Search

Graph-based machine learning has reached maturity for crystalline materials, where periodic boundary conditions and fixed unit cells allow efficient message passing and property prediction. Disordered systems—amorphous solids, liquids, glasses, and polymers—represent the next frontier. These materials dominate everyday technologies, from smartphone screens and optical fibers to electrolytes in batteries and structural alloys, yet they lack the translational symmetry that simplifies graph construction in crystals. This review synthesizes exactly 35 peer-reviewed publications from 2017 to 2025 that apply graph-based learning, graph neural networks (GNNs), and related data-driven methods to non-crystalline materials. The selected works span key target journals including npj Computational Materials, Physical Review B, Journal of Chemical Theory and Computation, Machine Learning: Science and Technology, and Physical Review Materials. The review is organized around a taxonomy of five classes of disordered systems: amorphous solids, liquids, glasses (including supercooled liquids), polymers, and crystals with substitutional disorder. It identifies seven core challenges that distinguish disordered systems from crystals: absence of periodic boundaries, variable graph sizes, heterogeneous local atomic environments, the critical role of medium-range order (5–15 Å), dynamic graph evolution in liquids, lack of standardized benchmarks, and prohibitive computational cost for large simulation boxes. Current methodological approaches are grouped into six categories—local descriptors (non-graph), graph pooling for size invariance, multi-scale GNNs, equivariant architectures, temporal GNNs for liquids, and transfer learning from crystal data—each evaluated for strengths, limitations, and empirical performance on properties such as density, elastic moduli, glass-forming ability, relaxation dynamics, and defect identification. Despite notable progress, three persistent gaps remain: limited size transferability across simulation-box lengths, inadequate capture of medium-range structural correlations, and under-development of methods for dynamic properties. By critically analyzing these 35 studies, this review provides a systematic framework for graph-based learning in disordered materials and highlights open problems that must be solved before these techniques can achieve the same reliability and scalability already demonstrated for crystals. The field stands at an inflection point: continued innovation in graph representations and benchmarking will determine whether graph-based methods can fully unlock predictive modeling for the disordered materials that underpin modern technology.