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.

翻译：学习心脏电生理学中生物物理精确的解算子，其根本挑战在于患者特异性心脏解剖结构间的几何变异性。现有大多数神经算子方法局限于结构化或弱变形域，限制了其在真实心房与心室几何结构中的适用性。本文提出一种统一的算子学习框架，将输入与输出投影至标准化的解剖坐标系，从而将电生理动力学与网格拓扑结构解耦。该表述在保持生理学意义空间组织的同时实现了几何无关学习，并允许将预测结果插值回患者特异性几何结构以进行解剖学解释。为支持框架内的大规模训练，我们开发了GPU加速的电生理求解器，并在具有不同起搏与传导特性的多样化患者特异性左心房几何结构上生成了超过30万例高保真模拟。在此解剖坐标域内，我们设计了一个神经算子来预测全场局部激活时间图，实现了5.1毫秒的平均绝对误差和每样本0.12毫秒的推理时间，其性能优于现有的算子学习与卷积基线方法。我们进一步在心室几何结构上验证了该框架，证明了其超越心房场景的鲁棒泛化能力。该框架共同为快速、几何不变的心脏电生理建模建立了可扩展的基础，对实时及群体规模的临床工作流程具有潜在应用价值。