Out-of-Sample Voltage Prediction for PEM Electrolyzers via Knowledge Distillation to a Physics-Based Model

Voltage models for Proton Exchange Membrane (PEM) electrolyzers calibrated under one set of operating conditions often fail when required to predict under different conditions, a task known in machine learning as Out-of-Sample (OOS) prediction. We address this problem with knowledge distillation, in which a hybrid teacher combining the electrochemical equations (Nernst equation, Butler–Volmer kinetics, Ohm's law) with a bounded neural network correction is distilled into a 12-parameter physics-based student. Using OOS datasets from a Static Water Vapour Feed (SWVF) PEM electrolyzer, we show that the student predicts voltage more accurately than conventional fitting of the same equations, with a mean absolute error (MAE) of 9.2 mV across two evaluation campaigns with different operating protocols, approximately 75% lower than Levenberg–Marquardt nonlinear least squares (37.2 mV) and 70% lower than gradient-based fitting (30.4 mV). The deployed model is a closed-form expression of 12 constants (six effective electrochemical parameters, six empirical correction constants) and runs without machine-learning software.