A Machine Learning Framework for Modeling Ensemble Properties of Atomically Disordered Materials

Disorder, though naturally present in experimental samples and strongly influencing a wide range of material phenomena, remains underexplored in first-principles studies due to the computational cost of sampling the large supercell and configurational space. The recent development of machine learning techniques, particularly graph neural networks (GNNs), has enabled the efficient and accurate predictions of complex material properties, offering promising tools for studying disordered systems. In this work, we introduce a computational framework that integrates GNNs with Monte Carlo simulations for efficient calculations of thermodynamic properties and ensemble-averaged functional properties of disordered materials. Using the surface-termination-disordered MXene monolayer \ch{Ti3C2T}$_{2-x}$ as a representative system, we investigate the effect of surface termination disorder involving \ch{-F}, \ch{-O}, and termination vacancies on the electrical and optical conductivity spectra. We find that surface termination disorder affects the temperature dependence of electrical conductivity, inducing a peak close to the order-disorder phase transition temperature that reflects the competition between scattering and electron filling effects of the surface termination groups across the phase transition. In contrast, optical conductivity remains robust to local disorder across a wide temperature range and is governed primarily by the global chemical composition of surface terminations. These results demonstrate the utility of our machine-learning-assisted framework for statistically modeling disorder effects and ensemble properties in complex materials, opening new avenues for future studies of disorder-driven phenomena in systems such as high-entropy alloys and disordered magnetic compounds.