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Figure 7. Performance comparison of machine learning models and IGNN model in classification tasks. (A) Comparison of performance
metrics for different models in classification tasks, including Precision, Recall, F1 Score, and micro-average AUC; (B-E) Multi-class ROC
curves for different models, with larger AUC values indicating stronger classification ability. (B) SVM; (C) KNN; (D) XGBoost; (E) IGNN.
IGNN: Intermetallics graph neural network; AUC: Area under the curve; ROC: receiver operating characteristic; SVM: support vector
machine; KNN: K-nearest neighbors; XGBoost: EXtreme gradient boosting.

Overall, this study contributes by proposing a GNN method that is suitable for multi-crystal structure data
modeling, providing a novel computational framework for density prediction in intermetallic compounds.
This research offers significant advancements in the predictive modeling of intermetallic compounds,
facilitating more efficient material design and contributing to the development of high-performance
materials in various industrial applications.

DECLARATIONS
Authors’ contributions
Writing - original draft, software, methodology, formal analysis, data curation: Zhu, D.; Nie, M.; Shang, C.
Writing - review and editing, supervision, project administration, investigation: Wu, H. H.; Gao, J.;
Zhao, H.
Validation, investigation, data collection: Zhu, J.; Zhu, Y.; Wang, S.
Visualization, resources, formal analysis, conceptualization: Zhou, X.; Wang, F.; Wang, B.
Supervision, conceptualization, revision, and finalization of the manuscript: Zhang, C.; Mao, X.

Availability of data and materials
The data that support the findings of this study are available from the corresponding author upon
reasonable request.

Financial support and sponsorship
The present work is supported by the National Natural Science Foundation of China (Nos. 52122408 and
52071023). Wu, H. H. also thanks the financial support from the Fundamental Research Funds for the
Central Universities (University of Science and Technology Beijing, Nos. FRF-TP-2021-04C1 and
06500135). The computing work is supported by USTB MatCom of Beijing Advanced Innovation Center
for Materials Genome Engineering.

Conflicts of interest
Wu, H. H. serves as a Junior Editorial Board Member of Journal of Materials Informatics. However, Wu, H.
H. was not involved in any aspect of the editorial process for this manuscript, including reviewer selection,
manuscript handling, or decision-making. The remaining authors declare that they have no conflicts of
interest.

Ethical approval and consent to participate
Not applicable.

Consent for publication
Not applicable.

Copyright
© The Author(s) 2025.