Tracking the Lithiation State of Li$_x$Si from Machine-Learned XPS Binding Energies
X-ray Photoelectron Spectroscopy (XPS) is a powerful technique to probe chemical states and interfacial processes in battery materials, but a quantitative interpretation is often hindered by the complex, heterogeneous microstructures that form during operation and dominate electrochemical cycling. Silicon based anodes represent a paradigmatic example in Li batteries, as (de)lithiation proceeds through the formation of strongly disordered Li$_x$Si phases and crystal-amorphous transformations that are hard to characterize. Here, we introduce a computational framework that combines machine-learning (ML) prediction of core-level binding energies to large-scale atomistic simulations -- Grand Canonical Monte Carlo (GCMC) complemented with molecular dynamics (MD), driven by a ML potential -- for a systematic sampling of lithiation states and local atomic environments. This approach yields stoichiometry maps that match the characteristic experimental trends observed in operando and ex situ XPS measurements, including the distinctive Si $2p$ spectroscopic signatures associated with the crystal-to-amorphous disordering driving early delithiation.