A physics-informed neural network-based method for predicting degradation trajectories and remaining useful life of supercapacitors

Supercapacitors are widely used in transportation and renewable energy fields due to their high power density, stable cycling performance, and rapid charge–discharge capabilities. To ensure efficient applications of supercapacitors, accurately predicting their degradation trajectories and remaining useful life (RUL) is crucial. For this purpose, a physics-informed neural network (PINN) model is developed using Long Short-Term Memory (LSTM) as the base architecture. Physical equations are embedded into the loss function to ensure consistency with domain knowledge, allowing the loss function to incorporate both physical and data-driven components. The balance between these two loss components is dynamically determined through Bayesian optimization, to enhance the model's accuracy further. Validation results show a root mean square error (RMSE) of 3 ​mF (the rated capacity is 1 F) in the degradation trajectory prediction and a RMSE of 269 cycles (the average cycle life is 5180 cycles) for the RUL. Ablation experiments were conducted to validate the effectiveness of integrating physical information into the LSTM framework. Results demonstrate that the proposed model outperforms both the data-driven LSTM method and the empirical equation-based method that the PINN model can reduce the RMSE by 85% and 87.5% for degradation trajectory prediction, and 86.5% and 94.6% for RUL prediction, respectively. In addition, a comparison with advanced models demonstrates that our model reduces the requirement significantly on training data while maintaining comparable prediction accuracy, which favors scenarios where data is scarce. Overall process of degradation trajectory and remaining useful life prediction for supercapacitors based on the proposed model. • Integration of physical and data-driven models for accurate degradation prediction. • Considering both degradation trajectories and RUL enhances the comprehensiveness of health assessment. • Dynamic adjustment of hyperparameters improves the predictive capability of the network. • Limited training data shows strong early prediction capability. • Future trends in health management driven by PINN and Bayesian optimization.