Learning chemical potentials and parameters from voltage data for multi-phase battery modeling

Phase transition is a crucial phenomenon in many battery chemistries, especially for lithium-ion cells based on graphite electrodes. Accurately modeling this phenomenon is important for predicting and optimizing the performance of batteries. Traditional approaches rely on the first-principle derivation of the chemical potential or, more simply, adopt open-circuit potential (OCP) data, often present limited predictive accuracy, and fail to capture the complex free-energy barriers and multi-phase intercalation dynamics. In this work, we introduce a physics-based learning framework, termed Bayesian model-integrated neural networks (BMINN), that infers electrode-specific chemical potentials and Gibbs free energies directly from current-voltage data, without relying on restrictive assumptions about their functional forms. By integrating physics-based equations with Bayesian neural networks, our method uncovers hidden physics while quantifying uncertainties, enabling enhanced robustness and accurate modeling of chemical potentials. Validated by experimental results, the proposed physics-based learning approach outperforms conventional OCP-fitted and porous electrode theory (PET)-based chemical potential models. It successfully captures critical features such as staging structures and energy barriers that govern battery dynamics and phase transitions. Furthermore, we illustrate the utility of accurate chemical potentials in operando X-ray diffraction (XRD) spectra, which provides deeper insights into the dynamics of lithium intercalation in graphite electrodes.