Fourier neural operators enhanced with physics guided loss for modeling fuel cell degradation and lifetime forecasting

Reliable lifetime forecasting of proton-exchange membrane fuel cells (PEMFCs) is essential for durable hydrogen-energy systems, yet degradation dynamics are nonlinear, regime-dependent, and difficult to model efficiently at scale. We propose a physics-guided Fourier Neural Operator (FNO) for voltage degradation forecasting and health-state tracking. The method augments spectral operator learning with a soft constraint derived from the PEMFC polarization relation, decomposing voltage into reversible potential and activation, ohmic, and concentration losses to penalize thermodynamically inconsistent predictions during training and stabilize autoregressive rollout. The approach is evaluated on the IEEE PHM 2014 PEMFC durability benchmark under two contrasting regimes: quasi-stationary operation (FC1) and ripple-current operation (FC2). We compare against MLP, LSTM, Transformer, and additional recent PEMFC-inspired benchmark variants, including TCN–LSTM, Informer-style causal Transformer, and residual–CNN–LSTM with random attention. Under the sparse 500 h chronological protocol, the physics-guided FNO achieves the lowest error across the reported autoregressive and true-past-voltage metrics among the recent-method benchmarks, including AR RMSE values of 0.01428 on FC1 and 0.02192 on FC2. In the FNO objective ablation, the physics-guided loss reduces FC1 autoregressive RMSE by 51% relative to an MSE-trained FNO (0.0143 vs. 0.0289). Cross-regime transfer experiments further show consistent reductions in absolute error relative to MSE-trained FNOs, with paired moving-block bootstrap confidence intervals remaining below zero in both FC1 → FC2 and FC2 → FC1 directions. These results indicate that physics-guided operator learning improves rollout stability, sparse-data robustness, and transfer behavior for PEMFC degradation forecasting, while remaining computationally lightweight under the reported configuration.