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Zulqurnain Sabir is native of Pothi, district Jhelum, Pakistan. He has completed his MSc degree in Mathematics from Punjab University, Lahore, Pakistan and M.Phil in mathematics from Preston University Kohat, Islamabad Campus, Pakistan. He is currently perusing his PhD in mathematics from Hazara University, Mansehra Pakistan. He has published more than 50 papers in reported international WoS journals with impact factors. His area of interests includes mathematical modeling, unsupervised neural networks, supervised neural networks, artificial intelligence and implementation of computational techniques based on traditional as well as heuristic methodology. He is famous to solve singular models, functional models, fractional models, biological models and fluid models. He is a pioneer to design and solve second order pantograph Emden-Fowler model, prediction differential model, nonlinear fifth order Emden-Fowler model, nervous stomach model and nonlinear multi-singular SITR model based on coronavirus (COVID 19).
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.
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 StyleAdiqa 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 StyleAdiqa 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.
The current investigation communicates the characteristics of upper-convected second grade nanofluid thin film flow over a time-dependent stretching sheet with variable thermal conductivity and Cattaneo–Christov double diffusion theory. The mathematical model generates a system of nonlinear partial differential equations (PDEs) for heat, momentum, and mass transfer phenomena. Similarity variables converted the PDEs into nonlinear ordinary differential equations (ODEs). Furthermore, received ODEs are numerically rescued with the built-in program Bvp4c in MATLAB. The impact of physical parameters like second-grade fluid λ , unsteadiness parameter S , Prandtl number Pr , Schmidt number Sc , variable thermal conductivity ε , variable diffusivity ε 1 , the square of dimensionless film thickness γ , relaxation time δ e , and retardation time δ c are scrutinized. Tables revealed numerical exposure and graphs depict the geometrical aspect of the current study. The velocity field is improved by heightening the λ, magnification in temperature is found for greater conductivity parameter ε . Greater δ e in the temperature profile goes smaller. The rate of mass transfer diminishes by uplifting the estimations in relaxation time parameter δ c .
Ali Haider; Assad Ayub; Naeem Madassar; Rao K. Ali; Zulqurnain Sabir; Syed Z. H. Shah; Syed H. Kazmi. Energy transference in time‐dependent Cattaneo–Christov double diffusion of second‐grade fluid with variable thermal conductivity. Heat Transfer 2021, 1 .
AMA StyleAli Haider, Assad Ayub, Naeem Madassar, Rao K. Ali, Zulqurnain Sabir, Syed Z. H. Shah, Syed H. Kazmi. Energy transference in time‐dependent Cattaneo–Christov double diffusion of second‐grade fluid with variable thermal conductivity. Heat Transfer. 2021; ():1.
Chicago/Turabian StyleAli Haider; Assad Ayub; Naeem Madassar; Rao K. Ali; Zulqurnain Sabir; Syed Z. H. Shah; Syed H. Kazmi. 2021. "Energy transference in time‐dependent Cattaneo–Christov double diffusion of second‐grade fluid with variable thermal conductivity." Heat Transfer , no. : 1.
The present study is related to design a novel multi-fractional multi-singular Lane–Emden model (MFMS-LEM) by keeping the ideas of the literature LEM and by extension of the work of doubly singular multi-fractional LEM. This mathematical novel MFMS-LEM is numerically treated by applying the fractional Meyer neuro-evolution intelligent solver (FMNEICS). The optimization is performed using the mutual heuristics of fractional Mayer wavelet neural networks (FMW-NN), the global search aptitude of genetic algorithms (GAs) and interior-point algorithm (IPA), i.e., FMW-NN-GAIPA. The derivation steps, details of the singular points, fractional terms, shape factors and singular points are also provided. The modeling strength of MW-NN is implemented to characterize the novel model in the sagacity of mean squared error of objective function and network optimization is performed with the integrated capability of GAIPA. The authentication, perfection and verification of FMNEICS is checked for three diverse cases of the novel model which are conventional via relative studies through the reference solutions based on accuracy, stability, robustness and convergence procedures. Furthermore, the explanations via the statistical measures validate the value of the designed stochastic solver FMW-NN-GAIPA.
Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Juan L. G. Guirao; Tareq Saeed. Solution of novel multi-fractional multi-singular Lane–Emden model using the designed FMNEICS. Neural Computing and Applications 2021, 1 -16.
AMA StyleZulqurnain Sabir, Muhammad Asif Zahoor Raja, Juan L. G. Guirao, Tareq Saeed. Solution of novel multi-fractional multi-singular Lane–Emden model using the designed FMNEICS. Neural Computing and Applications. 2021; ():1-16.
Chicago/Turabian StyleZulqurnain Sabir; Muhammad Asif Zahoor Raja; Juan L. G. Guirao; Tareq Saeed. 2021. "Solution of novel multi-fractional multi-singular Lane–Emden model using the designed FMNEICS." Neural Computing and Applications , no. : 1-16.
Current work unfolds the transport of energy of blood containing nanoparticles of iron oxide (Fe3O4) and mass transport is focalized by considering the homogeneous-heterogeneous chemical process with attached mathematical model of Cross nanofluid. The chemical process is carried out by chemical species and autocatalysis. Nonlinear Partial differential equations (PDEs) are appeared by mathematical model of Cross nanofluid and further delt with transformation for conversion of PDEs into Ordinary differential equations (ODEs). Purpose of numerical outcome of this study is analyzed by two schemes named as two schemes i.e., bvp4c and KELLER-BOX. Comparison of these schemes are investigated through tabular data and statistical bar graphs. From conclusion it is noticed that mass transport is increased with greater homogeneous-heterogeneous chemical parameter. Nanoparticles in fluid boosts the heat transfer. Melting process increase the transport of heat and skin friction. Both schemes are compared and found smooth agreements.
Syed Zahir Hussain Shah; Assad Ayub; Zulqurnain Sabir; Waleed Adel; Nehad Ali Shah; Se-Jin Yook. Insight into the dynamics of time-dependent cross nanofluid on a melting surface subject to cubic autocatalysis. Case Studies in Thermal Engineering 2021, 27, 101227 .
AMA StyleSyed Zahir Hussain Shah, Assad Ayub, Zulqurnain Sabir, Waleed Adel, Nehad Ali Shah, Se-Jin Yook. Insight into the dynamics of time-dependent cross nanofluid on a melting surface subject to cubic autocatalysis. Case Studies in Thermal Engineering. 2021; 27 ():101227.
Chicago/Turabian StyleSyed Zahir Hussain Shah; Assad Ayub; Zulqurnain Sabir; Waleed Adel; Nehad Ali Shah; Se-Jin Yook. 2021. "Insight into the dynamics of time-dependent cross nanofluid on a melting surface subject to cubic autocatalysis." Case Studies in Thermal Engineering 27, no. : 101227.
This work is related to the chemical process in nanomaterial that has prominent applications in water-solubility, octanol-water partition coefficient, melting points, vapor pressure and various astonishing features. Nanoparticles have unique chemical effects in the field of nanoscience and nanotechnology. This study determines the impacts of homogeneous heterogeneous reactions along with nanoscale heat transport of inclined magnetized three-dimensional (3-D) water-based Hybrid nanofluid. The geometry of rotating and shrinking/stretching sheet with the effects of thermal radiation is also presented. Nanoparticles of aluminum oxide and silver are being used with water as base fluid. Mathematical model of Hybrid nanofluid generates the set of partial differential equation (PDEs) and these are transmuted into ordinary differential equations (ODEs) by using the similarity of variables. MATLAB built-in bvp4c procedures are implemented to find the numerical solutions. Moreover, physical descriptions of current study are revealed out through graphs and tables. Statistical analysis of physical quantities is presented in the form of bar graphs to show the regulating parameter effects.
Assad Ayub; Zulqurnain Sabir; Dac-Nhuong Le; Ayman A. Aly. Nanoscale heat and mass transport of magnetized 3-D chemically radiative hybrid nanofluid with orthogonal/inclined magnetic field along rotating sheet. Case Studies in Thermal Engineering 2021, 26, 101193 .
AMA StyleAssad Ayub, Zulqurnain Sabir, Dac-Nhuong Le, Ayman A. Aly. Nanoscale heat and mass transport of magnetized 3-D chemically radiative hybrid nanofluid with orthogonal/inclined magnetic field along rotating sheet. Case Studies in Thermal Engineering. 2021; 26 ():101193.
Chicago/Turabian StyleAssad Ayub; Zulqurnain Sabir; Dac-Nhuong Le; Ayman A. Aly. 2021. "Nanoscale heat and mass transport of magnetized 3-D chemically radiative hybrid nanofluid with orthogonal/inclined magnetic field along rotating sheet." Case Studies in Thermal Engineering 26, no. : 101193.
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.
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 StyleZulqurnain 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 StyleZulqurnain 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.
In this work, a new heuristic computing design is presented with an artificial intelligence approach to exploit the models with feed-forward (FF) Gudermannian neural networks (GNN) accomplished with global search capability of genetic algorithms (GA) combined with local convergence aptitude of active-set method (ASM), i.e., FF-GNN-GAASM to solve the second kind of Lane–Emden nonlinear singular models (LE-NSM). The proposed method based on the computing intelligent Gudermannian kernel is incorporated with the hidden layer configuration of FF-GNN models of differential operatives of the LE-NSM, which are arbitrarily associated with presenting an error-based objective function that is used to optimize by the hybrid heuristics of GAASM. Three LE-NSM-based examples are numerically solved to authenticate the effectiveness, accurateness, and efficiency of the suggested FF-GNN-GAASM. The reliability of the scheme via statistical valuations is verified in order to authenticate the stability, accuracy, and convergence.
Kashif Nisar; Zulqurnain Sabir; Muhammad Zahoor Raja; Ag. Ag. Ibrahim; Joel Rodrigues; Adnan Shahid Khan; Manoj Gupta; Aldawoud Kamal; Danda Rawat. Evolutionary Integrated Heuristic with Gudermannian Neural Networks for Second Kind of Lane–Emden Nonlinear Singular Models. Applied Sciences 2021, 11, 4725 .
AMA StyleKashif Nisar, Zulqurnain Sabir, Muhammad Zahoor Raja, Ag. Ag. Ibrahim, Joel Rodrigues, Adnan Shahid Khan, Manoj Gupta, Aldawoud Kamal, Danda Rawat. Evolutionary Integrated Heuristic with Gudermannian Neural Networks for Second Kind of Lane–Emden Nonlinear Singular Models. Applied Sciences. 2021; 11 (11):4725.
Chicago/Turabian StyleKashif Nisar; Zulqurnain Sabir; Muhammad Zahoor Raja; Ag. Ag. Ibrahim; Joel Rodrigues; Adnan Shahid Khan; Manoj Gupta; Aldawoud Kamal; Danda Rawat. 2021. "Evolutionary Integrated Heuristic with Gudermannian Neural Networks for Second Kind of Lane–Emden Nonlinear Singular Models." Applied Sciences 11, no. 11: 4725.
The current study is related to present a novel neuro-swarming intelligent heuristic for nonlinear second-order Lane–Emden multi-pantograph delay differential (NSO-LE-MPDD) model by applying the approximation proficiency of artificial neural networks (ANNs) and local/global search capabilities of particle swarm optimization (PSO) together with efficient/quick interior-point (IP) approach, i.e., ANN-PSOIP scheme. In the designed ANN-PSOIP scheme, a merit function is proposed by using the mean square error sense along with continuous mapping of ANNs for the NSO-LE-MPDD model. The training of these nets is capable of using the integrated competence of PSO and IP scheme. The inspiration of the ANN-PSOIP approach instigates to present a reliable, steadfast, and consistent arrangement relates the ANNs strength for the soft computing optimization to handle with such inspiring classifications. Furthermore, the statistical soundings using the different operators certify the convergence, accurateness, and precision of the ANN-PSOIP scheme.
Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Dac-Nhuong Le; Ayman A. Aly. A neuro-swarming intelligent heuristic for second-order nonlinear Lane–Emden multi-pantograph delay differential system. Complex & Intelligent Systems 2021, 1 -14.
AMA StyleZulqurnain Sabir, Muhammad Asif Zahoor Raja, Dac-Nhuong Le, Ayman A. Aly. A neuro-swarming intelligent heuristic for second-order nonlinear Lane–Emden multi-pantograph delay differential system. Complex & Intelligent Systems. 2021; ():1-14.
Chicago/Turabian StyleZulqurnain Sabir; Muhammad Asif Zahoor Raja; Dac-Nhuong Le; Ayman A. Aly. 2021. "A neuro-swarming intelligent heuristic for second-order nonlinear Lane–Emden multi-pantograph delay differential system." Complex & Intelligent Systems , no. : 1-14.
The blood flow with heat transportation has prominent clinical importance during the levels where the blood flow needs to be checked (surgery) and the heat transportation rate must be controlled (therapy). This work presents an analysis of the melting heat transport of blood, which consists of iron nanoparticles along free convection with cross-model and solution of the partial differential equation (PDEs) are emerged by the mathematical model. Being the importance of iron oxide nanoparticles in applications of the biomedical field due to their intrinsic properties such as colloidal stability, surface engineering capability and low toxicity, this study has been launched. Furthermore, PDEs of the problem are converted into a set of nonlinear ordinary differential equations (ODEs) by proper transformations. The solution of this system of ODEs is calculated through RK 4 method and Keller–Box scheme. Some leading points and numerical results of this study of both types of presence and absence of meting effects are tabulated.
Assad Ayub; Zulqurnain Sabir; Gilder Cieza Altamirano; R. Sadat; Mohamed R. Ali. Characteristics of melting heat transport of blood with time-dependent cross-nanofluid model using Keller–Box and BVP4C method. Engineering with Computers 2021, 1 -15.
AMA StyleAssad Ayub, Zulqurnain Sabir, Gilder Cieza Altamirano, R. Sadat, Mohamed R. Ali. Characteristics of melting heat transport of blood with time-dependent cross-nanofluid model using Keller–Box and BVP4C method. Engineering with Computers. 2021; ():1-15.
Chicago/Turabian StyleAssad Ayub; Zulqurnain Sabir; Gilder Cieza Altamirano; R. Sadat; Mohamed R. Ali. 2021. "Characteristics of melting heat transport of blood with time-dependent cross-nanofluid model using Keller–Box and BVP4C method." Engineering with Computers , no. : 1-15.
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.
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 StyleMuhammad 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 StyleMuhammad 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.
The current study aims to design an integrated numerical computing-based scheme by applying the Levenberg–Marquardt backpropagation (LMB) neural network to solve the nonlinear susceptible (S), infected (I) and recovered (R) (SIR) system of differential equations, representing the spreading of infection along with its treatment. The solutions of both the categories of spreading infection and its treatment are presented by taking six different cases of SIR models using the designed LMB neural network. A reference dataset of the designed LMB neural network is established with the Adam numerical scheme for each case of the spreading infection and its treatment. The approximate outcomes of the SIR system based on the spreading infection and its treatment are presented in the training, authentication and testing procedures to adapt the neural network by reducing the mean square error (MSE) function using the LMB. Studies based on the proportional performance and inquiries based on correlation, error histograms, regression and MSE results establish the efficiency, correctness and effectiveness of the proposed LMB neural network scheme.
Muhammad Umar; Zulqurnain Sabir; Muhammad Zahoor Raja; Manoj Gupta; Dac-Nhuong Le; Ayman Aly; Yolanda Guerrero-Sánchez. Computational Intelligent Paradigms to Solve the Nonlinear SIR System for Spreading Infection and Treatment Using Levenberg–Marquardt Backpropagation. Symmetry 2021, 13, 618 .
AMA StyleMuhammad Umar, Zulqurnain Sabir, Muhammad Zahoor Raja, Manoj Gupta, Dac-Nhuong Le, Ayman Aly, Yolanda Guerrero-Sánchez. Computational Intelligent Paradigms to Solve the Nonlinear SIR System for Spreading Infection and Treatment Using Levenberg–Marquardt Backpropagation. Symmetry. 2021; 13 (4):618.
Chicago/Turabian StyleMuhammad Umar; Zulqurnain Sabir; Muhammad Zahoor Raja; Manoj Gupta; Dac-Nhuong Le; Ayman Aly; Yolanda Guerrero-Sánchez. 2021. "Computational Intelligent Paradigms to Solve the Nonlinear SIR System for Spreading Infection and Treatment Using Levenberg–Marquardt Backpropagation." Symmetry 13, no. 4: 618.
The present research work is to puts forth the numerical solutions of the nonlinear second-order Lane-Emden-pantograph (LEP) delay differential equation by using the approximation competency of the artificial neural networks (ANNs) trained with the combined strengths of global/local search exploitation of genetic algorithm (GA) and active-set (AS) method, i.e., ANNGAAS. In the proposed ANNGAAS, the objective function is designed by using the mean square error function with continuous mappings of ANNs for the LEP delay differential equation. The training of these constructed networks is conducted proficiently using the integrated capability of global search with GA and assisted local search along with AS approach. The performance of design computing paradigm ANNGAAS is evaluated effectively on variants of LEP delay differential models, while the statistical investigations based on different operators further validate the accuracy and convergence.
Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Hafiz Abdul Wahab; Gilder Cieza Altamirano; Yu-Dong Zhang; Dac-Nhuong Le. Integrated intelligence of neuro-evolution with sequential quadratic programming for second-order Lane–Emden pantograph models. Mathematics and Computers in Simulation 2021, 188, 87 -101.
AMA StyleZulqurnain Sabir, Muhammad Asif Zahoor Raja, Hafiz Abdul Wahab, Gilder Cieza Altamirano, Yu-Dong Zhang, Dac-Nhuong Le. Integrated intelligence of neuro-evolution with sequential quadratic programming for second-order Lane–Emden pantograph models. Mathematics and Computers in Simulation. 2021; 188 ():87-101.
Chicago/Turabian StyleZulqurnain Sabir; Muhammad Asif Zahoor Raja; Hafiz Abdul Wahab; Gilder Cieza Altamirano; Yu-Dong Zhang; Dac-Nhuong Le. 2021. "Integrated intelligence of neuro-evolution with sequential quadratic programming for second-order Lane–Emden pantograph models." Mathematics and Computers in Simulation 188, no. : 87-101.
In this paper, a neuro-evolution based numerical computing approach is presented for the solution of nonlinear third order multi-singular Emden–Fowler system of differential equations (MS-EF-SDEs) by manipulating the proficiency of continuous mapping through exploitation of feed-forward artificial neural networks (ANN). The weights or decision variables of these networks are optimized with genetic algorithms (GAs) and sequential quadratic programming (SQP), i.e., ANN-GA-SQP. An error based figure of merit is introduced using the differential model of MS EF-SDE along with corresponding boundary conditions. The objective/cost function is optimized by integrating capability of global and local search with GA and SQP, respectively. The competency of the designed ANN-GA-SQP approach in terms of significance, efficiency and consistency is perceived by solving MS-EF-SDEs. Moreover, statistical based investigations are implemented to validate the correctness of ANN-GA-SQP.
Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Chaudry Masood Khalique; Canan Unlu. Neuro-evolution computing for nonlinear multi-singular system of third order Emden–Fowler equation. Mathematics and Computers in Simulation 2021, 185, 799 -812.
AMA StyleZulqurnain Sabir, Muhammad Asif Zahoor Raja, Chaudry Masood Khalique, Canan Unlu. Neuro-evolution computing for nonlinear multi-singular system of third order Emden–Fowler equation. Mathematics and Computers in Simulation. 2021; 185 ():799-812.
Chicago/Turabian StyleZulqurnain Sabir; Muhammad Asif Zahoor Raja; Chaudry Masood Khalique; Canan Unlu. 2021. "Neuro-evolution computing for nonlinear multi-singular system of third order Emden–Fowler equation." Mathematics and Computers in Simulation 185, no. : 799-812.
In this numerical study, a class of nonlinear singular boundary value problem is solved by implementation of a novel meta-heuristic computing tool based on the artificial neural networks (ANNs) modeling of system and the optimization of decision variable of ANNs through the combined strength of global search via genetic algorithms (GA) and local search ability of active-set algorithm (ASA), i.e., ANN–GA–ASA. The proposed intelligent computing solver ANN–GA–ASA exploits the input, hidden, and output layers’ structure of ANNs. This is to represent the differential model in the nonlinear singular second-order periodic boundary value problems, which are connected to form an error-based objective function (OF) and optimize the OF by the integrated heuristics of GA–ASA. The purpose to present this research is to associate the operational legacy of neural networks and to challenge such kinds of inspiring models. Two different examples of the singular periodic model have been investigated to observe the robustness, proficiency and stability of the ANN–GA–ASA. The proposed outcomes of ANN–GA–ASA are compared with reference to true results so as to establish the value of the designed scheme. Exhaustive comparison has been made and presented between the Log-sigmoidal ANNs results and the radial basis ANNs outcomes. The reliability of the results obtained is endorsed by using both types of networks as well as the value of designed schemes.
Zulqurnain Sabir; Chaudry Masood Khalique; Muhammad Asif Zahoor Raja; Dumitru Baleanu. Evolutionary computing for nonlinear singular boundary value problems using neural network, genetic algorithm and active-set algorithm. The European Physical Journal Plus 2021, 136, 1 -19.
AMA StyleZulqurnain Sabir, Chaudry Masood Khalique, Muhammad Asif Zahoor Raja, Dumitru Baleanu. Evolutionary computing for nonlinear singular boundary value problems using neural network, genetic algorithm and active-set algorithm. The European Physical Journal Plus. 2021; 136 (2):1-19.
Chicago/Turabian StyleZulqurnain Sabir; Chaudry Masood Khalique; Muhammad Asif Zahoor Raja; Dumitru Baleanu. 2021. "Evolutionary computing for nonlinear singular boundary value problems using neural network, genetic algorithm and active-set algorithm." The European Physical Journal Plus 136, no. 2: 1-19.
The present study is related to present a novel design of intelligent solvers with a neuro-swarm heuristic integrated with interior-point algorithm (IPA) for the numerical investigations of the nonlinear SITR fractal system based on the dynamics of a novel coronavirus (COVID-19). The mathematical form of the SITR system using fractal considerations defined in four groups, ‘susceptible (S)’, ‘infected (I)’, ‘treatment (T)’ and ‘recovered (R)’. The inclusive detail of each group along with the clarification to formulate the manipulative form of the SITR nonlinear model of novel COVID-19 dynamics is presented. The solution of the SITR model is presented using the artificial neural networks (ANNs) models trained with particle swarm optimization (PSO), i.e., global search scheme and prompt fine-tuning by IPA, i.e., ANN-PSOIPA. In the ANN-PSOIPA, the merit function is expressed for the impression of mean squared error applying the continuous ANNs form for the dynamics of SITR system and training of these networks are competently accompanied with the integrated competence of PSOIPA. The exactness, stability, reliability and prospective of the considered ANN-PSOIPA for four different forms is established via the comparative valuation from of Runge-Kutta numerical solutions for the single and multiple executions. The obtained outcomes through statistical assessments verify the convergence, stability and viability of proposed ANN-PSOIPA.
Muhammad Umar; Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Fazli Amin; Tareq Saeed; Yolanda Guerrero-Sanchez. Integrated neuro-swarm heuristic with interior-point for nonlinear SITR model for dynamics of novel COVID-19. Alexandria Engineering Journal 2021, 60, 2811 -2824.
AMA StyleMuhammad Umar, Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Fazli Amin, Tareq Saeed, Yolanda Guerrero-Sanchez. Integrated neuro-swarm heuristic with interior-point for nonlinear SITR model for dynamics of novel COVID-19. Alexandria Engineering Journal. 2021; 60 (3):2811-2824.
Chicago/Turabian StyleMuhammad Umar; Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Fazli Amin; Tareq Saeed; Yolanda Guerrero-Sanchez. 2021. "Integrated neuro-swarm heuristic with interior-point for nonlinear SITR model for dynamics of novel COVID-19." Alexandria Engineering Journal 60, no. 3: 2811-2824.
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.
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 StyleZulqurnain 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 StyleZulqurnain 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.
The aim of the present study is to present a new model based on the nonlinear singular second order delay differential equation of Lane–Emden type and numerically solved by using the heuristic technique. Four different examples are presented based on the designed model and numerically solved by using artificial neural networks optimized by the global search, local search methods and their hybrid combinations, respectively, named as genetic algorithm (GA), sequential quadratic programming (SQP) and GA-SQP. The numerical results of the designed model are compared for the proposed heuristic technique with the exact/explicit results that demonstrate the performance and correctness. Moreover, statistical investigations/assessments are presented for the accuracy and performance of the designed model implemented with heuristic methodology.
Zulqurnain Sabir; Juan L.G. Guirao; Tareq Saeed. Solving a novel designed second order nonlinear Lane–Emden delay differential model using the heuristic techniques. Applied Soft Computing 2021, 102, 107105 .
AMA StyleZulqurnain Sabir, Juan L.G. Guirao, Tareq Saeed. Solving a novel designed second order nonlinear Lane–Emden delay differential model using the heuristic techniques. Applied Soft Computing. 2021; 102 ():107105.
Chicago/Turabian StyleZulqurnain Sabir; Juan L.G. Guirao; Tareq Saeed. 2021. "Solving a novel designed second order nonlinear Lane–Emden delay differential model using the heuristic techniques." Applied Soft Computing 102, no. : 107105.
The intension of the recent study is to solve a class of biological nonlinear HIV infection model of latently infected CD4+T cells using feed-forward artificial neural networks, optimized with global search method, i.e. particle swarm optimization (PSO) and quick local search method, i.e. interior-point algorithms (IPA). An unsupervised error function is made based on the differential equations and initial conditions of the HIV infection model represented with latently infected CD4+T cells. For the correctness and reliability of the present scheme, comparison is made of the present results with the Adams numerical results. Moreover, statistical measures based on mean absolute deviation, Theil's inequality coefficient as well as root mean square error demonstrates the effectiveness, applicability and convergence of the designed scheme.
Yolanda Guerrero–Sánchez; Muhammad Umar; Zulqurnain Sabir; Juan L. G. Guirao; Muhammad Asif Zahoor Raja. Solving a class of biological HIV infection model of latently infected cells using heuristic approach. Discrete & Continuous Dynamical Systems - S 2021, 14, 3611 .
AMA StyleYolanda Guerrero–Sánchez, Muhammad Umar, Zulqurnain Sabir, Juan L. G. Guirao, Muhammad Asif Zahoor Raja. Solving a class of biological HIV infection model of latently infected cells using heuristic approach. Discrete & Continuous Dynamical Systems - S. 2021; 14 (10):3611.
Chicago/Turabian StyleYolanda Guerrero–Sánchez; Muhammad Umar; Zulqurnain Sabir; Juan L. G. Guirao; Muhammad Asif Zahoor Raja. 2021. "Solving a class of biological HIV infection model of latently infected cells using heuristic approach." Discrete & Continuous Dynamical Systems - S 14, no. 10: 3611.
The purpose of the current work is to solve the SIR nonlinear model based on dengue fever using a stochastic numerical computing scheme together with the artificial neural networks (ANNs) optimized by a well-known global genetic algorithm (GA) and local refinements of sequential quadratic programming (SQP), i.e., ANN-GA-SQM. The optimization of an error based merit function is performed by using the concepts of differential model along with the initial conditions to solve the SIR nonlinear model based dengue fever. The stochastic ANN-GA-SQM capability to solve the SIR nonlinear model based dengue fever is scrutinized to examine the correctness, precision, efficiency and constancy of the ANN-GA-SQM. The obtained numerical results of the SIR nonlinear model based dengue fever via ANN-GA-SQP are compared with the Adams results that authenticate the significance of the ANN-GA-SQM. Furthermore, statistical deliberations using the ‘semi interquartile range’, ‘mean absolute deviation’ and ‘Theil’s inequality coefficient’ have been implemented to authenticate the convergence and precision of the designed ANN-GA-SQM.
Muhammad Umar; Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Yolanda Guerrero Sánchez. A stochastic numerical computing heuristic of SIR nonlinear model based on dengue fever. Results in Physics 2020, 19, 103585 .
AMA StyleMuhammad Umar, Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Yolanda Guerrero Sánchez. A stochastic numerical computing heuristic of SIR nonlinear model based on dengue fever. Results in Physics. 2020; 19 ():103585.
Chicago/Turabian StyleMuhammad Umar; Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Yolanda Guerrero Sánchez. 2020. "A stochastic numerical computing heuristic of SIR nonlinear model based on dengue fever." Results in Physics 19, no. : 103585.
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.
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 StyleZulqurnain 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 StyleZulqurnain 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.