A deep physics-informed virtual twin for out-of-distribution degradation and impedance estimation in hydrogen energy systems

Proton Exchange Membrane Fuel Cells (PEMFCs) are critical for zero-emission heavy-duty transportation and stationary power generation. However, multi-rate degradation mechanisms limit their operational lifespan. While data-driven machine learning models are widely utilized for health diagnostics, they frequently cross fundamental electrochemical boundaries during out-of-distribution extrapolation, causing non-physical parameter divergence and numerical instabilities. This study presents a physics-informed hybrid residual network (PI-Hybrid-ResNet) architecture that structurally decouples physical electrochemical parameters from non-linear statistical shifts to ensure stable, long-term prognostic accuracy. The architecture combines a parallel linear component which maps normalized execution time directly to the terminal output layer to eliminate deep hidden-layer activation saturation with an in-loop, batch-vectorized differentiable solver. Furthermore, Butler-Volmer kinetics and a dual-arc distributed Randles equivalent circuit model are integrated directly into the neural network's backpropagation loop. This configuration enforces physical consistency over a twelve-dimensional physical parameter vector (θ) preventing traditional internal parameter optimization such as the non-physical collapse of high-frequency charge transfer resistance. Trained on non-isothermal aging sequences from 500 to 5,000 hours and tested on an unseen 10,000-hour extrapolation trajectory, the PI-Hybrid-ResNet eliminates the limit-cycle gradient oscillations common in unconstrained baselines. The architecture achieves a polarization curve profile root mean square error (RMSE) of 0.0282 V and constrains the electrochemical impedance spectroscopy (EIS) Nyquist vector error to 0.0491 Ω. This study proposes a reliable framework for software-defined virtual sensing and predictive diagnostics in intelligent energy management systems. Therefore, it effectively integrates the numerical machine learning with physical electrochemical engineering.