Efficient Classification Method for Topological Quantum Materials Based on Graph Neural Networks and Persistent Homology Theory

Main Article Content

Yuanyuan Xu
School of Physics and Technology, Wuhan University, China

DOI: https://doi.org/10.70267/cai.25v2n2.5365

Keywords

topological quantum materials, graph isomorphism networks (GIN), atomic-specific persistent homology (ASPH), XGBoost classification

Abstract

Topological quantum materials hold considerable promise for applications in quantum computing and spintronic devices due to their unique electronic properties. However, traditional Density Functional Theory (DFT) methods encounter difficulties in predicting these topological properties, including high computational costs and classification errors. This study proposes a machine learning framework that combines Graph Isomorphism Networks (GIN) with Atomic-Specific Persistent Homology (ASPH) to achieve efficient classification of topological materials by integrating global crystal structure features with local atomic topological descriptors. GIN is used to capture the global graph representation of periodic crystal structures, while ASPH extracts local features of atomic environments through multiscale topological analysis. These two feature sets are integrated following dimensionality reduction and subsequently classified using XGBoost. Principal Component Analysis (PCA) was employed to reduce the dimensionality of the high-dimensional ASPH feature vectors, thereby enhancing both model efficiency and accuracy. Experimental results indicate that this method performs exceptionally well in binary classification (topologically trivial/non-trivial), achieving an accuracy of 87.32%, which is significantly better than models based on a single feature. However, performance in ternary classification (trivial, semi-metal, topological insulator) declines to 75.04% due to class imbalance and feature overlap. The study validates the feasibility of combining graph neural networks with topological data analysis, providing an efficient computational framework for high-throughput screening of topological materials and offering new ideas for the application of multimodal feature fusion in materials science.

Abstract 15 | PDF Downloads 14

References

  • Armitage, N. P., Mele, E. J., & Vishwanath, A. (2018). Weyl and dirac semimetals in three-dimensional solids. Reviews of Modern Physics, 90(1), Article 015001. https://doi.org/10.1103/REVMODPHYS.90.015001
  • Blaha, P., Schwarz, K., Tran, F., Laskowski, R., Madsen, G. K. H., & Marks, L. D. (2020). WIEN2k: An APW+lo program for calculating the properties of solids. The Journal of Chemical Physics, 152(7), Article 074101. https://doi.org/10.1063/1.5143061
  • Bradlyn, B., Elcoro, L., Cano, J., Vergniory, M. G., Wang, Z., Felser, C., Aroyo, M. I., & Bernevig, B. A. (2017). Topological quantum chemistry. Nature, 547(7663), 298-305. https://doi.org/10.1038/NATURE23268
  • Bramer, D., & Wei, G.-W. (2020). Atom-specific persistent homology and its application to protein flexibility analysis. Computational and Mathematical Biophysics, 8(1), 1-35. https://doi.org/10.1515/CMB-2020-0001
  • Cang, Z., & Wei, G. W. (2018). Integration of element specific persistent homology and machine learning for protein-ligand binding affinity prediction. International Journal for Numerical Methods in Biomedical Engineering, 34(2), Article e2914. https://doi.org/10.1002/CNM.2914
  • Chen, C., Ye, W., Zuo, Y., Zheng, C., & Ong, S. P. (2019). Graph networks as a universal machine learning framework for molecules and crystals. Chemistry of Materials, 31(9), 3564-3572. https://doi.org/10.1021/ACS.CHEMMATER.9B01294
  • de Jong, M., Chen, W., Notestine, R., Persson, K., Ceder, G., Jain, A., Asta, M., & Gamst, A. (2016). A statistical learning framework for materials science: Application to elastic moduli of k-nary inorganic polycrystalline compounds. Scientific Reports, 6(1), Article 34256. https://doi.org/10.1038/SREP34256
  • Fung, V., Zhang, J., Juarez, E., & Sumpter, B. G. (2021). Benchmarking graph neural networks for materials chemistry. npj Computational Materials, 7(1), Article 84. https://doi.org/10.1038/S41524-021-00554-0
  • Giustino, F., Lee, J. H., Trier, F., Bibes, M., Winter, S. M., Valentí, R., Son, Y.-W., Taillefer, L., Heil, C., Figueroa, A. I., Plaçais, B., Wu, Q., Yazyev, O. V., Bakkers, E. P. A. M., Nygård, J., Forn-Díaz, P., De Franceschi, S., McIver, J. W., Torres, L. E. F. F., Low, T., Kumar, A., Galceran, R., Valenzuela, S. O., Costache, M. V., Manchon, A., Kim, E.-A., Schleder, G. R., Fazzio, A., & Roche, S. (2020). The 2021 quantum materials roadmap. Journal of Physics: Materials, 3(4), Article 042006. https://doi.org/10.1088/2515-7639/ABB74E
  • Halász, G. B., & Balents, L. (2012). Time-reversal invariant realization of the weyl semimetal phase. Physical Review B, 85(3), Article 035103. https://doi.org/10.1103/PHYSREVB.85.035103
  • Hasan, M. Z., & Kane, C. L. (2010). Colloquium: Topological insulators. Reviews of Modern Physics, 82(4), 3045-3067. https://doi.org/10.1103/REVMODPHYS.82.3045
  • He, Y., De Breuck, P.-P., Weng, H., Giantomassi, M., & Rignanese, G.-M. (2025). Machine learning on multiple topological materials datasets. npj Computational Materials, 11(1), Article 181. https://doi.org/10.1038/S41524-025-01687-2
  • Jain, A., Ong, S. P., Hautier, G., Chen, W., Richards, W. D., Dacek, S., Cholia, S., Gunter, D., Skinner, D., Ceder, G., & Persson, K. A. (2013). Commentary: The materials project: A materials genome approach to accelerating materials innovation. APL Materials, 1(1), Article 011002. https://doi.org/10.1063/1.4812323
  • Janotti, A., & Van de Walle, C. G. (2009). Fundamentals of zinc oxide as a semiconductor. Reports on Progress in Physics, 72(12), Article 126501. https://doi.org/10.1088/0034-4885/72/12/126501
  • Jha, D., Choudhary, K., Tavazza, F., Liao, W.-k., Choudhary, A., Campbell, C., & Agrawal, A. (2019). Enhancing materials property prediction by leveraging computational and experimental data using deep transfer learning. Nature Communications, 10(1), Article 5316. https://doi.org/10.1038/S41467-019-13297-W
  • Jiang, Y., Chen, D., Chen, X., Li, T., Wei, G.-W., & Pan, F. (2021). Topological representations of crystalline compounds for the machine-learning prediction of materials properties. npj Computational Materials, 7(1), 28-28. https://doi.org/10.1038/S41524-021-00493-W
  • Moore, J. E. (2010). The birth of topological insulators. Nature, 464(7286), 194-198. https://doi.org/10.1038/NATURE08916
  • Otter, N., Porter, M. A., Tillmann, U., Grindrod, P., & Harrington, H. A. (2017). A roadmap for the computation of persistent homology. EPJ Data Science, 6(1), Article 17. https://doi.org/10.1140/EPJDS/S13688-017-0109-5
  • Peano, V., Sapper, F., & Marquardt, F. (2021). Rapid exploration of topological band structures using deep learning. Physical Review X, 11(2), Article 021052. https://doi.org/10.1103/PHYSREVX.11.021052
  • Perdew, J. P., Burke, K., & Ernzerhof, M. (1996). Generalized gradient approximation made simple. Physical Review Letters, 77(18), 3865-3868. https://doi.org/10.1103/PHYSREVLETT.77.3865
  • Qi, X. L., & Zhang, S. C. (2011). Topological insulators and superconductors. Reviews of Modern Physics, 83(4), 1057-1110. https://doi.org/10.1103/REVMODPHYS.83.1057
  • Raccuglia, P., Elbert, K. C., Adler, P. D. F., Falk, C., Wenny, M. B., Mollo, A., Zeller, M., Friedler, S. A., Schrier, J., & Norquist, A. J. (2016). Machine-learning-assisted materials discovery using failed experiments. Nature, 533(7601), 73-76. https://doi.org/10.1038/NATURE17439
  • Rasul, A., Hossain, M. S., Dastider, A. G., Roy, H., Hasan, M. Z., & Khosru, Q. D. M. (2024). A machine learning based classifier for topological quantum materials. Scientific Reports, 14(1), 31564-31564. https://doi.org/10.1038/S41598-024-68920-8
  • Soumyanarayanan, A., Reyren, N., Fert, A., & Panagopoulos, C. (2016). Emergent phenomena induced by spin-orbit coupling at surfaces and interfaces. Nature, 539(7630), 509-517. https://doi.org/10.1038/NATURE19820
  • Stanev, V., Oses, C., Kusne, A. G., Rodriguez, E., Paglione, J., Curtarolo, S., & Takeuchi, I. (2018). Machine learning modeling of superconducting critical temperature. npj Computational Materials, 4(1), Article 29. https://doi.org/10.1038/S41524-018-0085-8
  • Tao, Q., Xu, P., Li, M., & Lu, W. (2021). Machine learning for perovskite materials design and discovery. npj Computational Materials, 7(1), Article 23. https://doi.org/10.1038/S41524-021-00495-8
  • Tran, F., & Blaha, P. (2009). Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential. Physical Review Letters, 102(22), Article 226401. https://doi.org/10.1103/PHYSREVLETT.102.226401
  • Vergniory, M. G., Elcoro, L., Felser, C., Regnault, N., Bernevig, B. A., & Wang, Z. (2019). A complete catalogue of high-quality topological materials. Nature, 566(7745), 480-485. https://doi.org/10.1038/S41586-019-0954-4
  • Vergniory, M. G., Wieder, B. J., Elcoro, L., Parkin, S. S. P., Felser, C., Bernevig, B. A., & Regnault, N. (2022). All topological bands of all nonmagnetic stoichiometric materials. Science, 376(6595), Article eabg9094. https://doi.org/10.1126/SCIENCE.ABG9094
  • Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C., & Yu, P. S. (2021). A comprehensive survey on graph neural networks. IEEE Transactions on Neural Networks and Learning Systems, 32(1), 4-24. https://doi.org/10.1109/TNNLS.2020.2978386
  • Xia, K., Feng, X., Tong, Y., & Wei, G. W. (2015). Persistent homology for the quantitative prediction of fullerene stability. Journal of Computational Chemistry, 36(6), 408-422. https://doi.org/10.1002/JCC.23816
  • Xie, T., & Grossman, J. C. (2018). Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties. Physical Review Letters, 120(14), Article 145301. https://doi.org/10.1103/PHYSREVLETT.120.145301
  • Xu, K., Jegelka, S., Hu, W., & Leskovec, J. (2019). How powerful are graph neural networks? arXiv preprint, arXiv:1810.00826. https://doi.org/10.48550/arXiv.1810.00826
  • Xue, D., Balachandran, P. V., Hogden, J., Theiler, J., Xue, D., & Lookman, T. (2016). Accelerated search for materials with targeted properties by adaptive design. Nature Communications, 7(1), Article 11241. https://doi.org/10.1038/NCOMMS11241
  • Yamamoto, T. (2019). Crystal graph neural networks for data mining in materials science. Research Institute for Mathematical and Computational Sciences. https://www.researchgate.net/profile/Takenori-Yamamoto-2/publication/333667001_Crystal_Graph_Neural_Networks_for_Data_Mining_in_Materials_Science/links/5d008fb8a6fdccd13094038c/Crystal-Graph-Neural-Networks-for-Data-Mining-in-Materials-Science.pdf

Article Sidebar

PDF
Published
Aug 15, 2025
Issue
Vol. 2 No. 2 (2025)
Section
Research Articles
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Xu, Y. (2025). Efficient Classification Method for Topological Quantum Materials Based on Graph Neural Networks and Persistent Homology Theory. Computers and Artificial Intelligence, 2(2), 53-65. https://doi.org/10.70267/cai.25v2n2.5365