In the context of the rapid digitalization of educational systems and the exponential growth of available information, there is an increasing need for intelligent methods to structure knowledge and optimize curricula. Traditional approaches to designing educational trajectories often fail to account for the complex interdependencies between disciplines, skills, and competencies, resulting in reduced learning efficiency and insufficient personalization of the educational process. This study proposes the use of Graph Neural Networks (GNNs) as an effective tool for modeling knowledge structures in digital educational systems. The graph-based approach enables the representation of educational content as a network of interconnected elements, where nodes correspond to concepts or learning modules, and edges represent logical, semantic, or pedagogical relationships. Special attention is given to the development of a curriculum optimization model based on the analysis of knowledge graph structures. The proposed method enables the identification of key nodes, optimization of course sequencing, and adaptation of learning trajectories to individual learner needs. The study examines GNN training algorithms, feature aggregation methods, and information propagation mechanisms within graph structures. The experimental results demonstrate that the application of GNNs significantly improves the quality of educational recommendations, enhances curriculum coherence, and reduces redundancy in learning materials. The evaluation shows an increase in learning efficiency of up to 25% compared to traditional approaches. Thus, Graph Neural Networks represent a promising tool for the intellectualization of educational systems and the development of next-generation adaptive curricula.
T. N. Kipf and M. Welling, “Semi-supervised classification with graph convolutional networks,” in Proceedings of the International Conference on Learning Representations (ICLR), 2017.
P. Brusilovsky and E. Millán, “User models for adaptive hypermedia and adaptive educational systems,” in P. Brusilovsky, A. Kobsa, and W. Nejdl (eds.), The Adaptive Web, Berlin: Springer, pp. 3-53, 2007.
W. L. Hamilton, Z. Ying, and J. Leskovec, “Inductive representation learning on large graphs,” in Advances in Neural Information Processing Systems, vol. 30, pp. 1024-1034, 2017.
C. Romero and S. Ventura, “Educational data mining and learning analytics: An updated survey,” WIREs Data Mining and Knowledge Discovery, vol. 10, no. 3, Art. no. e1355, 2020, [Online]. Available: https://doi.org/10.1002/widm.1355.
Z. Wu, S. Pan, F. Chen, G. Long, C. Zhang, and P. S. Yu, “A comprehensive survey on graph neural networks,” IEEE Transactions on Neural Networks and Learning Systems, vol. 32, no. 1, pp. 4-24, 2021, [Online]. Available: https://doi.org/10.1109/TNNLS.2020.2978386.
K. R. Koedinger, S. K. D’Mello, E. A. McLaughlin, Z. A. Pardos, and C. P. Rosé, “Data mining and education,” WIREs Cognitive Science, vol. 6, no. 4, pp. 333-353, 2015, [Online]. Available: https://doi.org/10.1002/wcs.1350.
J. Zhou, G. Cui, S. Hu, Z. Zhang, C. Yang, Z. Liu, L. Wang, C. Li, and M. Sun, “Graph neural networks: A review of methods and applications,” AI Open, vol. 1, pp. 57-81, 2020, [Online]. Available: https://doi.org/10.1016/j.aiopen.2021.01.001.
P. Veličković, G. Cucurull, A. Casanova, A. Romero, P. Liò, and Y. Bengio, “Graph attention networks,” in Proceedings of ICLR, 2018.
M. M. Bronstein, J. Bruna, Y. LeCun, A. Szlam, and P. Vandergheynst, “Geometric deep learning: Going beyond Euclidean data,” IEEE Signal Processing Magazine, vol. 34, no. 4, pp. 18-42, 2017, [Online]. Available: https://doi.org/10.1109/MSP.2017.2693418.
G. Siemens, “Connectivism: A learning theory for the digital age,” International Journal of Instructional Technology and Distance Learning, vol. 2, no. 1, pp. 3-10, 2005.
J. Zhang, X. Shi, J. Zhao, and I. King, “Predicting user preferences via graph neural networks,” in Proceedings of the Web Conference (WWW), pp. 175-185, 2019.
R. S. Baker and P. S. Inventado, “Educational data mining and learning analytics,” in J. A. Larusson and B. White (eds.), Learning Analytics, New York: Springer, pp. 61-75, 2014.
M. Chen, Z. Wei, Z. Huang, B. Ding, and Y. Li, “Simple and deep graph convolutional networks,” in Proceedings of the International Conference on Machine Learning (ICML), pp. 1725-1735, 2020.
M. Defferrard, X. Bresson, and P. Vandergheynst, “Convolutional neural networks on graphs with fast localized spectral filtering,” in Advances in Neural Information Processing Systems, vol. 29, pp. 3844-3852, 2016.
C. Piech, J. Bassen, J. Huang, S. Ganguli, M. Sahami, L. J. Guibas, and J. Sohl-Dickstein, “Deep knowledge tracing,” in Advances in Neural Information Processing Systems, vol. 28, 2015.
D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” in Proceedings of ICLR, 2015.
C. Dede, “The role of digital technologies in deeper learning,” Students at the Center: Deeper Learning Research Series, Boston: Jobs for the Future, 2014.
K. P. Murphy, Machine Learning: A Probabilistic Perspective, Cambridge, MA: MIT Press, 2012.
M. Nickel, K. Murphy, V. Tresp, and E. Gabrilovich, “A review of relational machine learning for knowledge graphs,” Proceedings of the IEEE, vol. 104, no. 1, pp. 11-33, 2016, [Online]. Available: https://doi.org/10.1109/JPROC.2015.2483592.
R. S. Sutton and A. G. Barto, Reinforcement Learning: An Introduction, 2nd ed., Cambridge, MA: MIT Press, 2018.
A. Hogan, E. Blomqvist, M. Cochez, C. d’Amato, G. de Melo, C. Gutierrez, S. Kirrane, J. E. L. Gayo, R. Navigli, S. Neumaier, A.-C. N. Ngomo, A. Polleres, S. M. Rashid, A. Rula, L. Schmelzeisen, J. Sequeda, S. Staab, and A. Zimmermann, “Knowledge graphs,” ACM Computing Surveys, vol. 54, no. 4, pp. 1-37, 2021, [Online]. Available: https://doi.org/10.1145/3447772.
C. M. Bishop, Pattern Recognition and Machine Learning, New York: Springer, 2006.
Y. Chen, Q. Liu, E. Chen, Z. Huang, and Y. Su, “Personalized course recommendation based on knowledge graph embedding,” IEEE Access, vol. 7, pp. 51870-51880, 2019, [Online]. Available: https://doi.org/10.1109/ACCESS.2019.2912023.
M. A. Chatti, A. Muslim, and U. Schroeder, “Toward an open learning analytics ecosystem,” in Proceedings of the Fourth International Conference on Learning Analytics and Knowledge, pp. 195-203, 2014, [Online]. Available: https://doi.org/10.1145/2567574.2567589.
I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning, Cambridge, MA: MIT Press, 2016.