Physics-Informed Neural Networks for Real-Time Gas Crossover Prediction in PEM Electrolyzers: First Application with Multi-Membrane Validation

Green hydrogen production via polymer electrolyte membrane (PEM) water electrolysis is pivotal for energy transition, yet hydrogen crossover through membranes threatens safety and economic viability-approaching explosive limits (4 mol% H$_2$ in O$_2$) while reducing Faradaic efficiency by 2.5%. Current physics-based models require extensive calibration and computational resources that preclude real-time implementation, while purely data-driven approaches fail to extrapolate beyond training conditions-critical for dynamic electrolyzer operation. Here we present the first application of physics-informed neural networks (PINNs) for hydrogen crossover prediction, integrating mass conservation, Fick's diffusion law, and Henry's solubility law within a compact architecture (17,793 parameters). Validated across six membranes under industrially relevant conditions (0.05-5.0 A/cm$^2$, 1-200 bar, 25-85°C), our PINN achieves exceptional accuracy (R$^{2}$ = 99.84% $\pm$ 0.15\%, RMSE = 0.0932% $\pm$ 0.0438%) based on five-fold cross-validation, with sub-millisecond inference times suitable for real-time control. Remarkably, the model maintains R$^2$ > 86% when predicting crossover at pressures 2.5x beyond training range-substantially outperforming pure neural networks (R$^2$ = 43.4%). The hardware-agnostic deployment, from desktop CPUs to edge devices (Raspberry Pi 4), enables distributed safety monitoring essential for gigawatt-scale installations. By bridging physical rigor and computational efficiency, this work establishes a new paradigm for real-time electrolyzer monitoring, accelerating deployment of safe, efficient green hydrogen infrastructure crucial for net-zero emissions targets.