Soft computing articial intelligence of Schrödinger time independent equation arises in Wheeler–Dewitt model of quantum cosmology

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.