Lithium-ion battery degradation modelling using universal differential equations: Development of a cost-effective parameterisation methodology

The accuracy and reliability of physics-based lithium-ion battery degradation models are limited by incomplete understanding of degradation mechanisms. This article presents Universal Differential Equations (UDE) based degradation modelling, which integrates neural networks into physics-based model differential equations to learn partially understood degradation mechanisms. Therefore, this approach combines the function approximation capabilities of machine learning with the interpretability of physics-based models. However, the widespread adoption of this methodology is hindered by the high cost of training neural networks placed within a physics-based degradation model. To address this, we propose a cost-effective parameterisation method that exploits the large difference between electrochemical and degradation time scales, to speed up the gradient calculation using the continuous adjoint sensitivity analysis. Additionally, efficient scaling of this method to multiple ageing datasets is ensured through mini-batching. Finally, we demonstrate this approach by developing a novel UDE calendar ageing model and validating it against in-house experimental data covering 39 storage conditions (13 states of charge at 0 °C, 25 °C, and 45 °C). The predictions on full cell capacity and loss of active material (LAM) at negative electrode align well with experimental observations with an average RMSE of 0.66% and 1.11% respectively, which was a significant improvement over the baseline physics-based model.