Machine-Learning Accelerated Typical Medium Dynamical Cluster Approximation for Studying Phonon Localization in Real Materials

Anderson localization of lattice vibrations in disordered media has drawn sustained attention because it suppresses thermal transport, with direct implications for thermoelectric energy harvesting and phononic computing. Despite substantial progress, modeling phonon localization with realistic materials features remains challenging. Within the effective-medium framework, we recently developed a multi-branch cluster Dynamical Cluster Approximation (DCA) and its typical-medium variant, the Typical-Medium DCA (TMDCA), which uses the typical density of states (TDOS) as an order parameter.

However, evaluating the TDOS in realistic simulations is the dominant computational bottleneck. To overcome this, we introduce a machine-learning surrogate that accelerates TMDCA for realistic binary alloys. We generate training data from converged TMDCA calculations and train a dense neural network to predict the TDOS from the same inputs used in the self-consistency loop. The developed framework reproduces TDOS with high fidelity across the parameter space and preserves localization signatures (e.g., vanishing TDOS at the mobility edge). We demonstrate that this machine learning approach can serve as an efficient alternative to direct TDOS calculations, enabling large-scale investigations of phonon localization in real materials.