A physics-enhanced hybrid kolmogorov–arnold network with dynamic coupling for interpretable battery state-of-charge estimation

Estimating the state of charge (SOC) for lithium-ion batteries is a core task for battery management systems. However, SOC estimation faces challenges such as insufficient accuracy, poor robustness, and weak interpretability, especially under complex operating conditions. This paper proposes a physics-enhanced hybrid Kolmogorov–Arnold network (PEHKAN) method, which is the first method to integrate mechanical stress characteristics with electrochemical–thermodynamic multiphysics modeling. An improved Butler–Volmer equation electrochemical potential energy module and a temperature–pressure coupled diffusion dynamics module with collaborative control are constructed; these modules explicitly model the synergistic effects of electrochemistry, thermodynamics, and mechanical stress. Additionally, a dynamic gating fusion mechanism is designed to achieve adaptive weighting between the physical model and data-driven modules, addressing the performance degradation issue that is traditionally encountered during dynamic operating condition transitions. Furthermore, physical constraint terms are introduced to ensure that the model optimizes the SOC estimation accuracy while adhering to the physical properties of the battery. Symbolic regression and feature attribution analysis reveal the nonlinear correlations between these various physical quantities, enhancing the interpretability of the model. The experimental results on 174 battery datasets demonstrate that PEHKAN outperforms existing methods significantly across multiple operating conditions, temperatures, and battery types, achieving an MAE as low as 0.00312 under small-sample conditions (1/4 of the training data). This study offers a novel paradigm for battery state estimation in complex dynamic environments, combining physical interpretability with data-driven advantages.