State-space modeling for electrochemical performance of Li-ion batteries with physics-informed deep operator networks

Online estimation of unobservable internal states is significant for safe operation of Li-ion batteries, and it constitutes one of the main functions of battery management system (BMS). The next-generation BMS expects model-based state estimation, especially with electrochemical models, which are accurate but often costly for solving. Therefore, it is required to build more easily executable state-space representation of electrochemical models for online state estimation. However, the traditional numerical methods for time discretization are relatively complicated, and the discretized system is not very flexible in modifying predictive time intervals. To address such issues, we introduce the concept of physics-informed operator learning for state-space modeling. Specifically, we propose an architecture, termed the physics-informed multiple-input operator network (PIMIONet), to reformulate the state-space representation of the extended single particle (eSP) model. In this work, the PI-MIONet takes the Li-ion concentration of the whole electrode particle and current densities at the current time as the input functions, and predicts Li-ion concentration at any spatial-temporal location, which means that the forward predictions can be realized with user-defined step size. In addition, due to the capability of taking discretized functions as inputs, the PI-MIONet can be used for estimating states in the form of long vectors, and it can be conducted very efficiently, which makes it highly suitable for online applications in BMS. We verify the predictive performance of PI-MIONet through several synthetic experiments, and successfully apply it to the estimation of Li-ion concentration across the full particle with unscented Kalman filter algorithms.