# Deep learning-based reduced order models in cardiac electrophysiology

arXiv: https://arxiv.org/abs/2006.03040 · HTML: https://mlsanity.com/paper/2006.03040/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2020.

## Built on by (most cited first, 22 of 22)

- [POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition](https://mlsanity.com/paper/2101.11845/) (2021)
- [Continuous PDE Dynamics Forecasting with Implicit Neural Representations](https://mlsanity.com/paper/2209.14855/) (2022)
- [Generalizing to New Physical Systems via Context-Informed Dynamics Model](https://mlsanity.com/paper/2202.01889/) (2022)
- [LEADS: Learning Dynamical Systems that Generalize Across Environments](https://mlsanity.com/paper/2106.04546/) (2021)
- [Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems](https://mlsanity.com/paper/2212.03130/) (2022)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Multi-fidelity surrogate modeling using long short-term memory networks](https://mlsanity.com/paper/2208.03115/) (2022)
- [Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models](https://mlsanity.com/paper/2106.05722/) (2021)
- [Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models](https://mlsanity.com/paper/2201.10215/) (2022)
- [Deep-HyROMnet: A deep learning-based operator approximation for hyper-reduction of nonlinear parametrized PDEs](https://mlsanity.com/paper/2202.02658/) (2022)
- [Continual Learning of Dynamical Systems with Competitive Federated Reservoir Computing](https://mlsanity.com/paper/2206.13336/) (2022)
- [VC dimension of Graph Neural Networks with Pfaffian activation functions](https://mlsanity.com/paper/2401.12362/) (2024)
- [Phase2vec: Dynamical systems embedding with a physics-informed convolutional network](https://mlsanity.com/paper/2212.03857/) (2022)
- [Fast characterization of inducible regions of atrial fibrillation models with multi-fidelity Gaussian process classification](https://mlsanity.com/paper/2112.08075/) (2021)
- [An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes](https://mlsanity.com/paper/2202.06170/) (2022)
- [Branched Latent Neural Maps](https://mlsanity.com/paper/2308.02599/) (2023)
- [Learning Macroscopic Dynamics from Partial Microscopic Observations](https://mlsanity.com/paper/2410.23938/) (2024)
- [Full-field surrogate modeling of cardiac function encoding geometric variability](https://mlsanity.com/paper/2504.20479/) (2025)
- [Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flows](https://mlsanity.com/paper/2602.15472/) (2026)
- [Virtual twins of nonlinear vibrating multiphysics microstructures: physics-based versus deep learning-based approaches](https://mlsanity.com/paper/2205.05928/) (2022)
- [Learning cardiac activation and repolarization times with operator learning](https://mlsanity.com/paper/2505.08631/) (2025)
- [Parameterized Temporal Extrapolation of PDEs via Disentangled Latent Dynamics Manifold Fusion](https://mlsanity.com/paper/2603.12676/) (2026)

## Abstract (arXiv)

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the formulation and numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential, that is the polarization/depolarization cycle occurring at every heart beat that models the time evolution of the electrical potential across the cell membrane, as well as a set of ionic variables. Multiple solutions of these systems, corresponding to different model inputs, are required to evaluate outputs of clinical interest, such as activation maps and action potential duration. More importantly, these models feature coherent structures that propagate over time, such as wavefronts. These systems can hardly be reduced to lower dimensional problems by conventional reduced order models (ROMs) such as, e.g., the reduced basis (RB) method. This is primarily due to the low regularity of the solution manifold (with respect to the problem parameters) as well as to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To overcome this difficulty, in this paper we propose a new, nonlinear approach which exploits deep learning (DL) algorithms to obtain accurate and efficient ROMs, whose dimensionality matches the number of system parameters. Our DL approach combines deep feedforward neural networks (NNs) and convolutional autoencoders (AEs). We show that the proposed DL-ROM framework can efficiently provide solutions to parametrized electrophysiology problems, thus enabling multi-scenario analysis in pathological cases. We investigate three challenging test cases in cardiac electrophysiology and prove that DL-ROM outperforms classical projection-based ROMs.