Accelerating Cardiac Myocyte Simulations with Physics-Informed Neural Networks for Sodium Channel Gating

The increasing availability of human electrophysiological data has enabled the development of refined myocyte models with detailed transmembrane current descriptions. This fidelity is typically achieved via stiff systems of ordinary differential equations (ODEs) that span disparate time scales and force small integration steps, especially for the fast sodium current I$_{Na}$ conducted by Nav1.5. Explicit schemes may require sub-microsecond steps (e.g., 0.1 μs) to resolve upstroke and refractory dynamics, causing sub- stantial computational costs for single-cell, tissue, and organ simulations. We present a hybrid approach in which a physics-informed neural network (PINN) surrogates the Nav1.5 gating kinetics for the activation m and dual inactivation gates h$_1$, h$_2$ and replaces the corresponding ODE subsystem in a human atrial action potential model. The PINN is trained to match the observed current-voltage relation while penalizing violations of the known gating ODE structure. We assess fidelity and quantify speedups up to 2.5x faster and stability with enlarged time steps in paced simulations (0.18 mV RMSE). The resulting surrogate reproduces gating-dependent I$_{Na}$ behavior while materially reducing wall-clock time, suggesting a tractable path to high-fidelity, large-scale simulations and downstream personalization workflows.