Nested crystal graph neural networks for modeling chemically complex materials

Solid solution crystals, in which lattice sites are partially or fully occupied by multiple atomic species, represent a chemically complex class of materials where atomic-scale disorder strongly governs properties. However, geometric representation learning of such systems remains challenging due to the lack of site uniqueness and the presence of short-range order. Here, we introduce the Nested Crystal Graph Neural Network (NCGNN), a general-purpose and scalable framework that hierarchically integrates local compositional disorder and global structural characteristics via a nested graph architecture. NCGNN enables interpretable predictions without large supercells and outperforms existing models by up to 50 % across diverse solid solutions, ranging from fully random alloys to systems with sublattice structure. Additionally, NCGNN captures both short- and long-range ordering effects and reveals key composition-structure-property insights. Extensive benchmarks demonstrate that NCGNN is a universal framework for chemically disordered crystals, offering new opportunities for data-driven materials discovery.