Koopman operator-augmented physics-informed neural network with SEI kinetics for stable and explainable SOH estimation in battery packs

Accurate estimation of State of Health (SOH) is pivotal for battery management, yet existing data-driven methods often lack physical interpretability and struggle with generalization under complex operating conditions. To bridge the gap between data-driven flexibility and electrochemical mechanism consistency, this paper proposes a Koopman Operator-Augmented Physics-Informed Neural Network (Koopman-PINN) tailored for battery pack SOH estimation. Unlike traditional black-box models, the proposed method embeds the nonlinear SOH degradation into a high-dimensional Koopman observation space where it evolves linearly. Crucially, the Solid Electrolyte Interphase (SEI) growth kinetics and boundedness conditions are embedded as physical loss terms. A spectral domain constraint is further imposed on the Koopman operator matrix, which forces all eigenvalues inside the unit circle (|λi| < 1) and constrains their phase angles to guarantee the physical consistency and long-term stability of the degradation trajectory. Furthermore, the SEI degradation rate coefficient α is treated as an independent trainable parameter, enabling the end-to-end learning of physical parameters. Validated on extensive battery pack datasets under quasi-constant temperature (804 cycles) and variable temperature (667 cycles) conditions, the Koopman-PINN reduces the MAE by 46.0% and RMSE by 48.9% compared to standard PINNs in quasi-constant temperature. Under variable temperature conditions, Koopman-PINN reduces MAE by 30.0% and RMSE by 29.6% compared to the traditional PINN. Notably, the learned activation energy (≈30 kJ/mol) aligns well with the physical laws of SEI growth, and the spectral analysis reveals distinct dynamical modes governing the degradation process, providing a novel interpretable perspective on battery aging mechanisms.