Physics-informed neural networks for small sample state of health estimation of lithium-ion batteries

As lithium-ion batteries become increasingly prevalent in daily life, accurately estimating their State of Health (SOH) is crucial to reduce maintenance costs and prevent accidents. Due to the high costs of measurement, data collection, and storage, traditional data-driven methods struggle to make accurate estimations in small-sample scenarios, as they rely heavily on high-quality training data. To address this issue, we propose a method for SOH estimation that embeds physical information into a neural network . First, a semi-empirical model describing battery capacity degradation is constructed based on the Logistic equation . This model is then embedded into a neural network to form a Semi-empirical Physics-Informed Neural Networks (SPINN). The loss function combines the fitting error from the neural network with the error related to physical information, ensuring that the training of SPINN is guided by physical constraints. Experiments were conducted using three publicly available datasets for small-sample training. The results show that even with limited training data, the proposed method ensures accurate SOH estimation. Furthermore, comparative experiments with existing data-driven and electrochemical models demonstrate the superiority of the proposed approach. When trained on only 50 % of the available data, other data-driven models exhibited prediction failures, while SPINN maintained a maximum RMSPE below 5 %. • Proposed a dynamic physical model capable of describing the battery degradation rate. • Fusion of the physics-based model with a neural network architecture gives rise to a SPINN. • Using Huber loss and adaptive loss fixes inaccurate SOH predictions from imbalanced weights in SPINN learning. • The proposed SOH method outperforms mainstream models with limited training data.