Abstract
Despite the effectiveness of most graph-based representation methods in capturing the crystal geometry characteristics, they fall short in intuitively describing phenomena such as ionic transport behavior which are often determined by the atom-unoccupied regions in the mobile sublattice (namely interstitial network). Here, we develop a Structure Divide-and-Conquer Graph Representation method based on graph neural network (SDCGNNdk), for unveiling structure-activity relationships of transport barriers by incorporating Domain Knowledge (e.g., site energy information, thresholds for ion accessibility, etc.), where crystal geometry and interstitial network topology are combined to construct a dual-structure crystal graph. For driving the proposed model, we construct a graph-based dataset for the prediction of activation energy (\({E}_{a}\)), i.e., the energy barrier hindering ionic transport, covering over 18,000 ionic compounds from the Inorganic Crystal Structure Database (ICSD), including Li+, Na+, K+, Ag+, Cu(2,3)+, Mg2+, Zn2+, Ca2+, Al3+, Fâ, and O2â. SDCGNNdk achieves high prediction performance of \({E}_{{\rm{a}}}\) with R2 of 91.30%, outperforming conventional GNNs by more than 20% on average and offering insights into structure-activity relationships by quantifying the contributions of crystal geometry and interstitial network characteristics to transport barriers. This work provides an accurate graph representation and GNN framework, demonstrating potential for extension to predicting other properties relevant to interstitial network of inorganic compounds.
Data availability
The data that support the findings of this study are not openly available due to reasons of sensitivity and are available from the corresponding author upon reasonable request.
Code availability
The code and training configurations for SDCGNN and comparative models, as well as the result plotting scripts, are available on GitHub at https://github.com/ZHW-YANN/SDCGNN-DK.git.
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Acknowledgements
Y.L. acknowledges the support by the National Natural Science Foundation of China (92270124) and S.S. acknowledges the support by the National Natural Science Foundation of China (92472207). We acknowledge the High Performance Computing Center of Shanghai University and the Shanghai Engineering Research Center of Intelligent Computing System for providing computing resources and technical support.
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Y.L. and Z.Y. conceived and designed the project. Z.Y. and L.W. developed and implemented the algorithms under the guidance of Y.L. and S.S. Z.Y., L.W. and M.A. collected the datasets. Z.Y. and L.W. conducted the experiments, data analysis and method comparisons. Z.Y. and L.W. drew the figures and wrote the manuscript, with the guidance of Y.L. and S.S. M.A., Y.L. and S.S. finalized the manuscript and figures. S.S. and B.H. support domain knowledge of materials science and computer science. S.S, Y.L. and M.A. gave suggestions on improving the manuscript. All of the authors reviewed and approved the manuscript.
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Yang, Z., Wu, L., He, B. et al. Structure divide-and-conquer: dual graph representation for accurate ionic transport barrier prediction of inorganic compounds. npj Comput Mater (2026). https://doi.org/10.1038/s41524-026-02058-1
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DOI: https://doi.org/10.1038/s41524-026-02058-1
