Physics-informed neural networks combined with SVR for battery health and charge state diagnostics

Precise determination of battery state of charge (SoC) and state of health (SoH) is a key factor in providing safe, reliable, and long-term performance of lithium-ion batteries in electric vehicles and energy storage devices. However, nonlinear electrochemical behaviour, sensor noise, voltage variations, and cycle-dependent degradation make precise state estimation challenging for purely data-driven or purely physics-based methods. This study proposes a deterministic hybrid estimation framework for the SoC and SoH prediction by integrating physics-informed neural networks (PINNs) with machine learning models. The proposed architecture combines a PINN, which enforces charge- conservation consistency through coulomb counting-grounded loss functions, and a support vector regression (SVR) model, that performs deterministic residual learning to correct non-linearities and measurement noise. The framework adopts a two- stage learning process in which the PINN first estimates physically consistent SoC trajectories, followed by SVR-based residual refinement. SoH is subsequently derived from SoC- consistent capacity degradation, forming a unidirectional SoC-SoH diagnostic pipeline. The framework is evaluated using four lithium-ion battery datasets (B0007, B0025, B0028, and B0036) available in the NASA data repository and compared with the traditional machine learning and deep learning models, such as LSTM, GRU, Bi-LSTM, Ind-RNN, PINN, and SVR. Experimental results indicate stable cycle-to-cycle SoC tracking, bias-free and tighter residual distributions, and improved predictive accuracy with reduced MAE and RMSE compared to individual models. The proposed framework produces smooth and physically consistent SoH degradation trajectories across the evaluated cells. With offline training and lightweight online inference, the framework is suitable for real- time deployment in battery management systems.