Stochastic Physics-Guided Graph-Liquid Neural Networks for Explainable and RealTime Prognostics of Lithium-Ion Batteries

Reliable and explainable prediction of the Remaining Useful Life (RUL) of lithium-ion batteries is essential for electric vehicles and aerospace systems. Accurate RUL estimation is often hindered by nonlinear degradation behavior, variable operating conditions, and the limited transparency of deep learning models. To address these challenges, a physics-consistent Graph-Liquid Neural Network (GLNN) framework is proposed for real-time battery prognostics. In this framework, capacity degradation is represented as a dynamic graph, where inter-state dependencies are captured through a Graph Neural Network. The nonlinear temporal evolution of degradation is learned adaptively by a Liquid Neural Network with time-varying dynamics. A Wiener-process constraint is incorporated to ensure physical consistency and to improve uncertainty-aware prediction. The model parameters are optimized through joint learning of physical priors and data-driven representations. Two public lithium-ion battery datasets are used to validate the proposed method. Experimental results demonstrate that the GLNN achieves higher prediction accuracy, stronger robustness, and better interpretability compared with state-of-the-art approaches. The physical degradation trend can be effectively preserved, and the prediction uncertainty can be reduced. The results indicate that integrating physics knowledge with adaptive neural reasoning provides a reliable and explainable solution for lithium-ion battery health management under complex and time-varying operating conditions.

Keywords: Remaining Useful Life, Graph-Liquid Neural Network, Physics-Informed Prognostics, Wiener Degradation Process, Lithium batteries.