)
- [ImageCHD: A 3D Computed Tomography Image Dataset for Classification of Congenital Heart Disease](https://mlsanity.com/paper/2101.10799/) (2021)
- [Physics-constrained Deep Learning for Robust Inverse ECG Modeling](https://mlsanity.com/paper/2107.12780/) (2021)
- [A comprehensive and biophysically detailed computational model of the whole human heart electromechanics](https://mlsanity.com/paper/2207.12460/) (2022)
- [Modeling cardiac muscle fibers in ventricular and atrial electrophysiology simulations](https://mlsanity.com/paper/2101.10960/) (2021)
- [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)
- [Data-driven generation of 4D velocity profiles in the aneurysmal ascending aorta](https://mlsanity.com/paper/2211.00551/) (2022)
- [Branched Latent Neural Maps](https://mlsanity.com/paper/2308.02599/) (2023)
- [Probabilistic learning of the Purkinje network from the electrocardiogram](https://mlsanity.com/paper/2312.09887/) (2023)
- [Liquid Fourier Latent Dynamics Networks for fast GPU-based numerical simulations in computational cardiology](https://mlsanity.com/paper/2408.09818/) (2024)

## Built on by (most cited first, 3 of 3)

- [Learning cardiac activation and repolarization times with operator learning](https://mlsanity.com/paper/2505.08631/) (2025)
- [FalconBC: Flow matching for Amortized inference of Latent-CONditioned physiologic Boundary Conditions](https://mlsanity.com/paper/2603.19331/) (2026)
- [CoMetaPNS: Continually Meta-learning Personalized Neural Surrogates for Cardiac Electrophysiology Simulations](https://mlsanity.com/paper/2606.07488/) (2026)

## Abstract (arXiv)

Combining physics-based modeling with data-driven methods is critical to enabling the translation of computational methods to clinical use in cardiology. The use of rigorous differential equations combined with machine learning tools allows for model personalization with uncertainty quantification in time frames compatible with clinical practice. However, accurate and efficient surrogate models of cardiac function, built from physics-based numerical simulation, are still mostly geometry-specific and require retraining for different patients and pathological conditions. We propose a novel computational pipeline to embed cardiac anatomies into full-field surrogate models. We generate a dataset of electrophysiology simulations using a complex multi-scale mathematical model coupling partial and ordinary differential equations. We adopt Branched Latent Neural Maps (BLNMs) as an effective scientific machine learning method to encode activation maps extracted from physics-based numerical simulations into a neural network. Leveraging large deformation diffeomorphic metric mappings, we build a biventricular anatomical atlas and parametrize the anatomical variability of a small and challenging cohort of 13 pediatric patients affected by Tetralogy of Fallot. We propose a novel statistical shape modeling based z-score sampling approach to generate a new synthetic cohort of 52 biventricular geometries that are compatible with the original geometrical variability. This synthetic cohort acts as the training set for BLNMs. Our surrogate model demonstrates robustness and great generalization across the complex original patient cohort, achieving an average adimensional mean squared error of 0.0034. The Python implementation of our BLNM model is publicly available under MIT License at https://github.com/StanfordCBCL/BLNM.