Design Optimal Neural Network for Solving Unsteady State Confined Aquifer Problem

Abstract

This article presents the mathematical model of unsteady state horizontal radial flow in homogenous and anisotropic confined aquifers in polar coordinate which represented an important problem. We design optimal neural network to solve this problem. Also, we estimate the parameters of transmissivity aquifer with high accuracy. The optimality depending on choosing optimum architectural with suitable training algorithm and transfer function. The best design neural network is trained by new training algorithm say LNA. The retrained almost fast by suitable transferring function. Based on the modified architecture, the training and testing phases of the solving process are divided into two. The dataset is separated into three sections during the training phase: 60% of the training data, 20% of the validation data, and 20% of the test data. The total square error (TSE) for the trained phase with using the bach propagation algorithm (BPA) is 4.1499e+01 while it is 9.5898e-03 if we using suggested training algorithm (LNA). The LNA has a much smaller TSE when compared to the BPA. These much smaller values of the TSE indicate that LNA performs better than the BPA for the same number of iterations. So suggested architecture has many advantages such loss function computed on a random sample of the domain, high performance, avoid local minima and can be adapted for the online dynamic modeling, automation, control and robotics applications