Time-resolved classification of plasma crystals in a direct current discharge using an advanced graph neural network

Abstract The formation and classification of crystalline structures in complex plasmas is an interesting topic in plasma physics, particularly under dynamic conditions such as microgravity. While previous work has largely focused on well-ordered cubic structures, the identification of more complex symmetries remains challenging, especially in noisy experimental data. In this study, we present an SE(3)-equivariant graph neural network capable of classifying a broad range of plasma crystal symmetries, including face-centered cubic, hexagonal close-packed, body-centered cubic, face-centered orthorhombic, body-centered orthorhombic, and body-centered tetragonal. SE(3) denotes the Special Euclidean group in three dimensions, comprising all rotations and translations. SE(3) Transformers use attention-based, equivariant message passing on graphs so that learned features (scalars, vectors, higher-order tensors) respect 3D symmetry. This property is crucial for classifying crystals because orientation and translation should not change the predicted class. Our model combines equivariant message passing with Voronoi-based shape descriptors to capture both local geometric features and global symmetries. It is trained on synthetic datasets and validated against experimental data from PK-4 under laboratory and microgravity conditions. The network significantly outperforms previous approaches such as WignerNet_PointNet, particularly on non-cubic structures. Time-resolved analysis reveals how crystal formation depends sensitively on external parameters such as gas pressure and polarity-switching frequency. Under microgravity, crystalline phases appear less frequently, which we attribute to reduced particle compression and altered spatial confinement. Overall, the results highlight the effectiveness of symmetry-aware machine learning models in capturing structural complexity in physical systems. The method enables accurate classification of ordered structures and provides a powerful tool for investigating phase behavior in complex plasmas.