SOFT COMPUTING ARTICIAL INTELLIGENCE OF SCHRöDINGER TIME INDEPENDENT EQUATION ARISES IN WHEELER-DEWITT MODEL OF QUANTUM COSMOLOGY

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Abstract

Schrödinger time independent equation arises in Wheeler–DeWitt model of quantum cosmology to develop a wave function for the corrections of cosmologies. In this work, k=0  rödinger–Wheeler–DeWitt model is developed by using canonical transformation to transformed Hamiltonian equation. The exact solutions for flat universe (
) model is presented and then soft computing technique through Levenberg–Marquardt backpropagation neural networks (LMB-NNs) is implemented. The data set of the flat universe model is generated for four different cases of separation constant B  with step size 0.1  by Mathematica and imported into LMB-NNs for training, testing, and validation of the our proposed technique. The performance of LMB-NNs is provided by the validation of mean square error, error histogram, and regression analysis. The Statistical analysis; mean, minimum, maximum, and standard deviation, is also presented.

About the authors

Najam Ul Basat

Department of Mathematics, Grand Asian University Sialkot, Pasrur Road,

Email: najam.basat@gaus.edu.pk
Pakistan, 51310, Punjab, Sialkot

Mahmoona Asghar

Department of Mathematics, University of Gujrat, Haz Hayyat Campus,

Author for correspondence.
Email: 17016109-006@uog.edu.pk
Pakistan, 50700,, Punjab, Gujrat

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Copyright (c) 2023 Najam Ul Basat, Mahmoona Asghar