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Volume 13, Issue 2
A Novel Approach to Simulate Lane-Emden and Emden-Fowler Equations Using Curriculum Learning-Based Unsupervised Symplectic Artificial Neural Network

Arup Kumar Sahoo & S. Chakraverty

DOI: 10.4208/eajam.2022-115.300922

East Asian J. Appl. Math., 13 (2023), pp. 276-298.

Published online: 2023-04

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  • Abstract

This paper investigates the impact of the curriculum learning process in a multilayer neural network (NN) for solving the Lane-Emden and Emden-Fowler models. Starting from the training of a neural network in a small domain, we gradually expanded the domain. The symplectic NN trial solution is used for solving titled models. Feedforward NN and error back-propagation algorithms are used to minimize the error function and modify the parameters. The consistency of the algorithm is demonstrated by solving several problems. Calculating different types of errors (MSE up to 1E-10), we show an excellent agreement between the current simulations and existing results.

  • Keywords

Curriculum learning, symplectic neural network, unsupervised, Lane-Emden equation, Emden-Fowler equation.

  • AMS Subject Headings

34A12, 34A30, 34A34, 68T07, 85-08, 85-10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-13-276, author = {Sahoo , Arup Kumar and Chakraverty , S.}, title = {A Novel Approach to Simulate Lane-Emden and Emden-Fowler Equations Using Curriculum Learning-Based Unsupervised Symplectic Artificial Neural Network}, journal = {East Asian Journal on Applied Mathematics}, year = {2023}, volume = {13}, number = {2}, pages = {276--298}, abstract = {

This paper investigates the impact of the curriculum learning process in a multilayer neural network (NN) for solving the Lane-Emden and Emden-Fowler models. Starting from the training of a neural network in a small domain, we gradually expanded the domain. The symplectic NN trial solution is used for solving titled models. Feedforward NN and error back-propagation algorithms are used to minimize the error function and modify the parameters. The consistency of the algorithm is demonstrated by solving several problems. Calculating different types of errors (MSE up to 1E-10), we show an excellent agreement between the current simulations and existing results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2022-115.300922 }, url = {http://global-sci.org/intro/article_detail/eajam/21649.html} }
TY - JOUR T1 - A Novel Approach to Simulate Lane-Emden and Emden-Fowler Equations Using Curriculum Learning-Based Unsupervised Symplectic Artificial Neural Network AU - Sahoo , Arup Kumar AU - Chakraverty , S. JO - East Asian Journal on Applied Mathematics VL - 2 SP - 276 EP - 298 PY - 2023 DA - 2023/04 SN - 13 DO - http://doi.org/10.4208/eajam.2022-115.300922 UR - https://global-sci.org/intro/article_detail/eajam/21649.html KW - Curriculum learning, symplectic neural network, unsupervised, Lane-Emden equation, Emden-Fowler equation. AB -

This paper investigates the impact of the curriculum learning process in a multilayer neural network (NN) for solving the Lane-Emden and Emden-Fowler models. Starting from the training of a neural network in a small domain, we gradually expanded the domain. The symplectic NN trial solution is used for solving titled models. Feedforward NN and error back-propagation algorithms are used to minimize the error function and modify the parameters. The consistency of the algorithm is demonstrated by solving several problems. Calculating different types of errors (MSE up to 1E-10), we show an excellent agreement between the current simulations and existing results.

Sahoo , Arup Kumar and Chakraverty , S.. (2023). A Novel Approach to Simulate Lane-Emden and Emden-Fowler Equations Using Curriculum Learning-Based Unsupervised Symplectic Artificial Neural Network. East Asian Journal on Applied Mathematics. 13 (2). 276-298. doi:10.4208/eajam.2022-115.300922
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