Fractional Differential Equation Physics-Informed Neural Network and Its Application in Battery State Estimation

Accurate estimation of the State of Charge (SOC) is critical for ensuring the safety, reliability, and performance optimization of lithium-ion battery systems. Conventional data-driven neural network models often struggle to fully characterize the inherent complex nonlinearities and memory-dependent dynamics of electrochemical processes, significantly limiting their predictive accuracy and physical interpretability under dynamic operating conditions. To address this challenge, this study proposes a novel neural architecture termed the Fractional Differential Equation Physics-Informed Neural Network (FDIFF-PINN), which integrates fractional calculus with deep learning. The main contributions of this paper include: (1) Based on a fractional-order equivalent circuit model, a discretized fractional-order partial differential equation is constructed. (2) Comparative experiments were conducted using a dynamic charge/discharge dataset of Panasonic 18650PF batteries under multi-temperature conditions (from -10$^{\circ}$C to 20$^{\circ}$C).

Gate Recurrent Unit Network based on Hilbert-Schmidt Independence Criterion for State-of-Health Estimation

State-of-health (SOH) estimation is a key step in ensuring the safe and reliable operation of batteries. Due to issues such as varying data distribution and sequence length in different cycles, most existing methods require health feature extraction technique, which can be time-consuming and labor-intensive. GRU can well solve this problem due to the simple structure and superior performance, receiving widespread attentions. However, redundant information still exists within the network and impacts the accuracy of SOH estimation. To address this issue, a new GRU network based on Hilbert-Schmidt Independence Criterion (GRU-HSIC) is proposed. First, a zero masking network is used to transform all battery data measured with varying lengths every cycle into sequences of the same length, while still retaining information about the original data size in each cycle. Second, the Hilbert-Schmidt Independence Criterion (HSIC) bottleneck, which evolved from Information Bottleneck (IB) theory, is extended to GRU to compress the information from hidden layers. To evaluate the proposed method, we conducted experiments on datasets from the Center for Advanced Life Cycle Engineering (CALCE) of the University of Maryland and NASA Ames Prognostics Center of Excellence. Experimental results demonstrate that our model achieves higher accuracy than other recurrent models.