№ 60-1 (том 1): ОБРАЗОВАНИЕ И НАУКА В XXI ВЕКЕ, Март, 2025
Научно-образовательные статьи

THE CONCEPT OF NEURAL ODES AND THEIR MATHEMATICAL DESCRIPTION

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  • Mametsaliyev Resul
Mametsaliyev Resul
Oguzhan Engineering and Technology University of Turkmenistan. Ashgabat, Turkmenistan

Опубликован 03.04.2025

Ключевые слова

  • Neural ODEs,
  • deep learning,
  • differential equations,
  • continuous-depth models,
  • numerical solvers,
  • optimization,
  • machine learning
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Как цитировать

R. Mametsaliyev. (2025). THE CONCEPT OF NEURAL ODES AND THEIR MATHEMATICAL DESCRIPTION. ОБРАЗОВАНИЕ И НАУКА В XXI ВЕКЕ, 60-1 (том 1). https://mpcareer-google.ru/index.php/journal/article/view/1349

Аннотация

Neural Ordinary Differential Equations (Neural ODEs) are a powerful class of deep learning models that generalize residual networks (ResNets) by formulating the evolution of hidden states as a continuous-time differential equation. This approach provides benefits such as memory efficiency, adaptability to irregularly sampled data, and improved interpretability. This paper explores the mathematical formulation of Neural ODEs, their relation to classical ODE solvers, and key applications in machine learning. We also discuss numerical methods used for solving Neural ODEs and their challenges in optimization and stability.

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Библиографические ссылки

  1. Chen, R. T. Q., Rubanova, Y., Bettencourt, J., & Duvenaud, D. (2018). Neural Ordinary Differential Equations. Advances in Neural Information Processing Systems (NeurIPS).
  2. Rackauckas, C., & Nie, Q. (2020). Differentiable Programming for Scientific Machine Learning. Nature Machine Intelligence.
  3. Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep Learning. MIT Press.
  4. Hairer, E., Nørsett, S. P., & Wanner, G. (1993). Solving Ordinary Differential Equations I: Nonstiff Problems. Springer-Verlag.
  5. Kingma, D. P., & Welling, M. (2013). Auto-Encoding Variational Bayes. ICLR Proceedings.