Coupling a capacity fade model with machine learning for early prediction of the battery capacity trajectory

Early prediction of battery capacity degradation, including both the end of life and the entire degradation trajectory, can accelerate aging-focused manufacturing and design processes. However, most state-of-the-art research on early capacity trajectory prediction focuses on developing purely data-driven approaches to predict the capacity fade trajectory of cells, which sometimes leads to overconfident models that generalize poorly. This work investigates three methods of integrating empirical capacity fade models into a machine learning framework to improve the model's accuracy and uncertainty calibration when generalizing beyond the training dataset. A critical element of our framework is the end-to-end optimization problem formulated to simultaneously fit an empirical capacity fade model to estimate the capacity trajectory and train a machine learning model to estimate the parameters of the empirical model using features from early-life data. The proposed end-to-end learning approach achieves prediction accuracies of less than 2 % mean absolute error for in-distribution test samples and less than 4 % mean absolute error for out-of-distribution samples using standard machine learning algorithms. Additionally, the end-to-end framework is extended to enable probabilistic predictions, demonstrating that the model uncertainty estimates are appropriately calibrated, even for out-of-distribution samples.