Differential Equation-Informed Neural Networks for State-of-Charge Estimation

State-of-charge (SOC) estimation is crucial for improving the safety, reliability, and performance of the battery. Neural networks-based methods for battery SOC estimation have received extensive attention due to the flexibility and applicability. However, owing to complicated electrochemical dynamics and multiphysics coupling, a trivial, black-box emulation of batteries that senses only voltage, current, and surface temperature obviously cannot result in high-performance SOC estimation. To address this problem, this article proposes a class of differential equation-informed neural networks (DENNs) including differential equation-informed multilayer perception (DE-MLP), differential equation-informed recurrent neural network (DE-RNN), and differential equation-informed long short-term memory (DE-LSTM), to estimate battery SOC. In the proposed methods, the underlying physical laws in the form of the differential equation are embedded in the training of neural networks, such that the network parameters are updated toward optimal faster. We also implement an inverse problem in DENNs, which simultaneously estimates the unknown parameters of the differential equation and network parameters. In addition, the approximation theory and error analysis for DENNs are provided. The experiments in this article are performed in real datasets, and the results illustrate the effectiveness of the proposed methods under different working conditions. Compared with the traditional neural networks, the proposed DENNs achieve more stable and accurate SOC estimation performance.