Enhancing battery SOH prediction with Butler–Volmer informed neural networks in data-scarce environments

Accurate and robust estimation of Lithium-Ion Battery (LIB) state of health (SOH) is critical for the safety and reliability of electric vehicles, yet conventional machine learning models often suffer from limited interpretability and poor generalization under data-scarce conditions. In this work, we propose Butler–Volmer Informed Neural Network (BVINN), a physics-informed machine learning framework that directly embeds the closed-form analytical solution of the classical Butler–Volmer equation into the network loss function as a regularization term. By penalizing deviations from fundamental electrochemical kinetics during training, BVINN enforces physically consistent representations of degradation and narrows the solution space to regions that are both statistically and mechanistically plausible. The overall loss combines five components, namely data loss, Butler–Volmer loss, initial condition loss, boundary condition loss and regeneration loss, to ensure adherence to governing physical laws throughout the learning process. We validate BVINN on two well-known benchmark datasets, the NASA battery dataset and the BIT dataset, across various sequence length environments. Using BVINN yields improved RMSE, and MAE performance compared to models without the Butler–Volmer informed regularization. Furthermore, by exploiting the Butler–Volmer equation as an explicit regularizer, BVINN outperforms benchmark methods such as Deep Hidden Physics Model (DeepHPM) and other Physics-Informed Neural Network (PINN), maintaining higher performance even in data-scarce environments. The physical plausibility of the model is further corroborated by electrochemical analysis, which confirms that BVINN learns mechanistically consistent degradation behaviors.