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Soft Computing Artificial 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, Schrödinger–Wheeler–DeWitt model is developed by using canonical transformation to transformed Hamiltonian equation. The exact solutions for flat universe (\(k = 0\)) 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.

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  1. Department of Mathematics, Grand Asian University Sialkot, 51310, Sialkot, Punjab, Pakistan

    Najam Ul Basat

  2. Department of Mathematics, University of Gujrat, Hafiz Hayyat Campus, 50700, Gujrat, Punjab, Pakistan

    Mahmoona Asghar

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  1. Najam Ul Basat
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Basat, N.U., Asghar, M. Soft Computing Artificial Intelligence of Schrödinger Time Independent Equation Arises in Wheeler–DeWitt Model of Quantum Cosmology. Comput. Math. and Math. Phys. 63, 2212–2226 (2023). https://doi.org/10.1134/S0965542523110040

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