Data-efficient and interpretable long-term prognostics of PEMFC degradation via physics-constrained symbolic regression–physics-informed neural network

Accurate remaining useful life (RUL) prognostics for proton exchange membrane fuel cells (PEMFCs) are essential for reliable operation and cost-effective maintenance. Existing long-term prognostics approaches often improve accuracy by relying on large datasets and black-box neural networks, but provide limited interpretability of the predicted voltage degradation curve. This study develops a physics-constrained symbolic regression–physics-informed neural network (PhySR-PINN) framework that, under dimensional consistency constraints, identifies a compact and physically interpretable dual-time-constant exponential degradation representation from voltage time-series data within a physics-constrained symbolic search space. The extracted fast and slow time constants are associated with recoverable voltage loss at the scale of hundreds of hours and irreversible voltage-loss accumulation at the scale of thousands of hours, respectively, supporting an interpretable description of PEMFC voltage degradation. The identified degradation representation is then embedded into the PINN as an explicit structural constraint to strengthen degradation-consistent learning for long-term prognostics. Experiments with different activation functions and training-data proportions demonstrate sustained long-term prognostic performance under limited-data conditions. Cross-dataset validation under multiple training-data proportions further indicates stable long-term prognostic behavior, with the best tested case reaching 98.97% RUL prediction accuracy.