Unified Explicit–Implicit Degradation Dynamics with Physics-Informed Kolmogorov–Arnold Networks for Lithium-Ion Battery SOH Estimation and RUL Prediction Under Different Charging Protocols

To address challenges in state-of-health (SOH) estimation and remaining useful life (RUL) prediction for lithium-ion batteries under fast-charging conditions—strong nonlinear degradation, difficulty in explicit mechanism modeling, and unstable generalization due to distribution shifts across batteries and protocols—this paper proposes the PIKAN (Physics-Informed KAN) framework. Under the physics-informed machine learning (PIML) paradigm, PIKAN uses Kolmogorov–Arnold networks (KAN) to learn complex nonlinear degradation mappings. Leveraging automatic differentiation for derivative information, it constructs optimizable physics residuals to achieve end-to-end collaborative optimization of data fitting and physical consistency. For dynamics constraints, PIKAN adopts a unified scheme of “explicit mechanism constraints + implicit dynamics learning”: for explicitly characterizable mechanisms (e.g., Verhulst equation), residuals are directly constructed; and for hard-to-explicitly-express mechanisms (e.g., RUL prediction), DeepHPM is introduced to learn implicit dynamics terms and embed them into physics residuals, ensuring consistent modeling across tasks. Additionally, an uncertainty-based adaptive multi-task weighting strategy dynamically balances data loss, dynamics residual loss, and derivative-consistency loss, enhancing training stability and engineering applicability. Cross-protocol validation on the MIT–Stanford–Toyota fast-charging dataset (124 cells) shows: in the SOH task, PIKAN-D achieves RMSPE = 0.240/0.330 and MAE = 0.161/0.206 on #124/#100 (Case 1), outperforming PINN-D (RMSPE = 0.517/0.477); in Case 2 (stronger distribution shift), for cell #108, the RMSPE drops from 1.393 (1DCNN) to 0.699, improving robustness. In the RUL task, for #101 (Case 2), RMSE/MAE reduce from 52.12/40.70 (PINN-D) to 33.14/25.83, validating PIKAN’s effectiveness in cross-cell and multi-protocol scenarios.