A Joint Multi-Physics-Constrained Physics-Informed Neural Network and Adaptive Extended Kalman Filter Method for State-of-Charge Estimation of Lithium-Ion Batteries

We propose a two-stage joint estimation method combining a multi-physics-constrained physics-informed neural network (PINN) with an adaptive extended Kalman filter (AEKF) for lithium-ion battery state-of-charge (SOC) estimation. Three constraints—an RC polarization dynamics ODE residual, discharge voltage–SOC monotonicity, and terminal-voltage physical bounds—are embedded into the PINN loss function; the converged network then serves as the nonlinear observation model within the AEKF. On LG 18650HG2 cells across six temperatures (−20 to 40 °C) under a strict cross-condition setup (training on LA92/UDDS; testing on US06 and two mixed profiles), the method maintains a temperature-averaged SOC mean absolute error (MAE) of 2.33% (1.54–4.48%, three random seeds), whereas the MAE for the equivalent circuit model with the AEKF (ECM-AEKF) degrades to 9.46% and 11.66% at −20 °C and −10 °C, and remains 1.5–4.6× worse with the per-temperature re-identified parameters; an end-to-end long short-term memory (LSTM) baseline averages 1.90% but degrades to a per-condition maxima of 22.6% at low temperatures. Multi-seed ablations locate the constraints’ value in providing low-temperature stability and physical consistency, with the RC-ODE constraint contributing most. The study further reveals that goodness of terminal-voltage fit does not imply SOC accuracy; the controlled comparisons trace this to the model structure rather than parameter settings, exposing the risk of voltage-fitting-based evaluation over wide temperature ranges.