A Novel Approach to Simulate Lane-Emden and Emden-Fowler Equations Using Curriculum Learning-Based Unsupervised Symplectic Artificial Neural Network
Year: 2023
Author: Arup Kumar Sahoo, S. Chakraverty
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2022-115.300922
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 2 : pp. 276–298
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Curriculum learning symplectic neural network unsupervised Lane-Emden equation Emden-Fowler equation.