Data-Driven Performance Prediction of Lead–Carbon Batteries: Integrating Experimental Validation and Reduced-Order Model-Guided Neural Networks

Accurate and efficient prediction of battery degradation is essential for optimizing energy storage system design and control. This study introduces a hybrid modeling framework that combines reduced-order modeling (ROM) insights with experimentally validated deep neural networks (DNNs) to predict degradation in lead–carbon (PbC) batteries. Using voltage–capacity profiles from 258 experimental charge/discharge cycles, we extract four physically meaningful input features—cycle number, capacity, charge voltage, and discharge voltage—to train a ROM-guided DNN surrogate. The model predicts two key health indicators: capacity retention (CapRet) and end-of-discharge voltage (EoDV). It generalizes well across five scenario types, including extrapolated conditions up to 700 cycles and varying voltage/capacity inputs. Predictions remain smooth and physically consistent, with validation yielding R² > 0.99 and low MSE. In terms of computational performance, the DNN achieves sub-second inference (~ 0.02 s), offering over five orders of magnitude speedup compared to full COMSOL simulations (~ 25 h), and ~ 1000× faster than ROM (~ 22 s). This enables rapid scenario testing and real-time diagnostics. The proposed framework provides a scalable and interpretable solution for battery performance forecasting, well-suited for deployment in digital twins, battery management systems, and advanced energy storage design workflows.