Physics-informed operator learning for real-time battery state estimation

The rapid growth of electric vehicles (EVs) and hybrid electric vehicles (HEVs) has heightened the demand for efficient and safe lithium-ion (Li-ion) battery management systems (BMSs). Accurate state monitoring, such as state of charge (SOC) and state of health (SOH), is essential to prolong battery lifespan and ensure reliable EV performance. Although equivalent circuit models (ECMs) are widely used in BMSs for their simplicity, they provide limited insight into internal battery processes and struggle with high-dynamic applications. Physics-based models, particularly the Doyle-Fuller-Newman (DFN) model, offer a detailed representation of battery behavior, but their complexity demands model order reduction (MOR) for real-time applications. In recent years, deep learning, specifically operator learning techniques like the physics-informed multiple-input operator network (MIONet), has shown promising results in approximating complex partial differential equations (PDEs). In this work, we develop a physics-informed operator learning framework that learns the solution of Fick's law within the Single Particle Model (SPM). Our results demonstrate the superior computational efficiency and accuracy of this approach compared to established MOR methods. Furthermore, we demonstrate the flexibility of the method, which can be seamlessly retrained for different battery chemistries provided that the underlying physics remains unchanged. Finally, we evaluate the framework's effectiveness in SOC estimation tasks by embedding the reduced-order model within an observer, showing its potential to outperform traditional ECM-based methods. This study underscores the promise of operator learning in advancing BMSs development, paving the way for more reliable and efficient battery management in EVs and HEVs applications.