Proceedings of the 7th Scientific Conference on Information Technologies for Intelligent Decision Making Support (ITIDS 2019)

Investigation of the Functional Stability of Neural Network Algorithm for Solving the Ordinary Differential Equations

Authors
Irina Bolodurina, Lubov Zabrodina
Corresponding Author
Irina Bolodurina
Available Online May 2019.
DOI
https://doi.org/10.2991/itids-19.2019.21How to use a DOI?
Keywords
ordinary differential equations, artificial neural network, optimization methods, functional stability
Abstract

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.

Copyright
© 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/).

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Volume Title
Proceedings of the 7th Scientific Conference on Information Technologies for Intelligent Decision Making Support (ITIDS 2019)
Series
Advances in Intelligent Systems Research
Publication Date
May 2019
ISBN
978-94-6252-728-7
ISSN
1951-6851
DOI
https://doi.org/10.2991/itids-19.2019.21How to use a DOI?
Copyright
© 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  -