A Physics-Regularized Neural Network and Kirchhoff Markov Random Field Framework for Inferring Internal Electrochemical States from Operando Spectromicroscopy

TL;DR

This paper presents a physics-regularized neural network combined with a Kirchhoff Markov random field framework to infer internal electrochemical states in lithium-ion batteries from operando spectromicroscopy data, enabling visualization of internal transport phenomena.

Contribution

The study introduces a novel integrated analysis pipeline that combines physics-regularized neural networks and Kirchhoff-based Markov random fields for internal state estimation in LIBs.

Findings

Successfully estimated internal SOC and electrolyte concentration distributions.

Revealed distinct reaction propagation behaviors dependent on electrolyte concentration.

Qualitatively matched inferred electrolyte distributions with independent imaging data.

Abstract

Quantitative understanding of coupled reaction and transport processes in lithium-ion battery (LIB) composite electrodes remains challenging because key internal states cannot be measured directly. In this study, we develop a physics-integrated, data-driven analysis pipeline to estimate internal electrochemical states from operando microscopic X-ray absorption fine structure ($\mu$-XAFS) hyperspectral data of LIB cathodes with LiPF$_6$ electrolyte. State-of-charge (SOC) maps are first constructed from Co K-edge spectra. To resolve ambiguities in the two-phase reaction region, a physics-regularized three-layer neural network is introduced, enforcing spatial continuity of SOC and current conservation. The inferred SOC dynamics are then incorporated into a Kirchhoff-based Markov random field framework that integrates Kirchhoff's current and voltage laws, Ohm's law, and a symmetric Butler-Volmer relation to estimate interfacial current, ionic current, electrolyte potential, and effective ionic conductivity. Application to composite electrodes with different initial electrolyte concentrations (0.3, 1, and 2M LiPF$_6$) reveals distinct reaction propagation behaviors governed by electrolyte concentration-dependent conductivity. The inferred electrolyte concentration distributions show qualitative agreement with independent operando X-ray transmission imaging performed on LIB composite cathodes employing a LiAsF$_6$ electrolyte. This framework enables quantitative visualization of otherwise inaccessible internal transport phenomena.