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Muhammad Shoaib
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan

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Journal article
Published: 25 August 2021 in Sustainability
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The research community of environmental economics has had a growing interest for the exploration of artificial intelligence (AI)-based systems to provide enriched efficiencies and strengthened human knacks in daily live maneuvers, business stratagems, and society evolution. In this investigation, AI-based intelligent backpropagation networks of Bayesian regularization (IBNs-BR) were exploited for the numerical treatment of mathematical models representing environmental economic systems (EESs). The governing relations of EESs were presented in the form of differential models representing their fundamental compartments or indicators for economic and environmental parameters. The reference datasets of EESs were assembled using the Adams numerical solver for different EES scenarios and were used as targets of IBNs-BR to find the approximate solutions. Comparative studies based on convergence curves on the mean square error (MSE) and absolute deviation from the reference results were used to verify the correctness of IBNs-BR for solving EESs, i.e., MSE of around 10−9 to 10−10 and absolute error close to 10−5 to 10−7. The endorsement of results was further validated through performance evaluation by means of error histogram analysis, the regression index, and the mean squared deviation-based figure of merit for each EES scenario.

ACS Style

Adiqa Kausar Kiani; Wasim Ullah Khan; Muhammad Asif Zahoor Raja; Yigang He; Zulqurnain Sabir; Muhammad Shoaib. Intelligent Backpropagation Networks with Bayesian Regularization for Mathematical Models of Environmental Economic Systems. Sustainability 2021, 13, 9537 .

AMA Style

Adiqa Kausar Kiani, Wasim Ullah Khan, Muhammad Asif Zahoor Raja, Yigang He, Zulqurnain Sabir, Muhammad Shoaib. Intelligent Backpropagation Networks with Bayesian Regularization for Mathematical Models of Environmental Economic Systems. Sustainability. 2021; 13 (17):9537.

Chicago/Turabian Style

Adiqa Kausar Kiani; Wasim Ullah Khan; Muhammad Asif Zahoor Raja; Yigang He; Zulqurnain Sabir; Muhammad Shoaib. 2021. "Intelligent Backpropagation Networks with Bayesian Regularization for Mathematical Models of Environmental Economic Systems." Sustainability 13, no. 17: 9537.

Journal article
Published: 08 July 2021 in International Journal of Hydrogen Energy
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The aim of study is to investigate the mass and heat transfer phenomena in hybrid hydro-nanofluidic system involving Al2O3–Cu–H2O over the rotating disk in porous medium with viscous dissolution and Joule heating through the stochastic solver by way of Levenberg-Marquardt backpropagation neural networks. The mathematical model in system of PDEs describes the physical phenomena of the hybrid hydro-nanofluid flow problem are converted into set of ODEs by means of scaling group transformations. The datasets are constructed by utilizing the power of explicit Runge-Kutta numerical method that help to the develop a continuous neural networks mapping. The validation, training and testing processes are utilized to learn the neural network mapping to estimate the solution of various scenarios with cases that are constructed by varying different values of physical constraints such as porosity factor, inertia coefficient, Prandtl number, Brinkman number, radiation parameter, mgnetic parameter, concentration of nanoparticles on the velocities and temperature profiles. Determination, convergence, verification and stability of Levenberg-Marquardt backpropogation neural network mappings are validated on the assessment of achieved accuracy through regression based statistical analysis, mean squared error and error histograms for hybrid hydro-nanofluidic model.

ACS Style

Hira Ilyas; Iftikhar Ahmad; Muhammad Asif Zahoor Raja; Muhammad Bilal Tahir; Muhammad Shoaib. Neuro-intelligent mappings of hybrid hydro-nanofluid Al2O3–Cu–H2O model in porous medium over rotating disk with viscous dissolution and Joule heating. International Journal of Hydrogen Energy 2021, 46, 28298 -28326.

AMA Style

Hira Ilyas, Iftikhar Ahmad, Muhammad Asif Zahoor Raja, Muhammad Bilal Tahir, Muhammad Shoaib. Neuro-intelligent mappings of hybrid hydro-nanofluid Al2O3–Cu–H2O model in porous medium over rotating disk with viscous dissolution and Joule heating. International Journal of Hydrogen Energy. 2021; 46 (55):28298-28326.

Chicago/Turabian Style

Hira Ilyas; Iftikhar Ahmad; Muhammad Asif Zahoor Raja; Muhammad Bilal Tahir; Muhammad Shoaib. 2021. "Neuro-intelligent mappings of hybrid hydro-nanofluid Al2O3–Cu–H2O model in porous medium over rotating disk with viscous dissolution and Joule heating." International Journal of Hydrogen Energy 46, no. 55: 28298-28326.

Journal article
Published: 02 July 2021 in Arabian Journal for Science and Engineering
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A novel design of stochastic numerical computing method is introduced for computational fluid dynamics problem governed with nonlinear thin film flow (TFF) system by exploiting the competency of polynomial splines for discretization and optimization with evolutionary computing aided with brilliance of local search. The TFF model of second grade fluid is represented with nonlinear second-order differential system. The aim of the present work is to exploit the cubic spline approach (CSA) to transform the differential equations for TFF model into an equivalent set of nonlinear equations. The approximation in mean squared error sense is introduced for the formulation of cost function for solving the nonlinear system of equations representing TFF model. The optimization of the decision variables of the cost function is carried out with global search efficacy of evolution by genetic algorithms (GAs) integrated with sequential quadratic programming (SQP) for speedy adjustments. The designed spline–evolutionary computing paradigm, CSA–GA–SQP, is evaluated for different scenarios of TFF model by variation of second grade and magnetic parameters, as well as variation in the length of splines. Results endorsed the worth of CSA–GA–SQP solver as an efficient alternative, reliable, stable, and accurate framework for the variants of nonlinear TFF systems on the basis of multiple autonomous executions. The design computing spline paradigm CSA–GA–SQP is a promising alternative numerical solver to be implemented for the solution of stiff nonlinear systems representing the complex scenarios of computational fluid dynamics problems.

ACS Style

Aamir Rizwan; Iftikhar Ahmad; Muhammad Asif Zahoor Raja; Muhammad Shoaib. Design of Spline–Evolutionary Computing Paradigm for Nonlinear Thin Film Flow Model. Arabian Journal for Science and Engineering 2021, 1 -21.

AMA Style

Aamir Rizwan, Iftikhar Ahmad, Muhammad Asif Zahoor Raja, Muhammad Shoaib. Design of Spline–Evolutionary Computing Paradigm for Nonlinear Thin Film Flow Model. Arabian Journal for Science and Engineering. 2021; ():1-21.

Chicago/Turabian Style

Aamir Rizwan; Iftikhar Ahmad; Muhammad Asif Zahoor Raja; Muhammad Shoaib. 2021. "Design of Spline–Evolutionary Computing Paradigm for Nonlinear Thin Film Flow Model." Arabian Journal for Science and Engineering , no. : 1-21.

Journal article
Published: 29 June 2021 in Coatings
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The present study introduced the unsteady squeezing flow of two-dimensional viscous fluid with nanoparticles between two disks by using the Levenberg–Marquardt backpropagated neural network (LMB-NN). Conversion of the partial differential equations (PDEs) into equivalent ordinary differential equations (ODEs) is performed by suitable similarity transformation. The data collection for suggested (LMB-NN) is made for various magnetohydrodynamic squeezing flow (MHDSF) scenarios in terms of the squeezing parameter, Prandtl number, Brownian motion parameter, and the thermophoresis parameter by employing the Runge–Kutta technique with the help of Mathematica software. The worth of the proposed methodology has been established for the proposed solver (LMB-NN) with different scenarios and cases, and the outcomes are compared through the effectiveness and reliability of mean square error (MSE) for the squeezing flow problem MHDSF. Moreover, the state transition, Fitness outline, histogram error, and regression presentation also endorse the strength and reliability of the solver LMB-NN. The high convergence between the reference solutions and the solutions obtained by incorporating the efficacy of a designed solver LMB-NN indicates the strength of the proposed methodology, where the accuracy level is achieved in the ranges from 106 to 1012.

ACS Style

Maryam Almalki; Eman Alaidarous; Muhammad Raja; Dalal Maturi; Muhammad Shoaib. Optimization through the Levenberg—Marquardt Backpropagation Method for a Magnetohydrodynamic Squeezing Flow System. Coatings 2021, 11, 779 .

AMA Style

Maryam Almalki, Eman Alaidarous, Muhammad Raja, Dalal Maturi, Muhammad Shoaib. Optimization through the Levenberg—Marquardt Backpropagation Method for a Magnetohydrodynamic Squeezing Flow System. Coatings. 2021; 11 (7):779.

Chicago/Turabian Style

Maryam Almalki; Eman Alaidarous; Muhammad Raja; Dalal Maturi; Muhammad Shoaib. 2021. "Optimization through the Levenberg—Marquardt Backpropagation Method for a Magnetohydrodynamic Squeezing Flow System." Coatings 11, no. 7: 779.

Journal article
Published: 25 June 2021 in International Communications in Heat and Mass Transfer
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The design of integrated numerical computing through back-propagated neural networks with Levenberg-Marquard system (BNN-LMS) is presented to explore the fluid mechanics problems governing the system of heat transfer between two porous parallel plates of steady nanofluids (HTPSNF) under the stimulus of thermophoretic and Brownian motion. By introducing the similarity transformations, the original system model HTPSNF in terms of PDEs is converted to nonlinear ODEs. Strength of Homotopy Analysis Method (HAM) is utilized the governing equations of original model HTPSNF to obtain the data set. Reference collection for the suggest BNN-LMS scheme is originated in terms of various scenarios associated HTPSNF such as Porosity parameter, Schmidt number, Brownian parameter, viscosity parameter, Prandlt number and thermophoric parameter. To uphold the trueness of the suggest BNN-LMS, the validation, training and testing process of BNN-LMS are accomplished to govern the estimate solution of HTPSNF for various cases and evaluation with reference results. The comparative studies and performance analyses based on outcomes of MSE, error histograms, correlation and regression intimate the effectiveness and virtue of designed LMBNN technique. Mean Square Errors in the ranges of 10−07 to 10−14 confirm the perfection of the presented methodology for the closed correspondence between suggested and reference results.

ACS Style

Rafaqat Ali Khan; Hakeem Ullah; Muhammad Asif Zahoor Raja; Muhammad Abdul Rehman Khan; Saeed Islam; Muhammad Shoaib. Heat transfer between two porous parallel plates of steady nano fludis with Brownian and Thermophoretic effects: A new stochastic numerical approach. International Communications in Heat and Mass Transfer 2021, 126, 105436 .

AMA Style

Rafaqat Ali Khan, Hakeem Ullah, Muhammad Asif Zahoor Raja, Muhammad Abdul Rehman Khan, Saeed Islam, Muhammad Shoaib. Heat transfer between two porous parallel plates of steady nano fludis with Brownian and Thermophoretic effects: A new stochastic numerical approach. International Communications in Heat and Mass Transfer. 2021; 126 ():105436.

Chicago/Turabian Style

Rafaqat Ali Khan; Hakeem Ullah; Muhammad Asif Zahoor Raja; Muhammad Abdul Rehman Khan; Saeed Islam; Muhammad Shoaib. 2021. "Heat transfer between two porous parallel plates of steady nano fludis with Brownian and Thermophoretic effects: A new stochastic numerical approach." International Communications in Heat and Mass Transfer 126, no. : 105436.

Original article
Published: 13 June 2021 in Engineering with Computers
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The present investigations are related to design an integrated computing numerical approach through Levenberg–Marquardt backpropagation (LMB) neural networks (NNs), i.e., LMB-NNs. The designed LMB-NNs approach is presented to solve the fourth-order nonlinear system of Emden–Fowler model (FO-SEFM). The solution of six different examples based on the FO-SEFM using the designed methodology LMB-NNs is numerically treated along with the discussion of singular point and shape factor. The comparison of the obtained results from the LMB-NNs and the exact solutions of each example has been presented. To evaluate the approximate results of the FO-SEFM for different problems, the testing, training, and authentication procedures are accompanied to adapt the NNs by reducing the functions of mean square error (MSE) through the LMB. The proportional investigations and performance studies based on the results of error histograms, MSE, regression, and correlation establish the effectiveness and correctness of the designed LMB-NNs approach.

ACS Style

Zulqurnain Sabir; Mohamed R. Ali; Muhammad Asif Zahoor Raja; Muhammad Shoaib; Rafaél Artidoro Sandoval Núñez; R. Sadat. Computational intelligence approach using Levenberg–Marquardt backpropagation neural networks to solve the fourth-order nonlinear system of Emden–Fowler model. Engineering with Computers 2021, 1 -17.

AMA Style

Zulqurnain Sabir, Mohamed R. Ali, Muhammad Asif Zahoor Raja, Muhammad Shoaib, Rafaél Artidoro Sandoval Núñez, R. Sadat. Computational intelligence approach using Levenberg–Marquardt backpropagation neural networks to solve the fourth-order nonlinear system of Emden–Fowler model. Engineering with Computers. 2021; ():1-17.

Chicago/Turabian Style

Zulqurnain Sabir; Mohamed R. Ali; Muhammad Asif Zahoor Raja; Muhammad Shoaib; Rafaél Artidoro Sandoval Núñez; R. Sadat. 2021. "Computational intelligence approach using Levenberg–Marquardt backpropagation neural networks to solve the fourth-order nonlinear system of Emden–Fowler model." Engineering with Computers , no. : 1-17.

Journal article
Published: 05 June 2021 in Chinese Journal of Physics
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In this study, a design of integrated computational intelligent paradigm has been presented for numerical treatment of the one-dimensional boundary value problems represented with Falkner-Skan equations (FSE) by exploitation of Gaussian wavelet neural networks (GWNNs), genetic algorithms (GAs) and sequential quadratic programming (SQP), i.e., GWNN-GA-SQP. The GWNNs is used for mathematical modeling of the problem by constructing mean squared error based objective function while optimization of the cost function is initially conducted with efficacy of GAs as a global search and while fine tuning is performed with efficiency local search with SQP. The numerical results are obtained by proposed GWNN-GA-SQP for different FSEs arising in nonlinear regimes of computation fluid mechanics studies. A comparison of the results of proposed GWNN-GA-SQP stochastic numerical solver with reference state of the art solutions of Adams method establishes the accuracy, convergence and stability, which further endorsed through statistics on multiples runs. The T-Paired test is also applied to validate the effectiveness of the proposed GWNN-GA-SQP algorithm for solving nonlinear FSEs.

ACS Style

Hira Ilyas; Muhammad Asif Zahoor Raja; Iftikhar Ahmad; Muhammad Shoaib. A novel design of Gaussian Wavelet Neural Networks for nonlinear Falkner-Skan systems in fluid dynamics. Chinese Journal of Physics 2021, 72, 386 -402.

AMA Style

Hira Ilyas, Muhammad Asif Zahoor Raja, Iftikhar Ahmad, Muhammad Shoaib. A novel design of Gaussian Wavelet Neural Networks for nonlinear Falkner-Skan systems in fluid dynamics. Chinese Journal of Physics. 2021; 72 ():386-402.

Chicago/Turabian Style

Hira Ilyas; Muhammad Asif Zahoor Raja; Iftikhar Ahmad; Muhammad Shoaib. 2021. "A novel design of Gaussian Wavelet Neural Networks for nonlinear Falkner-Skan systems in fluid dynamics." Chinese Journal of Physics 72, no. : 386-402.

Journal article
Published: 31 May 2021 in Surfaces and Interfaces
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In this research article, artificial neural networks back-propagated with Levenberg Marquardt scheme (ANN-BLMS) is presented to analyze the entropy generation of carbon nanotubes (CNTs) between two rotating stretching discs under the influence of thermal radiation and magneto-hydrodynamic nano-fluid flow model. (MHD-NFM). The fluid flow is initially represented by system of PDEs is then transformed into system of ODEs. A set of data for proposed ANN-BLMS is generated for various scenarios by variation of stretching parameters of lower and upper disks A1 and A2 respectively, suction injection parameter (Ws), rotational parameter (Ω), the radiation parameter (R), the Eckert number (Ec), the Hartmann number (M) by using Adams Numerical method. The approximate solution of different cases is determined by testing, training and validation process of ANN-BLMS and comparison for verification of correctness of proposed model. Later on, regression analysis, mean square error and histogram studies endorse the performance of proposed ANN-BLMS.

ACS Style

Muhammad Shoaib; Muhammad Asif Zahoor Raja; Muhammad Abdul Rehman Khan; Imrana Farhat; Saeed Ehsan Awan. Neuro-computing networks for entropy generation under the influence of MHD and thermal radiation. Surfaces and Interfaces 2021, 25, 101243 .

AMA Style

Muhammad Shoaib, Muhammad Asif Zahoor Raja, Muhammad Abdul Rehman Khan, Imrana Farhat, Saeed Ehsan Awan. Neuro-computing networks for entropy generation under the influence of MHD and thermal radiation. Surfaces and Interfaces. 2021; 25 ():101243.

Chicago/Turabian Style

Muhammad Shoaib; Muhammad Asif Zahoor Raja; Muhammad Abdul Rehman Khan; Imrana Farhat; Saeed Ehsan Awan. 2021. "Neuro-computing networks for entropy generation under the influence of MHD and thermal radiation." Surfaces and Interfaces 25, no. : 101243.

Journal article
Published: 15 May 2021 in Ain Shams Engineering Journal
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In the artificial neural networks domain, the Levenberg-Marquardt technique is novel with convergent stability and generates a numerical solution of the wire coating system for Sisko fluid flow (WCS-SFF) through regression plots, histogram representations, state transition measures, and means squared errors. In this paper, the analysis of fluid flow problem based on WCS-SFF is studied with a new application of intelligent computing system via supervised learning mechanism using the efficacy of neural networks trained by Levenberg-Marquardt algorithm (NN-TLMA). The original mathematical formulation in terms of PDEs for WCS-SFF is converted into dimensionless nonlinear ODEs. The data collection for the projected NN-TLMA is produced for parameters associated with the system model WCS-SFF influencing the velocity using the explicit Runge-Kutta technique. The training, validation, and testing processes of NN-TLMA are utilized to evaluate the obtained results of WCS-SFF for various cases, and a comparison of the obtained results is performed with reference data set to check the accuracy and effectiveness of the proposed algorithm NN-TLMA for the analysis of non-Newtonian fluid problem-related WCS-SFF. The proposed NN-TLMA for solving the WCS-SFF is effectively confirmed through state transition dynamics, mean square error, regression analyses, and error histogram studies. The powerful consistency of suggested outcomes with reference solutions indicates the validity of the framework, and the accuracy of 10-8 to 10-6 is also achieved.

ACS Style

Jawaher Lafi Aljohani; Eman Salem Alaidarous; Muhammad Asif Zahoor Raja; Muhammed Shabab Alhothuali; Muhammad Shoaib. Backpropagation of Levenberg Marquardt artificial neural networks for wire coating analysis in the bath of Sisko fluid. Ain Shams Engineering Journal 2021, 1 .

AMA Style

Jawaher Lafi Aljohani, Eman Salem Alaidarous, Muhammad Asif Zahoor Raja, Muhammed Shabab Alhothuali, Muhammad Shoaib. Backpropagation of Levenberg Marquardt artificial neural networks for wire coating analysis in the bath of Sisko fluid. Ain Shams Engineering Journal. 2021; ():1.

Chicago/Turabian Style

Jawaher Lafi Aljohani; Eman Salem Alaidarous; Muhammad Asif Zahoor Raja; Muhammed Shabab Alhothuali; Muhammad Shoaib. 2021. "Backpropagation of Levenberg Marquardt artificial neural networks for wire coating analysis in the bath of Sisko fluid." Ain Shams Engineering Journal , no. : 1.

Journal article
Published: 20 April 2021 in Mathematics and Computers in Simulation
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In the investigations presented here, an efficient computing approach is applied to solve Human Immunodeficiency Virus (HIV) infection spread. This approach involves CD4+ T-cells by feed-forward artificial neural networks (FF-ANNs) trained with particle swarm optimization (PSO) and interior point method (IPM), i.e., FF-ANN-PSO-IPM. In the proposed solver FF-ANN-PSO-IPM, the FF-ANN models of differential equations are used to develop the fitness functions for an infection model of T-cells. The training of networks through minimization problem are proficiently conducted by integrated heuristic capability of PSO-IPM. The reliability, stability and exactness of the proposed FF-ANN-PSO-IPM are established through comparison with outcomes of standard numerical procedure with Adams method for both single and multiple autonomous trials with precision of order 4 to 8 decimal places of accuracy. The statistical measures are effectively used to validate the outcomes of the proposed FF-ANN-PSO-IPM.

ACS Style

Muhammad Umar; Zulqurnain Sabir; Muhammad Asif Zahoor Raja; J.F. Gómez Aguilar; Fazli Amin; Muhammad Shoaib. Neuro-swarm intelligent computing paradigm for nonlinear HIV infection model with CD4+ T-cells. Mathematics and Computers in Simulation 2021, 188, 241 -253.

AMA Style

Muhammad Umar, Zulqurnain Sabir, Muhammad Asif Zahoor Raja, J.F. Gómez Aguilar, Fazli Amin, Muhammad Shoaib. Neuro-swarm intelligent computing paradigm for nonlinear HIV infection model with CD4+ T-cells. Mathematics and Computers in Simulation. 2021; 188 ():241-253.

Chicago/Turabian Style

Muhammad Umar; Zulqurnain Sabir; Muhammad Asif Zahoor Raja; J.F. Gómez Aguilar; Fazli Amin; Muhammad Shoaib. 2021. "Neuro-swarm intelligent computing paradigm for nonlinear HIV infection model with CD4+ T-cells." Mathematics and Computers in Simulation 188, no. : 241-253.

Regular article
Published: 13 April 2021 in The European Physical Journal Plus
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Piezoelectric stage has become promising actuator for wide applications of micro-/nano-positioning systems represented mathematically with Bouc–Wen hysteresis model to examine the efficiency. In this investigation, the numerical study of piezostage actuator based on nonlinear Bouc–Wen hysteresis model is presented by neurocomputing intelligence via Levenberg–Marquardt backpropagated neural networks (LMB-NNs). Numerical computing strength of Adams method is implemented to generate a dataset of LMB-NNs for training, testing and validation process based on different scenarios of input voltage signals to piezostage actuator model. The performance of LMB-NNs of nano-positioning system model is validated through accuracy measures on means square error, histogram illustrations and regression analysis.

ACS Style

Sidra Naz; Muhammad Asif Zahoor Raja; Ammara Mehmood; Aneela Zameer; Muhammad Shoaib. Neuro-intelligent networks for Bouc–Wen hysteresis model for piezostage actuator. The European Physical Journal Plus 2021, 136, 1 -20.

AMA Style

Sidra Naz, Muhammad Asif Zahoor Raja, Ammara Mehmood, Aneela Zameer, Muhammad Shoaib. Neuro-intelligent networks for Bouc–Wen hysteresis model for piezostage actuator. The European Physical Journal Plus. 2021; 136 (4):1-20.

Chicago/Turabian Style

Sidra Naz; Muhammad Asif Zahoor Raja; Ammara Mehmood; Aneela Zameer; Muhammad Shoaib. 2021. "Neuro-intelligent networks for Bouc–Wen hysteresis model for piezostage actuator." The European Physical Journal Plus 136, no. 4: 1-20.

Journal article
Published: 09 April 2021 in Journal of the Taiwan Institute of Chemical Engineers
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Exploration and exploitation of artificial intelligence (AI) techniques have growing interest for the research community investigating in engineering and technological fields to provide improved efficiencies and augmented human abilities in daily live operations, business strategies and society evolution. A novel application of AI based backpropagating networks (BPNs) was presented for bioconvection model in transverse transportation of rheological fluid involving Lorentz force interaction and gyrotactic microorganisms. The governing nonlinear PDEs for bioconvection rheological fluidic system (BRFS) was reduced to nonlinear system of ODEs by competency of similarity adjustments. A reference data of designed BPNs was constructed for variants of BRFS representing scenarios for thermophoresis parameter, Brownian motion, Prandtl numbers, magnetic variables, squeezing and Lewis numbers by applying the Adams numerical solver. The said data were segmented arbitrary in training, testing, and validation sets to execute BPNs to calculate the approximate solutions for variants of BRFS and comparison with standard solution to validate the consistent accuracy. The worthy performance of AI based BPNs was additionally certified by learning curve on MSE based fitness, histograms and regression metrics.

ACS Style

Muhammad Asif Zahoor Raja; Muhammad Faizan Malik; Ching-Lung Chang; Muhammad Shoaib; Chi-Min Shu. Design of backpropagation networks for bioconvection model in transverse transportation of rheological fluid involving Lorentz force interaction and gyrotactic microorganisms. Journal of the Taiwan Institute of Chemical Engineers 2021, 121, 276 -291.

AMA Style

Muhammad Asif Zahoor Raja, Muhammad Faizan Malik, Ching-Lung Chang, Muhammad Shoaib, Chi-Min Shu. Design of backpropagation networks for bioconvection model in transverse transportation of rheological fluid involving Lorentz force interaction and gyrotactic microorganisms. Journal of the Taiwan Institute of Chemical Engineers. 2021; 121 ():276-291.

Chicago/Turabian Style

Muhammad Asif Zahoor Raja; Muhammad Faizan Malik; Ching-Lung Chang; Muhammad Shoaib; Chi-Min Shu. 2021. "Design of backpropagation networks for bioconvection model in transverse transportation of rheological fluid involving Lorentz force interaction and gyrotactic microorganisms." Journal of the Taiwan Institute of Chemical Engineers 121, no. : 276-291.

Journal article
Published: 12 March 2021 in International Journal of Hydrogen Energy
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The porous media transport theories are thoroughly operative to analyse transferral phenomenon in reducing the bio-convective flow instabilities and biological tissues. The present study is designed to investigate the heat transfer phenomena in nanofluidic system involving Cu − H2O over the stretched porous media with the strength of stochastic solver via Levenberg-Marquardt backpropagation networks. The mathematical model of physical phenomena is described in PDEs that are reduced to system of ODEs through scaling group transformations. The datasets are determined through explicit Runge-Kutta numerical method and used as a target parameter for the development of continuous neural networks mapping. The training, testing and validation processes are utilized in learning of neural network models based on backpropagation of Levenberg-Marquardt technique to determines the solution of different scenarios constructed on the various values of porosity parameter along with six different cases based on the stretching ratio values. Validation and verification of neural network model to find the solution of nanfluidic problem is endorsed on the assessment of achieved accuracy through mean squared error, error histograms and regression studies.

ACS Style

Hira Ilyas; Iftikhar Ahmad; Muhammad Asif Zahoor Raja; Muhammad Bilal Tahir; Muhammad Shoaib. Intelligent networks for crosswise stream nanofluidic model with Cu–H2O over porous stretching medium. International Journal of Hydrogen Energy 2021, 46, 15322 -15336.

AMA Style

Hira Ilyas, Iftikhar Ahmad, Muhammad Asif Zahoor Raja, Muhammad Bilal Tahir, Muhammad Shoaib. Intelligent networks for crosswise stream nanofluidic model with Cu–H2O over porous stretching medium. International Journal of Hydrogen Energy. 2021; 46 (29):15322-15336.

Chicago/Turabian Style

Hira Ilyas; Iftikhar Ahmad; Muhammad Asif Zahoor Raja; Muhammad Bilal Tahir; Muhammad Shoaib. 2021. "Intelligent networks for crosswise stream nanofluidic model with Cu–H2O over porous stretching medium." International Journal of Hydrogen Energy 46, no. 29: 15322-15336.

Journal article
Published: 26 February 2021 in International Communications in Heat and Mass Transfer
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The aim of this study is to analysis the mass and heat transfer in radiative three dimensional flow of hybrid nanofluid over the stretchable sheet by exploiting the strength of integrated computational intelligent algorithm by utilization of Gaussian wavelet neural networks (GWNNs) trained with the genetic algorithms (GAs) based global search supported with sequential quadratic programming (SQP) based local refinements i.e., GWNN-GA-SQP. The mean squared error based cost function is developed for the fluidic problem by applying Gaussian WaveNet GWNNs optimize with GAs and SQP. The numerical outcomes of the fluidic model are obtained by the proposed GWNN-GA-SQP solver to examine the thermal and velocities profile effect for three physical quantities based on magnetic parameter, nanomaterial concentration and transformated angular velocity. Moreover, a exhaustive analysis of the numerical solutions of GWNN-GA-SQP solver with reference Adams method endorse the stability, accuracy and consistency on multiple autonomous runs through different statistical performance operators and complexity analysis.

ACS Style

Hira Ilyas; Iftikhar Ahmad; Muhammad Asif Zahoor Raja; Muhammad Shoaib. A novel design of Gaussian WaveNets for rotational hybrid nanofluidic flow over a stretching sheet involving thermal radiation. International Communications in Heat and Mass Transfer 2021, 123, 105196 .

AMA Style

Hira Ilyas, Iftikhar Ahmad, Muhammad Asif Zahoor Raja, Muhammad Shoaib. A novel design of Gaussian WaveNets for rotational hybrid nanofluidic flow over a stretching sheet involving thermal radiation. International Communications in Heat and Mass Transfer. 2021; 123 ():105196.

Chicago/Turabian Style

Hira Ilyas; Iftikhar Ahmad; Muhammad Asif Zahoor Raja; Muhammad Shoaib. 2021. "A novel design of Gaussian WaveNets for rotational hybrid nanofluidic flow over a stretching sheet involving thermal radiation." International Communications in Heat and Mass Transfer 123, no. : 105196.

Journal article
Published: 18 January 2021 in Alexandria Engineering Journal
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In this study, a novel stochastic computational frameworks based on fractional Meyer wavelet artificial neural network (FMW-ANN) is designed for nonlinear-singular fractional Lane-Emden (NS-FLE) differential equation. The modeling strength of FMW-ANN is used to transformed the differential NS-FLE system to difference equations and approximate theory is implemented in mean squared error sense to develop a merit function for NS-FLE differential equations. Meta-heuristic strength of hybrid computing by exploiting global search efficacy of genetic algorithms (GA) supported with local refinements with efficient active-set (AS) algorithm is used for optimization of design variables FMW-ANN., i.e., FMW-ANN-GASA. The proposed FMW-ANN-GASA methodology is implemented on NS-FLM for six different scenarios in order to exam the accuracy, convergence, stability and robustness. The proposed numerical results of FMW-ANN-GASA are compared with exact solutions to verify the correctness, viability and efficacy. The statistical observations further validate the worth of FMW-ANN-GASA for the solution of singular nonlinear fractional order systems.

ACS Style

Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Juan L.G. Guirao; Muhammad Shoaib. A novel design of fractional Meyer wavelet neural networks with application to the nonlinear singular fractional Lane-Emden systems. Alexandria Engineering Journal 2021, 60, 2641 -2659.

AMA Style

Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Juan L.G. Guirao, Muhammad Shoaib. A novel design of fractional Meyer wavelet neural networks with application to the nonlinear singular fractional Lane-Emden systems. Alexandria Engineering Journal. 2021; 60 (2):2641-2659.

Chicago/Turabian Style

Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Juan L.G. Guirao; Muhammad Shoaib. 2021. "A novel design of fractional Meyer wavelet neural networks with application to the nonlinear singular fractional Lane-Emden systems." Alexandria Engineering Journal 60, no. 2: 2641-2659.

Journal article
Published: 20 December 2020 in Journal of the National Science Foundation of Sri Lanka
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The Journal of the National Science Foundation of Sri Lanka publishes the results of research in all aspects of Science and Technology. The journal also has a website at http://www.nsf.gov.lk/. 2018 Impact Factor 0.419The JNSF provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.

ACS Style

M. Awais; S. E. Awan; S. Irum; M. Shoaib; H. Ali; M. A. Z. Raja. Rheology of hydro-magnetic polymeric material with heat generation/absorption and chemical reaction. Journal of the National Science Foundation of Sri Lanka 2020, 48, 397 .

AMA Style

M. Awais, S. E. Awan, S. Irum, M. Shoaib, H. Ali, M. A. Z. Raja. Rheology of hydro-magnetic polymeric material with heat generation/absorption and chemical reaction. Journal of the National Science Foundation of Sri Lanka. 2020; 48 (4):397.

Chicago/Turabian Style

M. Awais; S. E. Awan; S. Irum; M. Shoaib; H. Ali; M. A. Z. Raja. 2020. "Rheology of hydro-magnetic polymeric material with heat generation/absorption and chemical reaction." Journal of the National Science Foundation of Sri Lanka 48, no. 4: 397.

Research article
Published: 07 November 2020 in Alexandria Engineering Journal
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The present investigation explores the impact of mass and heat transfer on the magneto-hydrodynamic (MHD) flow of Casson fluid through porous medium due to shrinking wall subject to Lorentz force and heat generation/absorption effects. Dual branches for the profiles of velocity, temperature and mass fraction have been computed numerically by exploitation of explicit Runge-Kutta procedure. Mathematical modelling is developed for the conversion of physical model into set of mathematical equations which are simplified using order analysis. The computations for the solution construction have been made numerically via shooting technique and the results are obtained for stream function, temperature and concentration profiles. The aim of presented analysis is to observed that the dual numerical solutions exist for stream functions, skin friction, temperature and concentration profiles. Graphical illustrations have been prepared for different physical quantities including transfer of mass, heat absorption/generation, influence of chemical reaction, Schmidt number and non-Newtonian parameter etc. Results of proposed method are also provided to describe the dual solutions for the local Nusselt and Sherwood numbers as well as for heat transfer rate for Propane and Ethelene Glycol. The Prandtl number and Schmidt number decay the temperature and concentration profiles, respectively.

ACS Style

Muhammad Awais; Muhammad Asif Zahoor Raja; Saeed Ehsan Awan; Muhammad Shoaib; Hafiz Muhammad Ali. Heat and mass transfer phenomenon for the dynamics of Casson fluid through porous medium over shrinking wall subject to Lorentz force and heat source/sink. Alexandria Engineering Journal 2020, 60, 1355 -1363.

AMA Style

Muhammad Awais, Muhammad Asif Zahoor Raja, Saeed Ehsan Awan, Muhammad Shoaib, Hafiz Muhammad Ali. Heat and mass transfer phenomenon for the dynamics of Casson fluid through porous medium over shrinking wall subject to Lorentz force and heat source/sink. Alexandria Engineering Journal. 2020; 60 (1):1355-1363.

Chicago/Turabian Style

Muhammad Awais; Muhammad Asif Zahoor Raja; Saeed Ehsan Awan; Muhammad Shoaib; Hafiz Muhammad Ali. 2020. "Heat and mass transfer phenomenon for the dynamics of Casson fluid through porous medium over shrinking wall subject to Lorentz force and heat source/sink." Alexandria Engineering Journal 60, no. 1: 1355-1363.

Article
Published: 31 October 2020 in Computational and Applied Mathematics
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In the present work, a novel neuro-swarming based heuristic solver is established for the numerical solutions of fourth-order multi-singular nonlinear Emden–Fowler (FO-MS-NEF) model using the function estimate capability of artificial neural networks (ANNs) modelling together with the global application of particle swarm optimization (PSO) enhanced by local search active set (AS) approach, i.e., ANN-PSO-AS solver. The design stimulation for the ANN-PSO-AS scheme for a numerical solver originates with an intention to present a viable, consistent and precise configuration that associates the ANNs strength under the optimization of unified soft computing backgrounds to tackle with such stimulating models for the FO-MS-NEF equation. The proposed ANN-PSO-AS solver is applied for three different variants of FO-MS-NEF equations. The comparison of the obtained results with the true solutions calmed its correctness, effectiveness, and robustness that is further validated with in-depth statistical investigations.

ACS Style

Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Juan L. G. Guirao; Muhammad Shoaib. Integrated intelligent computing with neuro-swarming solver for multi-singular fourth-order nonlinear Emden–Fowler equation. Computational and Applied Mathematics 2020, 39, 1 -18.

AMA Style

Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Juan L. G. Guirao, Muhammad Shoaib. Integrated intelligent computing with neuro-swarming solver for multi-singular fourth-order nonlinear Emden–Fowler equation. Computational and Applied Mathematics. 2020; 39 (4):1-18.

Chicago/Turabian Style

Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Juan L. G. Guirao; Muhammad Shoaib. 2020. "Integrated intelligent computing with neuro-swarming solver for multi-singular fourth-order nonlinear Emden–Fowler equation." Computational and Applied Mathematics 39, no. 4: 1-18.

Article
Published: 26 October 2020 in Computational and Applied Mathematics
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In the present study, a novel fractional Meyer neuro-evolution-based intelligent computing solver (FMNEICS) is presented for numerical treatment of doubly singular multi-fractional Lane–Emden system (DSMF-LES) using combined heuristics of Meyer wavelet neural networks (MWNN) optimized with global search efficacy of genetic algorithms (GAs) and sequential quadratic programming (SQP), i.e., MWNN-GASQP. The design of novel FMNEICS for DSMF-LES is presented after derivation from standard Lane–Emden equation, and the singular points and shape factors along with fractional-order terms are analyzed. The MWNN modeling strength is used to represent the system model DSMF-LES in the mean-squared error-based merit function and optimization of the networks is carried out with integrated optimization ability of GASQP. The verification, validation, and perfection of the FMNEICS for three different cases of DSMF-LES are established through comparative studies from reference solutions on convergence, robustness, accuracy, and stability measures. Moreover, the observations through the statistical analysis further authenticate the worth of proposed fractional MWNN-GASQP-based stochastic solver.

ACS Style

Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Muhammad Shoaib; J. F. Gómez Aguilar. FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system. Computational and Applied Mathematics 2020, 39, 1 -18.

AMA Style

Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Muhammad Shoaib, J. F. Gómez Aguilar. FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system. Computational and Applied Mathematics. 2020; 39 (4):1-18.

Chicago/Turabian Style

Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Muhammad Shoaib; J. F. Gómez Aguilar. 2020. "FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system." Computational and Applied Mathematics 39, no. 4: 1-18.

Journal article
Published: 13 October 2020 in Applied Soft Computing
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In this study, a novel design of integrated biological inspired computational heuristics is presented for the dynamics of nonlinear unipolar electrohydrodynamic (UP-EHD) pump flow model by exploiting the competency of finite difference method (FDM) for discretization, global search viability of genetic algorithms (GAs) and local search efficiency of active-set method (ASM), i.e., FDM-GA-ASM. The FDM is incorporated to transform the differential equations of the UP-EHD pump flow model into a system of nonlinear algebraic equations. The cost function is constructed through the mean-square residual error by mimicking forward, central and backward difference schemes viable for a broader range of physical models. The optimum solution is achieved by the integration of global search with GAs and local search of ASM for speedy refinements. The designed stochastic numerical solver FDM-GA-ASM investigates the critical physical parameters, i.e., charge density, electric field and electric potential by varying electrical slip, Reynolds number and source number of the UP-EHD model. Statistical observations in terms of probability plots, histogram illustrations, boxplots for the cost function, mean absolute error, root mean squared error and Nash–Sutcliffe efficiency metrics are used to validate the efficiency of the FDM-GA-ASM scheme for the three variants of the UP-EHD model. The designed FDM-GA-ASM is a promising numerical computing solver for nonlinear differential systems in engineering and technology.

ACS Style

Ihtesham Jadoon; Ashfaq Ahmed; Ata Ur Rehman; Muhammad Shoaib; Muhammad Asif Zahoor Raja. Integrated meta-heuristics finite difference method for the dynamics of nonlinear unipolar electrohydrodynamic pump flow model. Applied Soft Computing 2020, 97, 106791 .

AMA Style

Ihtesham Jadoon, Ashfaq Ahmed, Ata Ur Rehman, Muhammad Shoaib, Muhammad Asif Zahoor Raja. Integrated meta-heuristics finite difference method for the dynamics of nonlinear unipolar electrohydrodynamic pump flow model. Applied Soft Computing. 2020; 97 ():106791.

Chicago/Turabian Style

Ihtesham Jadoon; Ashfaq Ahmed; Ata Ur Rehman; Muhammad Shoaib; Muhammad Asif Zahoor Raja. 2020. "Integrated meta-heuristics finite difference method for the dynamics of nonlinear unipolar electrohydrodynamic pump flow model." Applied Soft Computing 97, no. : 106791.