Weibull Distribution-Informed Neural Networks (WDINNs): a probabilistic framework for enhanced degradation prediction in LIBs

Lithium-ion batteries (LIBs) are widely used in modern energy systems due to their high energy density and long service life. Accurate estimation of their remaining useful life (RUL) is essential for enhancing system reliability, optimizing maintenance strategies, and minimizing costs. In this work, battery degradation is inferred from voltage signal behavior, which serves as a reliable non-invasive indicator of aging. We propose a novel model called Weibull Distribution-Informed Neural Network (WDINN), which integrates the probabilistic characteristics of the Weibull distribution into a physics-informed deep learning framework. This approach addresses both the non-linear and stochastic nature of battery degradation. To train and validate the model, degradation profiles were extracted from aging datasets and reference performance testing (RPT) data. The WDINN model demonstrated superior performance compared to several state-of-the-art models, including Bi-LSTM, GRU, and ANN. It achieved an RMSE of 0.00027 ± 0.00003 on the aging dataset. Cluster-based evaluation further revealed that WDINN performs particularly well in scenarios of slow, long-term degradation (e.g., Cluster 0), achieving a test loss of 0.00018 ± 0.00001, while maintaining robustness across more variable short-term degradation patterns in the RPT data. This research introduces a robust and interpretable framework that enhances predictive accuracy, enables uncertainty modeling, and advances practical battery health estimation for reliable energy storage systems.