We consider representation learning on periodic graphs encoding crystal materials. Different from regular graphs, periodic graphs consist of a minimum unit cell repeating itself on a regular lattice in 3D space. How to effectively encode these periodic structures poses unique challenges not present in regular graph representation learning. In addition to being E(3) invariant, periodic graph representations need to be periodic invariant. That is, the learned representations should be invariant to shifts of cell boundaries as they are artificially imposed. Furthermore, the periodic repeating patterns need to be captured explicitly as lattices of different sizes and orientations may correspond to different materials. In this work, we propose a transformer architecture, known as Matformer, for periodic graph representation learning. Our Matformer is designed to be invariant to periodicity and can capture repeating patterns explicitly.

Accurately and comprehensively representing crystal structures is critical for advancing machine learning in large-scale crystal materials simulations, however, effectively capturing and leveraging the intricate geometric and topological characteristics of crystal structures remains a core, long-standing challenge for most existing methods in crystal property prediction. Here, we propose MGT, a multi-view graph transformer framework that synergistically fuses SE3 invariant and SO3 equivariant graph representations, which respectively captures rotation-translation invariance and rotation equivariance in crystal geometries. To strategically incorporate these complementary geometric representations, we employ a lightweight mixture of experts router in MGT to adaptively adjust the weight assigned to SE3 and SO3 embeddings based on the specific target task. Compared with previous state-of-the-art models, MGT reduces the mean absolute error by up to 21% on crystal property prediction tasks through multi-task self-supervised pretraining. Ablation experiments and interpretable investigations confirm the effectiveness of each technique implemented in our framework. Additionally, in transfer learning scenarios including crystal catalyst adsorption energy and hybrid perovskite bandgap prediction, MGT achieves performance improvements of up to 58% over existing baselines, demonstrating domain-agnostic scalability across diverse application domains. As evidenced by the above series of studies, we believe that MGT can serve as useful model for crystal material property prediction, providing a valuable tool for the discovery of novel materials.

Machine learning has become a crucial tool for predicting the properties of crystalline materials. However, existing methods primarily represent material information by constructing multi-edge graphs of crystal structures, often overlooking the chemical and physical properties of elements (such as atomic radius, electronegativity, melting point, and ionization energy), which have a significant impact on material performance. To address this limitation, we first constructed an element property knowledge graph and utilized an embedding model to encode the element attributes within the knowledge graph. Furthermore, we propose a multimodal fusion framework, ESNet, which integrates element property features with crystal structure features to generate joint multimodal representations. This provides a more comprehensive perspective for predicting the performance of crystalline materials, enabling the model to consider both microstructural composition and chemical characteristics of the materials. We conducted experiments on the Materials Project benchmark dataset, which showed leading performance in the bandgap prediction task and achieved results on a par with existing benchmarks in the formation energy prediction task.