Physics-Informed Neural Operators for Cardiac Electrophysiology

2025-11-11

AI Summary

To address the high computational cost, mesh dependency, large data requirements, and instability in long-term prediction inherent in partial differential equation (PDE)-based modeling of cardiac electrophysiology (EP), this work proposes a Physics-Informed Neural Operator (PINO). PINO uniquely integrates neural operators with hard physical constraints derived from EP PDEs, enabling learning of resolution- and initial-condition-invariant mappings in function space. It incorporates recursive temporal modeling and multi-scale input encoding to enhance generalization and stability. Experiments demonstrate that PINO achieves zero-shot transfer, 10× super-resolution inference, and stable long-horizon rollout. Across diverse cardiac wave propagation scenarios, it significantly outperforms conventional numerical solvers—accelerating simulation by an order of magnitude while maintaining high accuracy on unseen initial conditions and at ultra-high resolutions. Crucially, PINO breaks dual dependencies on problem-specific discretization and labeled training data.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Diffusion Models for Vision

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

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.

Problem

• Solving cardiac electrophysiology PDEs with computational efficiency
• Overcoming mesh resolution limitations in neural network simulations
• Enabling long-term stable predictions for chaotic cardiac dynamics

Innovation

• Learns mappings between function spaces for generalization
• Enables zero-shot evaluations on unseen propagation scenarios
• Scales predictive resolution up to 10x training resolution