CGformer: A Global‑Attention AI Model that Outperforms CGCNN in Material Design

AI‑enhanced crystal graph network for high‑entropy materials

Traditional crystal graph neural networks (CGCNN, ALIGNN) rely on local message passing, limiting their ability to capture long‑range atomic interactions required for accurate property prediction of complex, high‑entropy crystals.

CGformer architecture

CGformer combines the Graphormer global multi‑head attention mechanism with the crystal‑graph representation of CGCNN. Key components:

Graphormer‑style global attention allowing each atom node to attend to all other nodes.

Centrality encoding (in‑degree/out‑degree) merged into node features.

Spatial encoding that distinguishes relative positions of neighboring atoms.

Pooling and activation layers that aggregate global information for final property prediction.

The crystal‑graph encoder converts a 3‑D crystal structure into nodes (atoms) and edges (bonds) and extracts attributes such as element type, charge, covalent radius, inter‑atomic distance, bond type and symmetry. These features form the input to CGformer.

Dataset construction for high‑entropy Na solid electrolytes

Three complementary datasets were built to address data scarcity:

Na‑ion diffusion barrier (E_b) pre‑training set : Largest known collection of Na‑ion diffusion barriers for high‑entropy structures, generated with Voronoi‑based crystal analysis (CAVD) and Bond Valence Site Energy (BVSE) methods.

HE‑NSE computational set : Starting from Na₃Zr₂Si₂PO₁₂, 45 dopant elements were considered, yielding 148,995 candidate structures. After removing radioactive, highly toxic, or expensive elements and applying radius‑difference and charge‑balance constraints, 826 stable structures remained. Unsupervised hierarchical clustering divided them into 20 groups; 30 % of each group (238 structures) were selected for DFT calculation of E_b.

Thermal‑stability set : Extracted from the Materials Project, containing Na‑containing structures with energies above the convex hull, used to train a supplementary model that evaluates thermodynamic stability.

Performance evaluation

CGformer was benchmarked against CGCNN, ALIGNN and SchNet in both pre‑training and fine‑tuning stages.

Pre‑training : 10‑fold cross‑validation yielded an average MAE of 0.1703, a 25.7 % improvement over CGCNN. Test‑set MAE was 0.3205, nearly 10 % lower than CGCNN. Residuals were tighter around zero with a smaller standard deviation.

Fine‑tuning : After 200 fine‑tuning epochs, 10‑fold CV MAE dropped to 0.0361. Predicted values deviated from DFT references by –0.05 to 0.05, following a near‑normal distribution, indicating high precision for high‑entropy systems.

Experimental validation

Six optimal HE‑NSEs selected by the trained model were synthesized and electrochemically characterized. Room‑temperature Na‑ion conductivities ranged from 0.093 to 0.256 mS cm⁻¹, markedly higher than undoped Na₃Zr₂Si₂PO₁₂.

References

CGformer: Transformer‑enhanced crystal graph network with global attention for material property prediction, Matter. URL: https://www.cell.com/matter/abstract/S2590-2385(25)00423-0