D.D. Matorin1, A.Yu. Cherepkov2
1, 2 Bunin Yelets State University (Yelets, Russia)
1 dmitr.matorin@yandex.ru, 2 cherepkov.andrey@mai.ru

Mathematical modeling of the knowledge acquisition process is an urgent problem, and researchers use various methods to study it. These methods include, among others, the construction of dynamic models that take into account the complex interactions of cognitive components, such as understanding and memorizing information. With the development of intelligent educational systems and personalized learning, there is a need to develop models that use artificial intelligence technologies, such as neural networks, to account for the continuous dynamics of processes. This article focuses on the development and study of mathematical models of the knowledge acquisition process using neural ordinary differential equations (Neural ODE). The article explores models of the knowledge acquisition process based on systems of ordinary differential equations that describe the interaction of cognitive components of learning. The article then extends these models to Neural ODE models that use neural networks for approximation. The article identifies the parameters of the models and conducts a series of numerical experiments. The article compares the trajectories obtained from the classical differential model and the Neural ODE model. The results can be applied to mathematical modeling of educational processes, analyzing the dynamics of knowledge acquisition, and predicting learning outcomes.

Matorin D.D., Cherepkov A.Yu. Modeling the process of knowledge acquisition based on neural ordinary differential equations // Neurocomputers. 2026. V. 28. № 3. P. 35–43. DOI: https://doi.org/10.18127/j19998554-202603-05.

1. Majer R.V. Imitacionnoe modelirovanie usvoeniya i zaby`vaniya osmy`slennoj informacii. Uspexi sovremennoj nauki. 2017. T. 1. № 1. S. 42–44. EDN: XXENHT. (in Russian).
2. Majer R.V. Mnogokomponentnaya model` obucheniya i ee ispol`zovanie dlya issledovaniya didakticheskix system. Fundamental`ny`e issledovaniya. 2013. № 10. S. 2524–2528. EDN: RRWAFN. (in Russian).
3. Matorin D.D., Cherepkov A.Yu. Chislenny`j analiz mnogokomponentny`x dinamicheskix modelej poe`tapnogo usvoeniya znanij. Nelinejny`j mir. 2025. T. 23. № 1. S. 27–34. DOI: 10.18127/ j20700970-202501-04. EDN QTRHFB. (in Russian).
4. Chen R. T. Q., Rubanova Y., Bettencourt J., Duvenaud D. Neural Ordinary Differential Equations. Advances in Neural Information Processing Systems. 2018. V. 31. P. 6571–6583.
5. Emilien D., Arnaud D., Yee W.T. Augmented Neural ODEs. arXiv Preprint. 2019. DOI: 10.48550/arXiv.1904.01681.
6. Kidger P., Morrill J., Foster J., John Lyons T. Neural Controlled Differential Equations for Irregular Time Series. arXiv Preprint. 2020. DOI:10.48550/arXiv.2005.08926.