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

Abstract

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.