Design an efficient neural network for solving steady state problems

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.