Physics-guided learning framework based on a fractional single-particle model for battery state-of-health prediction

Accurate prediction of lithium-ion battery capacity degradation is crucial for ensuring safe and reliable energy storage systems. Traditional data-driven methods often lack physical interpretability, while existing physics-informed approaches typically rely on simplified integer-order models that cannot capture the history-dependent transport and polarization behaviors observed during aging. To address these limitations, this paper proposes a fractional single-particle-model-based physics-guided learning framework (FSPM-PGL) for capacity estimation. The framework incorporates a time-fractional diffusion formulation into the single-particle model to represent anomalous solid-phase lithium-ion transport with long-memory effects. A capacity-voltage coupled physics-consistency loss is further developed by mapping the predicted capacity to an equivalent input current and enforcing terminal-voltage consistency through the fractional-order model. To enable stable training with the non-differentiable fractional-order model, a gradient-bypass strategy is introduced to incorporate physical constraints into backpropagation. Experiments on the CALCE and TJU aging datasets, independently repeated using three random seeds, demonstrate that FSPM-PGL generally improves the prediction accuracy and stability of RNN, GRU, LSTM, CNN-LSTM, and Transformer-based models, supporting its robustness across different cathode chemistries and degradation-trajectory lengths.