MCTSGT: A graph theory-based Monte Carlo tree strategy for configuration search in disordered structures

Crystalline solids, especially ion conductors, often exhibit site-occupancy disorder, including partial occupation of the mobile ion sublattice or mixed occupation of the framework sublattice. The key to predicting physical properties, such as ionic transport barrier, lies in identifying appropriate configurations that can reflect the local features of site-occupancy disorder. However, as supercell size and compositional complexity increase, existing configuration search methods suffer from low search efficiency and insufficient universality. Here, we propose a multi-strategy configuration search method called MCTSGT, where the search space is represented as a tree structure using Monte Carlo Tree Search (MCTS) and equivalent nodes are dynamically pruned using the distance matrix of graph theory (GT) to improve search efficiency. Two alternative search strategies, Warren-Cowley short-range order parameters and configurational ground-state energy, are provided to enhance the adaptability of MCTSGT for different systems. Applied to nine typical disordered structures, MCTSGT achieves a maximum search efficiency improvement of 14% compared to Monte Carlo simulated annealing. Furthermore, energy barriers of obtained configurations via the bond valence site energy (BVSE) method exhibit a consistent trend with experimental studies. Our work provides important insights into machine-learning modeling of disordered structures and contributes to materials discovery across a broader compositional space.