Representation learning of crystal materials using Graph Neural Networks: Passive symmetry challenges and advances

Crystal structures are naturally represented as graphs, making Graph Neural Networks (GNNs) a powerful tool for capturing complex atomic interactions and geometric relationships. This review summarizes recent advances in GNNs-based representation learning for crystal materials, with a specific focus on addressing the critical challenge of passive symmetry. We critically analyze existing frameworks by classifying them into asymmetric and symmetric paradigms, evaluating how they address periodic invariance and geometric completeness through graph construction and architectural design. We also compile key datasets and benchmarks to provide a systematic performance comparison of representative models. Finally, we discuss unresolved challenges, including the trade-off between architectural rigor and computational efficiency, modeling complex non-ideal systems, and predicting high-order tensorial properties, highlighting promising directions for future research.