Investigation of the Functional Stability of Neural Network Algorithm for Solving the Ordinary Differential Equations
- https://doi.org/10.2991/itids-19.2019.21How to use a DOI?
- ordinary differential equations, artificial neural network, optimization methods, functional stability
The paper analyzes the neural network approach for solving the Cauchy problem of ordinary differential equations of the first order, based on the representation of the function as a superposition of elementary functions. The use of neural network approach allows obtaining the desired solution in the form of a functional dependence, which satisfies the required conditions of smoothness. On the basis of a two-layer perceptron, a model of neural network solution of the problem and a numerical algorithm implementing the search for a solution are constructed. The software-algorithmic solution of the Cauchy problem is obtained. To determine the stability of the neural network approach, a series of experiments were conducted to find a solution to a particular Cauchy problem of ordinary differential equation of the first order with an analytical solution. The study shows that the considered neural network algorithm has no functional stability. This may be due to the problems of weights minimization, scalability in network training and other factors.
- © 2019, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - CONF AU - Irina Bolodurina AU - Lubov Zabrodina PY - 2019/05 DA - 2019/05 TI - Investigation of the Functional Stability of Neural Network Algorithm for Solving the Ordinary Differential Equations BT - Proceedings of the 7th Scientific Conference on Information Technologies for Intelligent Decision Making Support (ITIDS 2019) PB - Atlantis Press SP - 111 EP - 116 SN - 1951-6851 UR - https://doi.org/10.2991/itids-19.2019.21 DO - https://doi.org/10.2991/itids-19.2019.21 ID - Bolodurina2019/05 ER -