A unified framework for geometry-independent operator learning in cardiac electrophysiology simulations

Learning biophysically accurate solution operators for cardiac electrophysiology is fundamentally challenged by geometric variability across patient-specific heart anatomies. Most existing neural operator approaches are limited to structured or weakly deformed domains, restricting their applicability to realistic atrial and ventricular geometries. Here, we introduce a unified operator-learning framework that projects inputs and outputs onto a standardised anatomical coordinate system, decoupling electrophysiological dynamics from mesh topology. This formulation enables geometry-independent learning while preserving physiologically meaningful spatial organisation, and allows predictions to be interpolated back onto patient-specific geometries for anatomical interpretation. To support large-scale training within the framework, we develop a GPU-accelerated electrophysiology solver and generate over 300,000 high-fidelity simulations across diverse patient-specific left atrial geometries with varied pacing and conduction properties. Within this anatomical coordinate domain, we design a neural operator to predict full-field local activation time maps, achieving a mean absolute error of 5.1 ms and an inference time of 0.12 ms per sample, outperforming existing operator learning and convolutional baselines. We further validate the framework on ventricular geometries, demonstrating robust generalisation beyond the atrial setting. Together, this framework establishes a scalable foundation for fast, geometry-invariant cardiac electrophysiology modelling, with potential relevance for real-time and population-scale clinical workflows.