Physics-Informed Neural Operators for Cardiac Electrophysiology

TL;DR

This work tackles the computational bottleneck of simulating cardiac electrophysiology PDEs by introducing Physics-Informed Neural Operators (PINO) that learn mappings between function spaces, enabling mesh-resolution invariant and initial-condition robust predictions. Leveraging a Fourier Neural Operator backbone and physics-informed losses, the approach trains on a family of Aliev-Panfilov PDEs to produce dynamics comparable to high-fidelity solvers but with substantial speed-ups. The model demonstrates zero-shot transfer to unseen propagation patterns and 10× resolution extrapolation, with strong long-rollout stability, suggesting suitability for online prediction in resource-limited medical devices. The results highlight PINOs as a scalable, data-efficient alternative for fast, accurate cardiac EP simulations across varying meshes and scenarios.

Abstract

Accurately simulating systems governed by PDEs, such as voltage fields in cardiac electrophysiology (EP) modelling, remains a significant modelling challenge. Traditional numerical solvers are computationally expensive and sensitive to discretisation, while canonical deep learning methods are data-hungry and struggle with chaotic dynamics and long-term predictions. Physics-Informed Neural Networks (PINNs) mitigate some of these issues by incorporating physical constraints in the learning process, yet they remain limited by mesh resolution and long-term predictive stability. In this work, we propose a Physics-Informed Neural Operator (PINO) approach to solve PDE problems in cardiac EP. Unlike PINNs, PINO models learn mappings between function spaces, allowing them to generalise to multiple mesh resolutions and initial conditions. Our results show that PINO models can accurately reproduce cardiac EP dynamics over extended time horizons and across multiple propagation scenarios, including zero-shot evaluations on scenarios unseen during training. Additionally, our PINO models maintain high predictive quality in long roll-outs (where predictions are recursively fed back as inputs), and can scale their predictive resolution by up to 10x the training resolution. These advantages come with a significant reduction in simulation time compared to numerical PDE solvers, highlighting the potential of PINO-based approaches for efficient and scalable cardiac EP simulations.

Figures (6)

• Figure 1: Propagation scenarios used for training the operator model, all sampled at $t = 500$ ms.
• Figure 2: Point-to-point long-time horizon predictions for the (a) spiral and (b) spiral break-up propagation scenarios. The dashed line represents the time horizon for the training data. The best- and worst-performing cells are marked on the voltage maps. The sample snapshots were taken at t=$1750$ms.
• Figure 3: Results using the multi-frame roll-out evaluation method for the spiral scenario. The dashed line represents the initial time window given as an input to the model and the best and worst performing cells are marked on the sample field, taken at $t=1250$ ms.
• Figure 4: Zero-shot mesh resolution tests. (a) Relative RMSE values for P2P evaluation on increasing target resolution scales. (b) Input for the chaotic scenario at training resolution ($t = 495$ ms). (c) Prediction at the highest evaluation resolution ($t = 500$ ms).
• Figure 5: Zero-shot transfer. Samples shown are the predictions for the stable spiral scenario at $t=500$ms using the (a) Stable spiral model. (b) Planar model. (c) Centrifugal model.