The proposed Coordination Polyhedron Graph Network (CPGN) is a multi-scale GNN that jointly learns atomic, bond, and coordination-polyhedron representations and outperforms existing state-of-the-art GNN models.
Abstract
Accurate prediction of crystal properties remains a key challenge in computational materials science. While graph neural networks (GNNs) such as CGCNN, MEGNet, ALIGNN, and SchNet have shown strong performance, they primarily represent crystals at the atomic level and implicitly learn local chemical environments through message passing. However, many material properties are governed by coordination polyhedra, the fundamental structural units formed by atoms and their neighboring atoms. To address this limitation, we propose the Coordination Polyhedron Graph Network (CPGN), a multi-scale GNN that jointly learns atomic, bond, and coordination-polyhedron representations. CPGN constructs three coupled graphs: an atom graph encoding elemental and bonding information, a line graph capturing angular interactions, and a coordination polyhedron graph describing Voronoi-derived local environments through corner-, edge-, and face-sharing relationships. Physically meaningful geometric descriptors are incorporated for each polyhedron, while an interleaved message-passing mechanism with bidirectional cross-attention enables effective information exchange across structural levels. Extensive evaluations on the Materials Project, JARVIS-DFT, and QM9 benchmark datasets demonstrate that CPGN outperforms existing state-of-the-art GNN models. It achieves a formation-energy MAE of 0.060 eV/atom and a band-gap MAE of 0.292 eV on the Materials Project, while providing competitive multi-property prediction on JARVIS-DFT and superior HOMO prediction on QM9. The results highlight that explicit modeling of coordination polyhedra improves crystal representation learning and enables accurate, physically interpretable prediction of material properties.
Reliable structure-property modeling is crucial for accelerating materials discovery, where crystal graphs and structure-derived crystallographic descriptions provide complementary geometric and semantic information. Existing multimodal materials models primarily incorporate textual information through post-encoding fusion, latent-space alignment, or attention-based representation interaction mechanisms. However, in most cases, crystallographic semantics are introduced after structural encoding and therefore cannot directly guide the formation of atom-level crystal-graph representations. Here, we present Semantics-Augmented Geometric Encoder Network (SAGE-Net), a flexible multimodal framework that injects description-derived chemical and crystallographic semantics into geometric message passing. SAGE-Net introduces Semantic-Guided Message Passing (SGMP), which gates atom-level updates and enables crystallographic semantics to directly modulate local geometric interactions across multiple graph neural network (GNN) backbones. Across benchmarks covering bandgap, mechanical, transport-related properties, and synthesizability assessment, the SAGE-Net instantiated with different GNN backbones achieves the lowest MAE on eight out of ten JARVIS-DFT regression targets and delivers strong or highly competitive performance against both structure-based and multimodal baselines. For synthesizability assessment, the SAGE-Net demonstrate outstanding classification performance and high recall rates. Interpretability analysis unravels that SAGE-Net effectively captures physically interpretable crystallographic features, viz. space group, dimensionality, polyhedral environments, among others. Together, these results demonstrate SGMP-based SAGE-Net as a general and transferable framework for deeply integrated multimodal materials learning.
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Learning effective molecular representations is crucial for accurate property prediction in AI-aided drug discovery. However, most existing molecular pre-training methods are still primarily based on 2D topological graphs, limiting their ability to exploit 3D geometric information. Moreover, methods that do incorporate 3D geometry often do not distinguish between the roles of atom-centered and bond-centered representations. To address these limitations, we propose GDGraph, a geometryenhanced dual-view framework for molecular representation learning. GDGraph models molecular geometry from two complementary structural perspectives: an atom view for capturing global spatial dependencies and a bond view for modeling local geometric patterns. To support this dual-view design, we introduce a multi-scale geometric feature encoding scheme and a view-specific geometry-aware learning strategy, enabling each view to focus on the geometric dependencies it is best suited to capture. Extensive experiments demonstrate that GDGraph achieves strong and stable performance on molecular property prediction benchmarks, and effectively predicts geometrysensitive quantum chemical properties on the QM9 dataset.
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