Browsing by Author "Sabir, Zulqurnain"

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Citation Count: 0
Design of stochastic neural networks for the fifth order system of singular engineering model
(Pergamon-elsevier Science Ltd, 2024) Sabir, Zulqurnain; Salahshour, Soheıl; Hashem, Atef F.; Abdelkawy, M. A.; Salahshour, Soheil; Umar, Muhammad
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.
Citation Count: 0
A Gudermannian neural network performance for the numerical environmental and economic model
(Elsevier, 2024) Sabir, Zulqurnain; Salahshour, Soheıl; Salahshour, Soheil; Nicolas, Rana
The present work is to exploit the Gudermannian neural network (GNN) using the global competency of genetic algorithm (GA) and quick local refinements of sequential quadratic programming approach (SQPA), i.e., GNNGA-SQPA for the nonlinear economic and environmental system. The differential form of the nonlinear system depends upon three classes, system capability of industrial elements, implementation cost of control values and a new diagnostics technical elimination cost. An error-based fitness function is constructed using the differential system and then optimized by using the hybrid competency of the GA-SQPA. Ten numbers of neurons, a merit Gudermannian function, and the suitable weight vectors are presented in the neural network construction. The accuracy of the GNN-GA-SQPA is assessed through the comparisons and the negligible performances of absolute error. The statistical observations using single and multiple trials validate the stability of the scheme.
Citation Count: 0
A neural network computational procedure for the novel designed singular fifth order nonlinear system of multi-pantograph differential equations
(Elsevier, 2024) Bhat, Shahid Ahmad; Salahshour, Soheıl; Sabir, Zulqurnain; Babatin, M. M.; Hashem, Atef F.; Abdelkawy, M. A.; Salahshour, Soheil
The current investigations present the numerical solutions of the novel singular nonlinear fifth-order (SNFO) system of multi-pantograph differential model (SMPDM), i.e., SNFO-SMPDM. The novel SNFO-SMPDM is obtained using the sense of the second kind of typical Emden-Fowler and prediction differential models. The features of shape factor, pantograph along with singular points are provided for all four obtained classes of the SNFO-SMPDM. The extensive use of the singular models is observed in the engineering and mathematical systems, e.g., inverse systems and viscoelasticity or creep systems. For the correctness of the proposed novel SNFO-SMPDM, one case of each class is numerically handled by applying supervised neural networks (SNNs) along with the optimization of Levenberg-Marquardt backpropagation scheme (LMBS), i.e., SNNs-LMBS. A dataset using the traditional variational iteration scheme is designed to compare the proposed results of each case of SNFO-SMPDM. The obtained approximate solutions of each class using the novel SNFO-SMPDM are presented based on the training (80 %), authentication (10 %) and testing (10 %) measures to evaluate the mean square error. Fifteen numbers of neurons, and sigmoid activation function are used in this SNN process. To authenticate the competence, and precision of SNFO-SMPDM, the numerical simulations are accessible by applying the relative measures of regression, error histogram plots, and correlation.
Citation Count: 0
A novel radial basis neural network for the Zika virus spreading model
(Elsevier Sci Ltd, 2024) Sabir, Zulqurnain; Salahshour, Soheıl; Kassem, Zeinab; Umar, Muhammad; Salahshour, Soheil
The motive of current investigations is to design a novel radial basis neural network stochastic structure to present the numerical representations of the Zika virus spreading model (ZVSM). The mathematical ZVSM is categorized into humans and vectors based on the susceptible S(q), exposed E(q), infected I(q) and recovered R (q), i.e., SEIR. The stochastic performances are designed using the radial basis activation function, feed forward neural network, twenty-two numbers of neurons along with the optimization of Bayesian regularization in order to solve the ZVSM. A dataset is achieved using the explicit Runge-Kutta scheme, which is used to reduce the mean square error (MSE) based on the process of training for solving the nonlinear ZVSM. The division of the data is categorized into training, which is taken as 78%, while 11 % for both authentication and testing. Three different cases of the nonlinear ZVSM have been taken, while the scheme's correctness is performed through the matching of the results. Furthermore, the reliability of the scheme is observed by applying different performances of regression, MSE, error histograms and state transition.
Citation Count: 0
A reliable neural network procedure for the novel sixth-order nonlinear singular pantograph differential model
(World Scientific Publ Co Pte Ltd, 2024) Sabir, Zulqurnain; Salahshour, Soheıl; Salahshour, Soheil; Saeed, Tareq
An innovative singular nonlinear sixth-order (SNSO) pantograph differential model (PDM), known as the SNSO-PDM, is the subject of this novel study along with its numerical investigation. The concepts of pantograph and conventional Emden-Fowler have been presented in the design of the novel SNSO-PDM. The models based on Emden-Fowler have huge applications in mathematics and engineering and are always difficult to solve due to singularity. For each class of the innovative SNSO-PDM, the singularity, shape and pantograph factors are described. A reliable stochastic Levenberg-Marquardt backpropagation neural network (LMBPNN) procedure is designed for the SNSO-PDM. The correctness of the SNSOs-PDM is observed through the comparison performances of the achieved and reference outputs. The obtained results of the SNSO-PDM are considered by applying the process of training, certification, and testing to reduce the mean square error. To authenticate the efficacy of the innovative SNSO-PDM, the numerical performances of the solutions are depicted in the sense of regression, error histograms and correlation.