Physics-Informed Operator Learning for Real-Time Battery State Estimation and Health Monitoring

Abstract

The increasing demand for reliable and safe lithium-ion (Li-ion) battery packs in the automotive sector has intensified the need for advanced diagnostics and prognostics capabilities within next-generation Battery Management Systems (BMSs). A key BMS function is the estimation of the battery State of Charge (SOC) and State of Health (SOH), typically achieved through Kalman-based observers that require an explicit state-space representation of the cell. Equivalent Circuit Models (ECMs), while computationally efficient, are fundamentally empirical constructs that offer limited physical insight and poor generalization outside their identification range. Electrochemical Models (EMs), by contrast, capture the underlying reaction kinetics, mass transport, and diffusion processes governing cell behavior, enabling higher fidelity across a broader range of operating conditions at the cost of computational complexity that has, so far, precluded their real-time deployment within BMS observers. This work addresses this barrier by relying on a physicsinformed surrogate of the Single Particle Model (SPM), based on a Multiple-Input Operator Network (MIONet) that directly encodes the SPM governing equations into a compact, real-time-executable state-space representation. The resulting EM-based observer is embedded within an Unscented Kalman Filter (UKF) for the joint estimation of SOC and SOH, where SOH is represented by the Loss of Lithium Inventory (LLI, in moles) augmented to the SPM concentration state. The framework is validated on a high-fidelity Doyle-Fuller-Newman (DFN) plant including electrochemically resolved Solid Electrolyte Interphase (SEI) growth, lithium plating, and loss of active material, simulated in PyBaMM. Six case studies covering Constant Current-Constant Voltage (CC-CV) charges followed by CC and Dynamic Stress Test (DST) discharges at 10◦C, 25◦C, and 40◦C are considered, in which the cell is cycled to its end-of-life (EOL, 80% of initial capacity). Quantitative comparisons against an ECM-based observer with an identical joint-UKF structure show that the EM-based observer consistently delivers lower SOC and SOH Root Mean Square Error (RMSE) and substantially better-calibrated confidence intervals (measured via the Coverage Width-based Criterion, CWC). The largest advantage is observed under highly dynamic load profiles, establishing the proposed approach as a viable pathway toward high-fidelity, real-time diagnosis in next-generation BMSs.