# Shape-informed cardiac mechanics surrogates in data-scarce regimes via geometric encoding and generative augmentation

arXiv: https://arxiv.org/abs/2602.20306 · HTML: https://mlsanity.com/paper/2602.20306/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 50 references that are in the map.
- First posted on arXiv 23 Feb 2026.

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

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [Optimizing the Latent Space of Generative Networks](https://mlsanity.com/paper/1707.05776/) (2017)
- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
- [AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fields](https://mlsanity.com/paper/2406.02176/) (2024)
- [Shape of my heart: Cardiac models through learned signed distance functions](https://mlsanity.com/paper/2308.16568/) (2023)
- [Shape-informed surrogate models based on signed distance function domain encoding](https://mlsanity.com/paper/2409.12400/) (2024)
- [A rule-based method to model myocardial fiber orientation in cardiac biventricular geometries with outflow tracts](https://mlsanity.com/paper/1809.08297/) (2018)
- [Handling geometrical variability in nonlinear reduced order modeling through Continuous Geometry-Aware DL-ROMs](https://mlsanity.com/paper/2411.05486/) (2024)
- [Parametric model order reduction and its application to inverse analysis of large nonlinear coupled cardiac problems](https://mlsanity.com/paper/1810.12033/) (2018)
- [lifex: a flexible, high performance library for the numerical solution of complex finite element problems](https://mlsanity.com/paper/2207.14668/) (2022)

## Built on by (most cited first, 2 of 2)

- [Learning geometry-dependent lead-field operators for forward ECG modeling](https://mlsanity.com/paper/2602.22367/) (2026)
- [Geometry-physics confounding impairs PDE learning across varying domains](https://mlsanity.com/paper/2609.38623/) (2026)

## Abstract (arXiv)

High-fidelity computational models of cardiac mechanics provide mechanistic insight into the heart function but are computationally prohibitive for routine clinical use. Surrogate models can accelerate simulations, but generalization across diverse anatomies is challenging, particularly in data-scarce settings. We propose a two-step framework that decouples geometric representation from learning the physics response, to enable shape-informed surrogate modeling under data-scarce conditions. First, a shape model learns a compact latent representation of left ventricular geometries. The learned latent space effectively encodes anatomies and enables synthetic geometries generation for data augmentation. Second, a neural field-based surrogate model, conditioned on this geometric encoding, is trained to predict ventricular displacement under external loading. The proposed architecture performs positional encoding by using universal ventricular coordinates, which improves generalization across diverse anatomies. Geometric variability is encoded using two alternative strategies, which are systematically compared: a PCA-based approach suitable for working with point cloud representations of geometries, and a DeepSDF-based implicit neural representation learned directly from point clouds. Overall, our results, obtained on idealized and patient-specific datasets, show that the proposed approaches allow for accurate predictions and generalization to unseen geometries, and robustness to noisy or sparsely sampled inputs.