A Physics-Regularized Neural Network and Kirchhoff Markov Random Field Framework for Inferring Internal Electrochemical States from Operando Spectromicroscopy
Quantitative understanding of coupled reaction-transport dynamics in lithium-ion battery (LIB) composite electrodes is limited by the inaccessibility of key internal electrochemical states. Here we present a physics-integrated, data-driven framework to reconstruct latent states from operando microscopic X-ray absorption fine structure ($μ$ -XAFS) hyperspectral data of LIB cathodes. Normalized-local-lithium-stoichiometry (NLLS) maps derived from Co K-edge spectra are refined using a physics-regularized neural network that enforces spatial continuity and current conservation to resolve ambiguities in the weak-sensitivity region. The reconstructed NLLS dynamics are embedded in a Kirchhoff-based Markov random field incorporating Kirchhoff's laws, Ohm's law, and Butler-Volmer kinetics to infer interfacial current density, ionic current, electrolyte potential, and effective ionic conductivity. Application to electrodes with differential initial electrolyte concentrations reveals distinct reaction-propagation modes that are consistent with a mechanism involving the non-monotonic concentration dependence of electrolyte conductivity. The inferred electrolyte concentration profiles qualitatively resemble the spatially extended concentration changes observed by independent operando X-ray transmission imaging using a 1 M LiAsF$_6$ electrolyte.