Design an efficient neural network for solving steady state problems

Volume 36, Issue 1, pp 84--98 https://dx.doi.org/10.22436/jmcs.036.01.06

Publication Date: June 22, 2024 Submission Date: March 13, 2024 Revision Date: May 09, 2024 Accteptance Date: May 27, 2024

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Authors

A‎. ‎A‎. ‎ Thirthar - Department of Studies and Planning, ‎University of Fallujah, Anbar, Iraq. ‎L‎. ‎N‎. ‎M‎. ‎ Tawfiq - Department of Mathematics‎, ‎College of Education for Pure Science Ibn Al-Haitham, ‎University of Baghdad, Iraq. K. Shah - Department of Mathematics and Sciences, ‎Prince Sultan University, ‎P.O‎. ‎Box 66833, Riyadh 11586, Saudi Arabia. Th. Abdeljawad - Department of Mathematics and Sciences, ‎Prince Sultan University, ‎P.O‎. ‎Box 66833, Riyadh 11586, Saudi Arabia.

Abstract

‎In this article‎, ‎the mathematical model of steady state problems based on horizontal radial flow in homogenous confined aquifers has been presented‎. ‎Then we design efficient neural network (ANN) to solve the equation in polar coordinates‎. ‎A reliable unconstrained optimization method has been used as training algorithm to get high accuracy results‎. ‎The results illustrated by contour maps‎. ‎The new effective Levenberg-Marquardt method (NLM) has been implemented to solve the problem‎. ‎A comparison between the training‎, ‎testing and validation results has been presented‎. ‎The weight of the ANN will be chosen such that satisfied local minimizer‎. ‎Furthermore‎, ‎the quadratic convergence of NLM has been proved‎. ‎The results reveal that the suggested design is effective‎, ‎time saver‎, ‎and applicable for solving steady state problems‎.

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Keywords

• Steady state problems
• neural networks
• unconstrained optimization
• Levenberg-Marquardt algorithm
• anisotropic confined aquifers model

MSC

•  37Dxx
•  34Dxx
•  76Fxx

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