Dynamic modeling of lithium-ion battery degradation using data-driven and physics-informed method

Accurate real‑time prediction of lithium‑ion battery (LIB) capacity degradation is essential for embedded battery‑management systems. Equivalent circuit models (ECMs) run quickly but lose accuracy over time, whereas purely data-driven networks achieve high precision at a high computational cost. This study introduces a physics‑informed neural network (PINN) that embeds the differential equations of a first‑order Thevenin ECM directly into the loss function. Using only terminal voltage and current as inputs, the network simultaneously estimates internal resistance, polarization resistance, polarization capacitance, open‑circuit voltage, and capacity loss. The model was trained and evaluated over 300 charge–discharge cycles of a 18650 lithium-ferrous phosphate (LFP) cell. The resulting capacity degradation estimation achieved a root mean squared error (RMSE) of 0.012 and a mean absolute percentage error (MAPE) of 0.974 %, surpassing a neural ordinary differential equation baseline with RMSE of 0.215. The trained network contains 261 parameters, requires 0.6 ms per sample for inference, and consumes 49 MB of memory. This computation cost is far lower than that of a long short‑term memory (LSTM) benchmark with comparable accuracy. In addition, the proposed model maintains its accuracy under limited dataset conditions. With a fourfold smaller training set, the PINN maintained an RMSE of 0.023, whereas the LSTM error increased to 0.72. The results demonstrate that lightweight neural networks guided by physics-based constraints can provide reliable, real-time health estimation on resource‑limited hardware.