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In the present study, a novel application of integrated evolutionary computing paradigm is presented for the analysis of nonlinear systems of differential equations representing the dynamics of virus propagation model in computer networks by exploiting the discretization strength of finite difference procedure, global search efficacy of genetic algorithms (GAs) aided with interior-point method (IPM) as efficient local search mechanism. Residual error based cost function is constructed by utilizing the effectiveness of approximation in mean square error sense and combined strength of GA-IPM is used as a viable optimization mechanism to find the solution of the problem. The proposed scheme is implemented for dynamical analysis of the model in terms of susceptible-infected and protected computer nodes by varying the probabilities of infections, countermeasures, curing and immunity while keeping connected and disconnected rates fixed. The statistical performance evaluated by means of deviations from reference Adams numerical results are practiced viably through performance metrics of accuracy and computational complexity to demonstrate the worth of integrated stochastic solver.

In the presented research article, the intelligence based numerical computation of artificial neural network backpropagated with Levenberg-Marquardt algorithm has been developed to analyze the novel ferrofluid flow model in the presence of magnetic dipole. Heat transfer effects are also incorporated along the horizontal. The designed fluid flow model initially represented by system of partial differential equations are converted into system of non-linear ordinary differential equations through suitable similarity transformations. The reference dataset of the possible outcomes is obtained from Adam numerical solver for the different scenarios of flow model by variation of co-efficient of the thermal expansion, Eckert number, suction parameter, magnetization and radiation parameter. The approximated solutions are interpreted for designed model by testing, training and validation process of backpropagated neural networks. Furthermore, the comparative studies and performance analysis of used algorithm is validated through regression analysis, histogram studies, correlation index and results of mean square error.

The aim of this study is to present the numerical solutions of the higher order singular nonlinear differential equations using an advanced intelligent computational approach by manipulating the Morlet wavelet (MW) neural networks (NNs), global approach as genetic algorithm (GA) and quick local search approach as interior-point method (IPM), i.e., GA-IPM. MWNNs is applied to discretize the higher order singular nonlinear differential equations to express the activation function using the mean square error. The performance of the designed MWNNs using the GA-IPM is observed to solve three different variants based on the higher order singular nonlinear differential model to check the significance, efficacy and consistency of the designed MWNNs using the GA-IPM. Furthermore, statistical performances are provided to check the precision, accuracy and convergence of the present approach.

The protection system has a vital role in subsystems of the power network including the generation, transmission and distribution system. This system combines several types of protection relays including directional over current relay, differential relay, distance relay, earth faults relay, inverse definite minimum time (IDMT) relay for the protection of line, generators bus bars, transformers, line to ground faults and feeder lines of the power system. In this research paper, the overall performance of the protection system is improved by reducing the overall operational time of directional over current relays (DOCRs) through the optimal coordination between the primary and backup over current protective relays while keeping the time multiplier setting (TMS), pickup tap setting (PTS) and coordination time of interval (CTI) within the allowable limits. A new optimization strategy, namely the FPSOGSA, is developed by integrating the concept of fractional calculus inside the mathematical model of canonical particle swarm optimization and combining with traditional gravitational search algorithm to enhance the optimizer characteristics and tested on coordination problem of DOCRs in standard power systems including the IEEE 3, 8 and 15 bus networks. The results, yielded by proposed algorithm and their comparison with other well-known recently established counterparts, reveal that the synergy of FC, PSO and GSA enhance the performance of the optimizer by combining the individual strengths of these tools and finding the best global solution. The consistency, stability and reliability of FPSOGSA is endorsed by comprehensive statistical analysis based on the empirical cumulative distribution function, histograms, boxplot illustrations, quantile–quantile plots, minimum fitness evolution in each independent simulation.

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.

The present research work is to put 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.

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.

In this research, the phenomenon of heat and mass transfer in 3D radiative flow of hybrid nanofluid over a rotational disk is investigated. Nanoparticles of Al2O3 and Cu are being used with water (H2O) as base fluid. The mathematical flow model in terms of PDEs is constructed by considering the heat transport mechanism due to Joule heating and viscous dissipation. This set of PDEs is converted into a system of ODEs by introducing the proper similarity transformations, which is then solved with the computational strength of Lobatto IIIA method. Demonstrations of graphical and numerical data are offered to examine the variation of velocity and thermal field against various physical constraints. The variable trend of heat transfer rate and skin friction coefficient through numerical data are also investigated. It is found that rate of heat transfer is proportional to Brinkman number, magnetic effect and concentration of nanoparticles. Achieved accuracy in term of relative error upto the level of 1e-14 shows the reliability and worth of solution methodology.

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.

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.

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.

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.

In this study, a new evolutionary optimized finite difference based computing paradigm is presented for dynamical analysis of dust density model for the ensemble of electrical charges and dust particles represented with nonlinear oscillatory system based on hybridization of Van-der Pol and Mathieu equation (VDP-ME). Strength of accurate and effective discretization ability of finite difference method (FDM) is exploited to transform VDP-ME to equivalent nonlinear system of algebraic equations. The residual error based fitness function of the transformed model is constructed by the competency of approximation theory in mean square sense. The optimization of the residual error of the system through hybrid meta-heuristic computing paradigm GA-SQP; genetic algorithm (GA) for viable global search aided with rapid fine tuning of sequential quadratic programming (SQP). The proposed GA-SQP-FDM is applied on variants of dust density model of VDP-ME by varying the rate of charged dust grain production, as well as, loss and comparison of results with state of art numerical procedure established the worth of the scheme in terms of accuracy and convergence measures endorsed through statistical observations on large dataset.

The present study aims to provide an innovative stochastic numerical solver's application by the use of neural networks with Levenberg-Marquardt backpropagation to examine the dynamics of hydrogen possessions and variable viscosity in the fluidic system of electrically conducting copper and silver nanoparticles with mixed convection. The system of PDEs obtained by mathematical modeling of the physical phenomena are reduced into non-linear ODEs by utilizing suitable transformations. The ODEs dataset is constructed through Adams numerical solver and target parameters for input and output parameter of neural networks. The testing, validation and training processes are exploited in neural network models with learning based on backpropagation of LM method to calculate the solution for different scenarios created on variation of physical parameters of the proposed flow of Reynolds and Vogel models. Validation and verification of neural network model to find the solution of fluid flow problem is endorsed on the assessment of achieved accuracy through mean squared error, error histograms and regression studies.

The present study presents numerical solution of the fourth order, singular, nonlinear Emden–Fowler equation integrated computational intelligence by exploiting the efficiency of feedforward artificial neural networks (ANNs), global optimization strength of genetic algorithms (GAs) and rapid local search of sequential quadratic programming (SQP). ANN is applied to discretize the nonlinear Emden–Fowler differential equation and consequentially construct a fitness/merit function on mean squared error sense. The optimization of the decision variables of ANN to solve the multi-singular, fourth order, nonlinear Emden–Fowler equation is performed by integrating capability GAs and SQP. The proficiency of the presented approach is certified on precision, convergence and stability indices, which are further enhanced through effectiveness, significance and reliability measures on statistical data for solving three different cases of the singular systems.

With the development of urban and rural infrastructure, the power system is enforced to operate nearly at its full capacity which result in heavily stressed power grid operation, greater loss, peak generation, security threat and instability of the electrical network. The performance of the legacy electric network can be enhanced by solving optimal reactive power dispatch (ORPD) problems such as, tuning of the grid voltages, transformers tap setting, capacitor bank rating, allocation and sizing of flexible AC transmission system (FACTS) through computational intelligence tools. In last few decades, several optimization strategies are developed to solve ORPD problems but still research is in progress to leverage the performance of power system. In this line of thought, this paper provides a comprehensive literature of major optimization tools designed for the solution of ORPD problems with aim of improving the power system performance. The purpose of this study is to document up to date information on the optimal reactive power dispatch (ORPD), ORPD incorporating FACTS, mathematical model of ORPD problems with corresponding constraints, mathematical model of FACTS in ORPD, and applications of ORPD. At the end, a new computational tool based on fractional calculus has also been introduced for performance improvement of traditional swarming techniques to support researchers in field of energy/power sector and carry out further research.

In the presented study, a novel application of intelligent numerical computing solver based on neural networks backpropagated with the Levenberg-Marquard scheme (NN-BLMS) is presented to interpret the chemical reactions and activation energy in unsteady 3D flow of Eyring-Powell magneto-nanofluidic system for convective heat and mass flux scenarios. The original nonlinear coupled PDEs representing the Eyring-Powell magneto-nanofluidic model (EPMNM) is transformed to an equivalent nonlinear ODEs system by exploiting similarity variables. A dataset for the proposed NN-BLMS is generated for different scenarios of EPMNM by variation of radiation, temperature ratio parameter, heat generation, Brownian motion and thermophoresis parameters by using Adam numerical method. The training, testing, and validation processes of NN-BLMS are performed to determine the approximate solution of EPMNM for different cases and comparison with reference results to verify the correctness of the proposed NN-BLMS. The performance of the proposed NN-BLMS to effectively solve the EPMNM is endorsed through mean squared error, histogram studies and regression analysis. The close matching of the proposed and reference results based on error analysis form level 10−05 to 10-07 validates the correctness of the proposed methodology.

Parameter estimation is an important issue for the quality monitoring and reliability assessment of power systems. In this study, an innovative fractional order least mean square (I-FOLMS) adaptive algorithm is presented for an effective parameter estimation. The I-FOLMS algorithm exploits the fractional gradient in its recursive parameter update mechanism, because its performance can be tuned by means of the fractional order. High values of the fractional order are good for fast convergence, but lead to steady state mis-adjustments. While, low values provide a smooth steady state behavior, but require a compromise in the convergence rate. The effective performance of I-FOLMS is verified and validated through two numerical examples of power signals estimation for different levels of noise variance and values of the fractional orders.

The purpose of this study is to design an epidemic model that portray the exploitation of hardware through embedded tiny chip based mini-computer within another computer such as Intel management engine (ME). The firmware level bugs allow escalation of privileges and remote execution of code beneath the running operating system for infiltration or completely intervene with computer. A mathematical model is presented for vulnerabilities of embedded tiny chip based hardware that portray exploitation and spread of infection in network infrastructures. Disease free and endemic equilibria are analyzed for the designed model in terms of the basic reproduction number R 0 , as well as global and local stability conditions for integer order scenarios of the system. Numerical experimentations are performed for distinct fractional order terms in the system and the results endorsed that fractional regimes provide enrich dynamics by means of super-fast transients as well as super slow evolutions of the steady-state which are rarely substantiated in integer order counterpart models.

For analysis of physical properties of different materials, rectangular porous fins are used to examine the heat transformation through a system. In this paper, a metaheuristic is combined with neural computing modelling to study the effects of temperature changes in a porous fin model. Cuckoo search algorithm is used as an efficient optimization technique to find the best weights to reduce the mean squared error in the required temperature profile. The governing partial differential equation is converted into a non-linear ordinary differential equation subject to certain boundary conditions. Two individual cases, of silicon nitride (Si3N4) and Aluminium (Al), are considered. In the proposed procedure, the Cuckoo Search(CS) algorithm is combined with the artificial neural network (ANN), namely CS-ANN, to solve the differential equations and obtain solutions with better accuracy. Keywords: Heat distribution, Porous fin, Artificial intelligence, Metaheuristics, Cuckoo search algorithm, Differential equations, Optimization problems

In this work, novel application of evolutionary computational heuristics is presented for parameter identification problem of nonlinear Hammerstein controlled auto regressive auto regressive (NHCARAR) systems through global search competency of backtracking search algorithm (BSA), differential evolution (DE) and genetic algorithms (GAs). The mean squared error metric is used for the fitness function of NHCARAR system based on difference between actual and approximated design variables. Optimization of the cost function is conducted with BSA for NHCARAR model by varying degrees of freedom and noise variances. To verify and validate the worth of the presented scheme, comparative studies are carried out with its counterparts DE and GAs through statistical observations by means of weight deviation factor, root of mean squared error, and Thiel’s inequality coefficient as well as complexity measures.

In the present study, strength of meta-heuristic computing techniques is exploited for estimation problem of Hammerstein controlled auto regressive auto regressive moving average (HCARARMA) system using differential evolution (DE), genetic algorithms (GAs), pattern search (PS) and simulated annealing (SA) algorithms. The approximation theory in mean squared error sense is utilized for construction of cost function for HCARARMA model and highly uncorrelated adjustable parameter of the system is optimized with global search exploration of DE, GAs, PS and SA algorithms. Comparative study is carried out from desired known parameters of the HCARARMA model for different degree of freedom and noise variation scenarios. Performance analysis of the DE, GAs, PS and SA algorithms is conducted through results of statistics based on sufficient large independent executions in terms of measure of central tendency and variation for both precision and complexity indices. The exhaustive simulations established that the population-based heuristics are more accurate than single solution-based methodologies for HCARARMA identification.

In this study, a new computing paradigm is presented for evaluation of dynamics of nonlinear prey–predator mathematical model by exploiting the strengths of integrated intelligent mechanism through artificial neural networks, genetic algorithms and interior-point algorithm. In the scheme, artificial neural network based differential equation models of the system are constructed and optimization of the networks is performed with effective global search ability of genetic algorithm and its hybridization with interior-point algorithm for rapid local search. The proposed technique is applied to variants of nonlinear prey–predator models by taking different rating factors and comparison with Adams numerical solver certify the correctness for each scenario. The statistical studies have been conducted to authenticate the accuracy and convergence of the design methodology in terms of mean absolute error, root mean squared error and Nash-Sutcliffe efficiency performance indices.

In this work, a novel application of bio-inspired computational heuristic paradigm is presented for micropolar fluid flow and heat transfer system in a channel with permeable walls by modeling competency of neural networks, global search of genetic algorithms, and rapid local convergence of sequential quadratic programming. Approximation theory in the mean squared error sense is exploited for the formulation of an objective function to solve the governing nonlinear fluidics system. The designed scheme is employed to study the dynamics of the model in terms of stream function, microrotation, concentration, and temperature profiles for prominent factors based on Reynolds number, Peclet number for diffusion of heat and mass, coupling, spin-gradient viscosity, micro inertia density parameters. The consistency and robustness of the solver are validated through statistical performance indices based on comparison with state of art Adams numerical method for accuracy and complexity measures.

The importance of rectangular porous fins for the transformation of heat through the system is well-recognized to analyze the physical characteristics of material in practical applications. In this study, a neuro-computing based stochastic numerical paradigm has been designed to study the dynamics of temperature distribution in porous fin model by exploiting the strength of artificial neural network (ANN) modeling integrated with global search exploration with genetic algorithms (GAs) and efficient local search with interior-point technique (IPT). The governing porous fin equation is transformed into an equivalent nonlinear second order ordinary differential equation. Effect of heat on rectangular type fin with thermal conductivity and temperature dependent internal heat generation is measured through stochastic solver based on ANN optimized with GA-IPT in case of two different materials, Silicon nitride Si 3 N 4 and Aluminium Al . The proposed technique ANN-GA-IPT has been applied on transformed equation for multi-times and the accuracy, convergence and robustness of designed model has been validated by analysis of variance test.