Design of stochastic neural networks for the fifth order system of singular engineering model

The current investigations provides a stochastic platform using the computational Levenberg-Marquardt Backpropagation (LMB) neural network (NN) approach, i.e., LMB-NN for solving the fifth order Emden-Fowler system (FOEFS) of equations. The singular models are always considered tough due to the singularity by using the traditional schemes, hence the stochastic solvers handle efficiently the singular point exactly at zero. The solution of four types of equations based on the FOEFS is presented by using the singularity and shape factor values. To calculate the approximate solutions of the FOEFS of equations, the training, validation and testing performances are used to reduce the mean square error. The selection of the training data is 70%, while testing and validation performances are used as 10% and 20%. The scheme's correctness is performed through the result's comparison along with the negligible absolute error performances for each example of the FOEFS. Moreover, the relative study through different investigations-based error histograms, and correlation update the efficacy of the scheme.