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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.

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.

Non-technical loss is a serious issue around the globe. Consumers manipulate their smart meter (SM) data to under-report their readings for financial benefit. Various manipulation techniques are used. This paper highlights novel false data injection (FDIs) techniques, which are used to manipulate the smart meter data. These techniques are introduced in comparison to six theft cases. Furthermore, various features are engineered to analyze the variance, complexity, and distribution of the manipulated data. The variance and complexity are created in data distribution when FDIs and theft cases are used to poison SM data, which is investigated through skewness and kurtosis analysis. Furthermore, to tackle the data imbalance issue, the proximity weighted synthetic oversampling (ProWsyn) technique is used. Moreover, a hybrid attentionLSTMInception is introduced, which is an integration of attention layers, LSTM, and inception blocks to tackle data dimensionality, misclassification, and high false positive rate issues. The proposed hybrid model outperforms the traditional theft detectors and achieves an accuracy of 0.95%, precision 0.97%, recall 0.94%, F1 score 0.96%, and area under-the-curve (AUC) score 0.98%.

Abstract Estimation of the effectiveness of Au nanoparticles concentration in peristaltic flow through a curved channel by using a data driven stochastic numerical paradigm based on artificial neural network is presented in this study. In the modelling, nano composite is considered involving multi-walled carbon nanotubes coated with gold nanoparticles with different slip conditions. Modeled differential system of the physical problem is numerically analyzed for different scenarios to predict numerical data for velocity and temperature by Adams Bashforth method and these solutions are used as a reference dataset of the networks. Data is processed by segmentation into three categories i.e., training, validation and testing while Levenberg–Marquart training algorithm is adopted for optimization of networks results in terms of performance on mean square errors, train state plots, error histograms, regression analysis, time series responses, and auto-correlation, which establish the accurate and efficient recognition of trends of the system.

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.

Abstract In the present research, a novel mathematical model for the motion of cilia using non-linear rheological fluid in a symmetric channel is developed. The strength of analytical perturbation technique is employed for the solution of proposed physical process using mectachoronal rhythm based on Cilia induced flow for pseudo plastic nano fluid model by considering the low Reynolds number and long wave length approximation phenomena. The role of ciliary motion for the fluid transport in various animals is explained. Analytical expressions are gathered for stream function, concentration, temperature profiles, axial velocity, and pressure gradient. Whereas, transverse velocity, pressure rise per wave length, and frictional force on the wall of the tubule are investigated with aid of numerical computations and their outcomes are demonstrated graphically. A comprehensive analysis for comparison of Perturb and numerical solution is done. This analysis validates the analytical solution.

Abstract In this study, the unsteady squeezing flow between circular parallel plates (USF-CPP) is investigated through the intelligent computing paradigm of Levenberg–Marquard backpropagation neural networks (LMBNN). Similarity transformation introduces the fluidic system of the governing partial differential equations into nonlinear ordinary differential equations. A dataset is generated based on squeezing fluid flow system USF-CPP for the LMBNN through the Runge–Kutta method by the suitable variations of Reynolds number and volume flow rate. To attain approximation solutions for USF-CPP to different scenarios and cases of LMBNN, the operations of training, testing, and validation are prepared and then the outcomes are compared with the reference data set to ensure the suggested model’s accuracy. The output of LMBNN is discussed by the mean square error, dynamics of state transition, analysis of error histograms, and regression illustrations.

Abstract This study presents a novel application of soft-computing through intelligent, neural networks backpropagated by Levenberg–Marquardt scheme (NNs-BLMS) to solve the mathematical model of unsteady thin film flow of magnetized Maxwell fluid with thermo-diffusion effects and chemical reaction (TFFMFTDECR) over a horizontal rotating disk. The expression for thermophoretic velocity is accounted. Energy expression is deliberated with the addition of non-uniform heat source. The PDEs of mathematical model of TFFMFTDECR are transformed to ODEs by the application of similarity transformations. A dataset is generated through Adams method for the proposed NNs-BLMS in case of various scenarios of TFFMFTDECR model by variation of rotation parameter, magnetic parameter, space dependent heat sink/source parameter, temperature dependent heat sink/source parameter and chemical reaction controlling parameter. The designed computational solver NNs-BLMS is implemented by performing training, testing and validation for the solution of TFFMFTDECR system for different variants. Variation of various physical parameters are designed via plots and explain in details. It is depicted that thin film thickness increases for higher values of disk rotation parameter, while it diminishes for higher magnetic parameter. Furthermore, higher values of Dufour number and the corresponding diminishing values of Soret number causes enhancement in fluid temperature profile. Further the effectiveness of NNs-BLMS is validated by comparing the results of the proposed solver and the standard solution of TFFMFTDECR model through error analyses, histogram representations and regression analyses.

The accurate estimation of power signal parameters allows smart grids to optimize power delivery efficiency, improve equipment utilization, and control power flow among generation nodes and loads. However, practically it becomes a challenging task because of the presence of harmonic distortions. In this study, a parameter estimation of the power system harmonics is investigated through swarm intelligence–based optimization strength of the cuckoo search algorithm. The performance evaluation is conducted in detail for different generations and particle sizes and for different signal-to-noise ratios. The simulation results reveal that the cuckoo search optimization heuristic accurately estimates the amplitude and phase parameters of the power system harmonics and is robust against different signal-to-noise ratios.

The application of hybrid nanomaterials for the improvement of thermal efficiency of base fluid has increasingly gained attention during the past few decades. The basic purpose of this study is to investigate the flow characteristics along with heat transfer in an unsteady three-dimensional flow of hybrid nanofluid over a stretchable and rotatory sheet (3D-UHSRS). The flow model in the form of PDEs was reduced to the set of ordinary differential equations utilizing the appropriate transformations of similarity. The influence of the rotation parameter, unsteadiness parameter, stretching parameter, radiation parameter, and Prandtl number on velocities and thermal profile was graphically examined. A reference solution in the form of dataset points for the 3D-UHSRS model are computed with the help of renowned Lobatto IIIA solver, and this solution is exported to MATLAB for the proper implementation of proposed solution methodology based on the Levenberg–Marquardt supervised neural networks. Graphical and numerical results based on the mean square error (MSEs), time series response, error distribution plots, and regression plots endorses the precision, validity, and consistency of the proposed solution methodology. The MSE up to the level of 10–12 confirms the accuracy of the achieved results.

Multilayer piezocomposite transducers are widely used in many applications where broad bandwidth is required for tracking and detection purposes. However, it is difficult to operate these multilayer transducers efficiently under frequencies of 100 kHz. Therefore, this work presents the modeling and optimization of a five-layer piezocomposite transducer with ten variables of nonuniform layer thicknesses and different volume fractions by exploiting the strength of the genetic algorithm (GA) with a one-dimensional model (ODM). The ODM executes matrix manipulation by resolving wave equations and produces mechanical output in the form of pressure and electrical impedance. The product of gain and bandwidth is the required function to be maximized in this multi-objective and multivariate optimization problem, which is a challenging task having ten variables. Converting it into the minimization problem, the reciprocal of the gain-bandwidth product is considered. The total thickness is adjusted to keep the central frequency at approximately 50–60 kHz. Piezocomposite transducers with three active materials, PZT5h, PZT4d, PMN-PT, and CY1301 polymer, as passive materials were designed, simulated, and statistically evaluated. The results show significant improvement in gain bandwidth compared to previous existing techniques.

The objective of this paper is to present a novel design of intelligent neuro-supervised networks (INSNs) in order to study the dynamics of a mathematical model for Parkinson’s disease illness (PDI), governed with three differential classes to represent the rhythms of brain electrical activity measurements at different locations in the cerebral cortex. The proposed INSNs are constructed by exploiting the knacks of multilayer structure neural networks back-propagated with the Levenberg–Marquardt (LM) and Bayesian regularization (BR) optimization approaches. The reference data for the grids of input and the target samples of INSNs were formulated with a reliable numerical solver via the Adams method for sundry scenarios of PDI models by way of variation of sensor locations in order to measure the impact of the rhythms of brain electrical activity. The designed INSNs for both backpropagation procedures were implemented on created datasets segmented arbitrarily into training, testing, and validation samples by optimization of mean squared error based fitness function. Comparison of outcomes on the basis of exhaustive simulations of proposed INSNs via both LM and BR methodologies was conducted with reference solutions of PDI models by means of learning curves on MSE, adaptive control parameters of algorithms, absolute error, histogram error plots, and regression index. The outcomes endorse the efficacy of both INSNs solvers for different scenarios in PDI models, but the accuracy of the BR-based method is relatively superior, albeit at the cost of slightly more computations.

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.

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.

The purpose of the present work is to solve a third kind of multi-singular nonlinear system using the neuro-swarm computing solver based on the artificial neural networks (ANNs) optimized with the effectiveness of particle swarm optimization (PSO) maintained by a local search proficiency of interior-point algorithm (IPA), i.e., ANN-PSO-IPA. An objective function is designed using the continuous mapping of ANN for nonlinear multi-singular third order system of Emden-Fowler equations and optimization of fitness function carried out with the integrated strength of PSO-IPA. The motivation to design the ANN-PSO-IPA is to present a feasible, reliable and feasible framework to handle with such complicated nonlinear multi-singular third order system of Emden-Fowler model. The designed ANN-PSO-IPA is tested for three different nonlinear variants of the multi-singular third kind of Emden-Fowler system. The obtained numerical results on single/multiple executions of the designed ANN-PSO-IPA are used to endorse the precision, viability and reliability.

This paper presents an innovative artificial neural networks (ANNs) based hybrid algorithm of genetics optimization and sequential quadratic programming (AGOSQP) to construct the mathematical model for the dynamics of Lassa fever (DLF) in Nigeria. The model designated by the transmission of disease between two populations: human population i.e. susceptible Sh, exposed Eh, infectious Ih and recovered Rh humans and rodent population i.e. susceptible Sr and infectious Ir rodents. The log sigmoid function as an objective function based on mean squared error is constructed to optimize AGOSQP where genetic algorithm work as global searching optimization and SQP serve as the local searching optimization. To assess the correctness, robustness and convergence stability, the comparison between state of art Adam method and proposed AGOSQP is established. The Theil’s inequality coefficient (TIC), root mean square error (RMSE) and mean absolute deviation (MAD) are also computed to authenticate the efficiency of proposed AGOSQP to solve the model for the dynamics of Lassa fever.

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.

Abstract In the current study, a modern implementation of intelligent numerical computational solver introduced using the Levenberg Marquardt algorithm based trained neural networks (LMA-TNN) to analyze the wire coating system (WCS) for the elastic-viscous non-Newtonian Eyring–Powell fluid (EPF) with the impacts of Joule heating, magnetic parameter and heat transfer scenarios in the permeable medium. The nonlinear PDEs describing the WCS-EPF are converted into dimensionless nonlinear ODEs containing the heat and viscosity parameters. The reference data for the designed LMA-TNN is produced for various scenarios of WCS-EPF representing with porosity parameter, non-Newtonian parameter, heat transfer parameter and magnetic parameter for the proposed analysis using the state of the art explicit Runge–Kutta technique. The training, validation, and testing operations of LMA-TNN are carried out to obtain the numerical solution of WCS-EPF for various cases and their comparison with the approximate outcomes certifying the reasonable accuracy and precision of LMA-TNN approach. The outcomes of LMA-TNN solver in terms of state transition (ST) index, error-histograms (EH) illustration, mean square error, and regression (R) studies further established the worth for stochastic numerical solution of the WCS-EPF. The strong correlation between the suggested and the reference outcomes indicates the structure’s validity, for all four cases of WCS-EPF, fitting of the precision $$10^{-5}$$ 10 - 5 to $$10^{-9}$$ 10 - 9 is also accomplished.

Swarm-based metaheuristics have shown significant progress in solving different complex optimization problems, including the parameter identification of linear, as well as nonlinear, systems. Nonlinear systems are inherently stiff and difficult to optimize and, thus, require special attention to effectively estimate their parameters. This study investigates the parameter identification of an input nonlinear autoregressive exogenous (IN-ARX) model through swarm intelligence knacks of the nonlinear marine predators’ algorithm (NMPA). A detailed comparative analysis of the NMPA with other recently introduced metaheuristics, such as Aquila optimizer, prairie dog optimization, reptile search algorithm, sine cosine algorithm, and whale optimization algorithm, established the superiority of the proposed scheme in terms of accurate, robust, and convergent performances for different noise and generation variations. The statistics generated through multiple autonomous executions represent box and whisker plots, along with the Wilcoxon rank-sum test, further confirming the reliability and stability of the NMPA for parameter estimation of IN-ARX systems.

In this article, a chaotic computing paradigm is investigated for the parameter estimation of the autoregressive exogenous (ARX) model by exploiting the optimization knacks of an improved chaotic grey wolf optimizer (ICGWO). The identification problem is formulated by defining a mean square error-based fitness function between true and estimated responses of the ARX system. The decision parameters of the ARX model are calculated by ICGWO for various populations, generations, and noise levels. The comparative performance analyses with standard counterparts indicate the worth of the ICGWO for ARX model identification, while the statistical analyses endorse the efficacy of the proposed chaotic scheme in terms of accuracy, robustness, and reliability.

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.

Abstract The objective of the current investigation is to examine the influence of variable viscosity and transverse magnetic field on mixed convection fluid model through stretching sheet based on copper and silver nanoparticles by exploiting the strength of numerical computing via Lobatto IIIA solver. The nonlinear partial differential equations are changed into ordinary differential equations by means of similarity transformations procedure. A renewed finite difference based Lobatto IIIA method is incorporated to solve the fluidic system numerically. Vogel's model is considered to observe the influence of variable viscosity and applied oblique magnetic field with mixed convection along with temperature dependent viscosity. Graphical and numerical illustrations are presented to visualize the behavior of different sundry parameters of interest on velocity and temperature. Outcomes reflect that volumetric fraction of nanoparticles causes to increase the thermal conductivity of the fluid and the temperature enhances due to blade type copper nanoparticles. The convergence analysis on the accuracy to solve the problem is investigated viably though the residual errors with different tolerances to prove the worth of the solver. The temperature of the fluid accelerates due the blade type nanoparticles of copper and skin friction coefficient is reduced due to enhancement of Grashof Number.

The present work is to design a novel Neuro swarm computing standards using artificial intelligence scheme to exploit the Gudermannian neural networks (GNN)accomplished with global and local search ability of particle swarm optimization (PSO) and sequential quadratic programming scheme (SQPS), called as GNN-PSO-SQPS to solve a class of the second order Lane-Emden singular nonlinear model (SO-LES-NM). The suggested intelligent computing solver GNN-PSO-SQPS using the Gudermannian kernel are unified with the configuration of the hidden layers of GNN of differential operators for solving the SO-LES-NM. An error based fitness function (FF) applying the differential form of the differential model and corresponding boundary conditions. The FF is optimized together with the combined heuristics of PSO-SQPS. Three problems of the SO-LES-NM are solved to validate the correctness, effectiveness and competence of the designed GNN-PSO-SQPS. The performance of the GNN-PSO-SQPS through statistical operators is tested to check the constancy, convergence and precision.

Optimal reactive power dispatch (ORPD) intended for reducing the real power losses of the transmission scheme remains one of the supreme concerns for the research community to explore the competence of power schemes. Numerous systems have been deliberate to increase the performance of the optimization method in tunning the operational variables as well as explored through estimating the final results. The research offering a novel approach based on the entropy evolution technique implemented into Fractional PSOGSA algorithm to solve the optimal reactive power dispatch problem. To alleviate the drawback of PSOGSA the fractional and entropy techniques are implemented into the algorithm which enhanced memory effect, stability and robustness of the algorithm. The novel design of FPSOGSA-Entropy is further tested for the optimal reactive power dispatch problems on IEEE-30 and IEEE-57 bus standards to find the two objective functions; minimization of power line losses and voltage deviation. The superior performance of the proposed FPSOGSA-Entropy is further verified with the results of simple FPSOGSA for both single and multiple runs through comparative analysis study with state of art counterparts for each scenario of optimal reactive power dispatch problems.

Parameter estimation of Direction of Arrival (DOA) using deterministic and stochastic computing paradigms is an enabling development for underwater acoustic signal processing beside its applications in the field of seismology, astronomy, earthquake and bio-medicine. In this work, the comparative study between state of the art deterministic and heuristics algorithms is presented for viable DOA estimation for different underwater dynamic objects. A Uniform Linear Array (ULA) of eight hydrophones is used for impinging acoustic waves from far-field targets. In order to evaluate the performance, the viability of innovative statistical indices is utilized to explain. Performance analysis of Genetic Algorithm(GA) and Particle Swarm Optimization(PSO) is conducted with standard counterparts including MVDR, MUSIC, ESPRIT and UESPRIT for different number of targets in terms of estimation accuracy, robustness against the number of elements and noise, cumulative distribution function of Root Mean Sqaure Error(RMSE), frequency distribution of the RMSE over the monte carlo trials, the resolution ability and computational complexity in the presence of white Gaussian measurement noise. Crammer Rao Bound (CRB) based analysis is also performed for the validation assessments and results on Monte Carlo simulations depict that the Genetic Algorithm(GA) showed the outperform counterparts on precision, convergence and complexity indices.

The aim of this study is to design a layer structure of feed-forward artificial neural networks using the Morlet wavelet activation function for solving a class of pantograph differential Lane-Emden models. The Lane-Emden pantograph differential equation is one of the important kind of singular functional differential model. The numerical solutions of the singular pantograph differential model are presented by the approximation capability of the Morlet wavelet neural networks (MWNNs) accomplished with the strength of global and local search terminologies of genetic algorithm (GA) and interior-point algorithm (IPA), i.e., MWNN-GAIPA. Three different problems of the singular pantograph differential models have been numerically solved by using the optimization procedures of MWNN-GAIPA. The correctness of the designed MWNN-GAIPA is observed by comparing the obtained results with the exact solutions. The analysis for 3, 6 and 60 neurons are also presented to check the stability and performance of the designed scheme. Moreover, different statistical analysis using forty number of trials is presented to check the convergence and accuracy of the proposed MWNN-GAIPA scheme.

The utmost advancements of artificial neural networks (ANNs), software-defined networks (SDNs) and internet of things (IoT) technologies find beneficial in different applications of the smart healthcare sector. Aiming at modern technology’s use in the future development of healthcare, this paper presents an advanced heuristic based on Morlet wavelet neural network for solving the mosquito release ecosystem in a heterogeneous atmosphere. The mosquito release ecosystem is dependent of six classes, eggs density, larvae density, pupae density, mosquitoes searching for hosts density, resting mosquito’s density and mosquitoes searching for ovipositional site density. An artificial neural network with the layer structure of Morlet wavelet (MWNN) kernel is presented using the global and local search optimization schemes of genetic algorithm (GA) and active-set algorithm (ASA), i.e., MWNN-GA-ASA. The accurateness, reliability and constancy of the proposed MWNN-GA-ASA is established through comparative examinations with Adams method based numerical results to solve the proposed nonlinear system with matching of order 10−06 to 10−09. The accuracy and convergence of the proposed MWNN-GA-ASA is certified using the statistical operators based on root mean square error (RMSE), Theil’s inequality coefficient (T.I.C) and mean absolute deviation (MAD) operators.

Abstract Reactive power dispatch is a vital problem in the operation, planning and control of power system for obtaining a fixed economic load expedition. An optimal dispatch reduces the grid congestion through the minimization of the active power loss. This strategy involves adjusting the transformer tap settings, generator voltages and reactive power sources, such as flexible alternating current transmission systems (FACTS). The optimal dispatch improves the system security, voltage profile, power transfer capability and overall network efficiency. In the present work, a fractional evolutionary approach achieves the desired objectives of reactive power planning by incorporating FACTS devices. Two compensation arrangements are possible: the shunt type compensation, through Static Var compensator (SVC) and the series compensation through the Thyristor controlled series compensator (TCSC). The fractional order Darwinian Particle Swarm Optimization (FO-DPSO) is implemented on the standard IEEE 30, IEEE 57 and IEEE 118 bus test systems. The power flow analysis is used for determining the location of TCSC, while the voltage collapse proximity indication (VCPI) method identifies the location of the SVC. The superiority of the FO-DPSO is demonstrated by comparing the results with those obtained by other techniques in terms of measure of central tendency, variation indices and time complexity.

In the current study, a novel intelligent numerical computing paradigm based upon the foundation of the artificial neural networks legacy involving the Bayesian regularization (ANN-BR) approach has been implemented for the investigation of the non-uniform heat preoccupation process with the bio-convective flow dynamics of nanomaterial involving gyro-tactic microorganisms. The designed bio-convective stratified nanofluid flow (BCSNF) model initially represented by a system of PDEs is transformed into nonlinear ODEs by exploring appropriate transformations. The reference dataset for the BCSNF model was generated by the Adams numerical method for six scenarios by variation of the magnetic number, Brownian motion parameter, Prandtl number, bio-convection Lewis number, thermophoretic parameter, and bio-convection Peclet number. The approximate solutions were determined with 5–7 decimal places of accuracy and interpreted for the BCSNF model by the testing, training, and validation processes of the designed ANN-BR scheme. To check the efficiency of the introduced ANN-BR method, absolute error analysis, histogram studies, regression indices, and mean squared error (MSE) based figures of merit were used exhaustively to solve the variants of the BCSNF model involving gyro-tactic microorganisms with viscous dissipation, stratification, and heat immersion to study the influence of prominent parameters on the velocity, temperature, concentration, and motile density profiles.

In this study, an advanced computational artificial neural network (ANN) procedure is designed using the novel characteristics of the Levenberg–Marquardt backpropagation (LBMBP), i.e., ANN-LBMBP, for solving the waste plastic management in the ocean system that plays an important role in the economy of any country. The nonlinear mathematical form of the waste plastic management in the ocean system is categorized into three groups: waste plastic material W(χ), marine debris M(χ), and reprocess or recycle R(χ). The learning based on the stochastic ANN-LBMBP procedures for solving mathematical waste plastic management in the ocean is used to authenticate the sample statics, testing, certification, and training. Three different statistics for the model are considered as training 70%, while for both validation and testing are 15%. To observe the performances of the mathematical model, a reference dataset using the Adams method is designed. To reduce the mean square error (MSE) values, the numerical performances through the ANN-LBMBP procedures are obtained. The accuracy of the designed ANN-LBMBP procedures is observed using the absolute error. The capability, precision, steadfastness, and aptitude of the ANN-LBMBP procedures are accomplished based on the multiple topographies of the correlation and MSE.

Novel application of integrated swarming intelligence computing paradigm is exploited for reliable treatment of nonlinear active noise control (ANC) systems using global search capacity of grasshopper optimization algorithm (GOA) combined with local search efficacy of sequential quadratic programming (SQP), i.e., GOA-SQP. The designed optimization mechanism GOA-SQP is applied to minimize the cost function of ANC controller incorporating the nonlinear Volterra filtering having linear/nonlinear primary/secondary paths in case of different noise interferences of sinusoidal, random, and complex random type signals. The comparison of the results through statistical observations in terms of accuracy, convergence and complexity indices reveals that the GOA-SQP based ANC controllers are operative, resilient and viable.

Hybrid nanofluid is an emerging field due to the rapid enhancement of heat transfer and stable nanoparticles in base fluid properties. A three dimensional hybrid nanofluid flow model is constructed over biaxial porous stretching/shrinking sheet with heat transfer, Radiative heat and mass flux (3D-HNF-RHF). Bayesian Regularization technique based on Backpropagated neural networks (BRT-BNNs) is employed to estimate the solution of proposed model. It is the mathematical process which converts nonlinear regression fitting into a well-posed statistical process in the form of ridge regression. This method diminishes length cross validation need and more robust then Backpropagation technique. The proposed flow system 3D-HNF-RHF is transferred to ordinary differential equations (ODEs) possessing physical variations through self-similar transformations. The effect of derived variations such as thermal relaxation parameter, mass flux parameter, Stretching/shrinking parameter, Prandtl number, Skin friction and Nusselt number observed over the velocity and temperature fields. Numerical results of these physical parameters have been presented in tabulated form obtained from a dataset constructed through Homotopy Analysis Method imposed on 3D-HNF-RHF model. Statistical tests through mean square error, histogram curve and regression fitting curves are employed to check the accuracy and convergences of the solution obtained through BRT-BNNs. It is observed that Stretching/shrinking quantity and mass flux parameter slow down the flow rate whereas, increase radiative heat flux upsurges the temperature gradient. The impacts of surface drag force and heat transfer are illustrated through the different graphical illustrations.

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.

Robust modeling of a multimodal dynamic system is a challenging and fast-growing area of research. In this study, an integrated bi-modal computing paradigm based on Nonlinear Autoregressive Radial Basis Functions (NAR-RBFs) neural network model, a new family of deep learning with the strength of hybrid artificial neural network, is presented for the solution of nonlinear chaotic dusty system (NCDS) of tiny ionized gas particles arising in fusion devices, industry, astronomy, and space. In the proposed methodology, special transformations are introduced for a class of differential equations, which convert the local optimum to a global optimum. The proposed NAR-RBFs neural network model is implemented on bi-model NCDS represented with Van der Pol-Methiew Equation (VdP-ME) for different scenarios based on variation in dust gain production and loss for both small and large time domains. Excellent agreement for proposed bimodal computing paradigm by the result with the standard state of the arts numerical solvers is verified by attaining RMSE up to 1E−38 for the nonlinear VDP-ME. Accuracy of the proposed model in the critical time domain is also validated by convergence, stability and consistency analysis on statistics calculated from absolute error, root-mean-square error, and analysis of variance metrics.

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

Research community has a growing interest in neural networks because of their practical applications in many fields for accurate modeling and prediction of the complex behavior of systems arising from engineering, economics, business, financial and metrological fields. Artificial neural networks (ANN) are very flexible function approximations tool used as universal modeling based on the separating of the past dynamics into clusters, in which we construct local models to capture the potential growth of the series depends on the previously known values. In this study, rain data of five major cities of Sindh province of Pakistan is considered, and summer rainfall of these five synoptic stations are statistically evaluated for prediction. The nonlinear autoregressive network with exogenous inputs (NARX) model for a time series is analyzed to evaluate the pattern of precipitation. We train a highly nonlinear NARX network model from randomly generated initial weights that converged to the best solution with the help of the Levenberg-Marquardt algorithm. A multi-step ahead NARX response time predictor is developed for rain forecasting. The performance of the NARX model is viable to capture nonlinear behavior with a high value of correlation coefficient R ranging from 0.70 to 0.99 for different synoptic stations. The results calculated using the proposed NARX neural network time series approach are accurate and reliable based on the coefficient of correlation and mean square error indices for rainfall forecasting. Keywords: Artificial neural network, NARX model, Levenberg-Marquardt algorithm, Summer rainfall

In this paper, novel computing paradigm by exploiting the strength of feed-forward artificial neural networks (ANNs) with Levenberg-Marquardt Method (LMM), and Bayesian Regularization Method (BRM) based backpropagation is presented to find the solutions of initial value problems (IVBs) of linear/nonlinear pantograph delay differential equations (LP/NP-DDEs). The dataset for training, testing and validation is created with reference to known standard solutions of LP/NP-DDEs. ANNs are implemented using the said dataset for approximate modeling of the system on mean squared error based merit functions, while learning of the adjustable parameters is conducted with efficacy of LMM (ANN-LMM) and BRMs (ANN-BRM). The performance of the designed algorithms ANN-LMM and ANN-BRM on IVPs of first, second and third order NP-FDEs are verified by attaining a good agreement with the available solutions having accuracy in the range from 10-5 to 10-8 and are further endorsed through error histograms and regression measures.

Optimal reactive power dispatch (ORPD) problems in power system have been solved by using several variants of traditional nature inspired particle swam optimization (PSO) with aim to achieve a promising solution for a given objective such as line loss, voltage deviation and overall cost minimization. Several schemes have been designed to improve the performance of the optimization technique in tunning the operational variables and analyzed by evaluating the final results. In this article, a different method is designed to solve ORPD problems, by introducing Shannon entropy based diversity in the fractional order PSO dynamics, i.e., FOPSO-EE. The results show that synergy of both, the Shannon entropy and the fractional calculus can be used as the useful tools for enhancing the optimization strength of algorithm while solving the ORPD problems in standard IEEE 30 and 57 bus power systems. The performance of the design FOPSO-EE is further validated through results of statistical interpretations in terms of histogram analysis, box plot illustration, quantile-quantile probability plot and empirical probability distribution function.

Forecasting of fast fluctuated and high-frequency financial data is always a challenging problem in the field of economics and modelling. In this study, a novel hybrid model with the strength of fractional order derivative is presented with their dynamical features of deep learning, long-short term memory (LSTM) networks, to predict the abrupt stochastic variation of the financial market. Stock market prices are dynamic, highly sensitive, nonlinear and chaotic. There are different techniques for forecast prices in the time-variant domain and due to variability and uncertain behavior in stock prices, traditional methods, such as data mining, statistical approaches, and non-deep neural networks models are not suited for prediction and generalized forecasting stock prices. While autoregressive fractional integrated moving average (ARFIMA) model provides a flexible tool for classes of long-memory models. The advancement of machine learning-based deep non-linear modelling confirms that the hybrid model efficiently extracts profound features and model non-linear functions. LSTM networks are a special kind of recurrent neural network (RNN) that map sequences of input observations to output observations with capabilities of long-term dependencies. A novel ARFIMA-LSTM hybrid recurrent network is presented in which ARFIMA model-based filters having the linear tendencies better than ARIMA model in the data and passes the residual to the LSTM model that captures nonlinearity in the residual values with the help of exogenous dependent variables. The model not only minimizes the volatility problem but also overcome the over fitting problem of neural networks. The model is evaluated using PSX company data of the stock market based on RMSE, MSE and MAPE along with a comparison of ARIMA, LSTM model and generalized regression radial basis neural network (GRNN) ensemble method independently. The forecasting performance indicates the effectiveness of the proposed AFRIMA-LSTM hybrid model to improve around 80% accuracy on RMSE as compared to traditional forecasting counterparts.

In this paper, the computational strength in terms of soft computing neural networks backpropagated with the efficacy of Levenberg-Marquard training (NN-BLMT) is presented to study the squeezing flow with the heat transfer model (SF-HTM). The governing system of PDEs is reduced to an equivalent system of nonlinear ODEs using similarity transformations. NN-BLMT dataset for all problem scenarios progresses through the standard Adam numerical method by the influence of Prandtl number, Eckert number, and thermal slip. The processing of NN-BLMT training, testing, and validation, is employed for various scenarios and cases to find and compare approximation solutions with reference results. For the fluidic system SF-HTM, convergence analysis based on mean square errors, histogram presentations, and statistical regression plots is considered for the proposed computing infrastructure's performance in terms of NN-BLMT. Matching of the results for the fluid flow system SF-HTM based on proposed and reference results in terms of convergence up-to 10-07 to 10-03 proves the worth of proposed NN-BLMT.

In this paper, a multi sample compressive sensing (CS) technique is presented for the direction of arrival (DOA) estimation using sparse antenna array that has applications in several fields including radars and sonars. Two different types of sparse antenna arrays are considered. One is linear sparse array for DOA estimation in one dimension and other is L shaped sparse array for DOA estimation in two dimensions. To make the algorithm robust against impulsive and Gaussian noise, a preprocessing stage is introduced. First, in the preprocessing stage median difference correntropy is used that combines median difference and the generalized correntropy. This suppresses the amplitude of impulsive noise. Second, the strength of weighted moving average filter is exploited before applying the CS technique to make the algorithm more robust. In the CS techniques, the source energy is distributed among the adjacent grid due to grid mismatch. Therefore, a fitness function based on the difference of the source energy among the adjacent grid is introduced. This provides the best discretization value through iterative grid refinement for the grid. The effectiveness and robustness of the proposed method is verified through exhaustive simulations for different number of sources and noise scenarios using one dimensional and two-dimensional sparse array structures.

In fact, optimal RPD is one of the most critical optimization matters related to electrical power stability and operation. The minimization of overall real power losses is obtained by adjusting the power systems control variables, for instance; generator voltage, compensated reactive power and tap changing of the transformer. In this search, a new heuristic computing method named as fractional particle swarm optimization gravitational search algorithm (FPSOGSA) is presented by introducing fractional derivative of velocity term in standard optimization mechanism. The designed FPSOGSA is implemented for the optimal RPD problems with IEEE-30 and IEEE-57 standards by attaining the near finest outcome sets of control variables along with minimization of two fitness objectives; active power transmission line losses ( $P_{loss,}$ MW) and voltage deviation ( $\text{V}_{\mathrm {D}}$ ). The superior performance of the proposed FPSOGSA is verified for both single and multiple runs through comparative study with state of art counterparts for each scenario of optimal RPD problems.

In the present study, a neuro-evolutionary scheme is presented for solving a class of singular singularly perturbed boundary value problems (SSP-BVPs) by manipulating the strength of feed-forward artificial neural networks (ANNs), global search particle swarm optimization (PSO) and local search interior-point algorithm (IPA), i.e., ANNs-PSO-IPA. An error-based fitness function is designed using the differential form of the SSP-BVPs and its boundary conditions. The optimization of this fitness function is performed by using the computing capabilities of ANNs-PSO-IPA. Four cases of two SSP systems are tested to confirm the performance of the suggested ANNs-PSO-IPA. The correctness of the scheme is observed by using the comparison of the proposed and the exact solutions. The performance indices through different statistical operators are also provided to solve the SSP-BVPs using the proposed ANNs-PSO-IPA. Moreover, the reliability of the scheme is observed by taking hundred independent executions and different statistical performances have been provided for solving the SSP-BVPs to check the convergence, robustness and accuracy.

The motive of the current work is related to solving the coronavirus-based mathematical system of susceptible (S), exposed (E), infected (I), recovered (R), overall population (N), civic observation (D), and cumulative performance (C), called as SEIR-NDC. The numerical solutions of the SEIR-NDC model are presented by using the computational framework of artificial neural networks (ANNs) together with the swarming optimization procedures aided with the sequential quadratic programming. The swarming procedure based on the particle swarm optimization (PSO) works as a global search, while the sequential quadratic programming (SQP) is used as a local search algorithm. A merit function is constructed by using the nonlinear dynamics of the SEIR-NDC mathematical system based on its 7 classes, and the optimization of the merit function is performed through the PSOSQP. The numerical expressions of system are accessible with the ANNs using the PSOSQP optimization with 30 variables. The correctness of the stochastic computing scheme performances is verified by using the comparison of the obtained performances of the mathematical SEIR-NDC system and the reference Runge–Kutta scheme. Furthermore, the graphical illustrations of the performance indices, absolute error, and convergence curves are derived to validate the robustness of the proposed ANN-PSOSQP approach for the mathematical SEIR-NDC system.

In this study, the stochastic numerical solutions of the fractional myeloma bone disease system (FMBDS) have been presented. The fractional order investigation provides more accurate solutions of the FMBDS. The FMBDS is classified into three dynamics and the solution of each class is presented by using the artificial neural network enhanced by the scale conjugate gradient procedures (ANN-SCGPs). Three different fractional order performances have been used to present the solutions of the FMBDS by applying the ANN-SCGPs. The statics is chosen as 11%, 12% and 77% for training, testing and verification. Twelve number of hidden neurons with input and output layers have been proposed for the FMBDS. The comparison of proposed and reference solutions is performed that shows the accuracy of the ANN-SCGPs. The consistency, validity, precision, and capability of the ANN-SCGPs can be judged based on the state transitions values, regression actions, correlation behaviors, error histograms, and mean square error data.

Developing the parameter estimation, particularly direction of arrival (DOA), utilizing the swarming intelligence-based flower pollination algorithm (FPA) is considered an optimistic solution. Therefore, in this paper, the features of FPA are applied for viable DOA in the case of several robust underwater scenarios. Moreover, acoustic waves impinging from the far-field multitarget are evaluated using the different number of hydrophones of uniform linear array (ULA). The measuring parameters like robustness against noise and element quantity, estimation accuracy, computation complexity, various numbers of hydrophones, variability analysis, frequency distribution and cumulative distribution function of root mean square error (RMSE), and resolution ability are applied for analyzing the performance of the proposed model with additive white Gaussian noise (AWGN). For this purpose, particle swarm optimization (PSO), minimum variance distortion-less response (MVDR), multiple signal classification (MUSIC), and estimation of signal parameter via rotational invariance technique (ESPRIT) standard counterparts are employed along with Crammer–Rao bound (CRB) to improve the worth of the proposed setup further. The proposed scheme for estimating the DOA generates efficient outcomes compared to the state-of-the-art algorithms over the Monte Carlo simulations.

The purpose of this study is to present the numerical investigations of an infection-based fractional-order nonlinear prey-predator system (FONPPS) using the stochastic procedures of the scaled conjugate gradient (SCG) along with the artificial neuron networks (ANNs), i.e., SCGNNs. The infection FONPPS is classified into three dynamics, susceptible density, infected prey, and predator population density. Three cases based on the fractional-order derivative have been numerically tested to solve the nonlinear infection-based disease. The data proportions are applied 75%, 10%, and 15% for training, validation, and testing to solve the infection FONPPS. The numerical representations are obtained through the stochastic SCGNNs to solve the infection FONPPS, and the Adams-Bashforth-Moulton scheme is implemented to compare the results. The infection FONPPS is numerically treated using the stochastic SCGNNs procedures to reduce the mean square error (MSE). To check the validity, consistency, exactness, competence, and capability of the proposed stochastic SCGNNs, the numerical performances using the error histograms (EHs), correlation, MSE, regression, and state transitions (STs) are also performed.

A recommender system not only “gains users’ confidence” but also helps them in other ways, such as reducing their time spent and effort. To gain users’ confidence, one of the main goals of recommender systems in an e-commerce industry is to estimate the users’ interest by tracking the users’ transactional behavior to provide a fast and highly related set of top recommendations out of thousands of products. The standard ranking-based models, i.e., the denoising auto-encoder (DAE) and collaborative denoising auto-encoder (CDAE), exploit positive-only feedback without utilizing the ratings’ ranks for the full set of observed ratings. To confirm the rank of observed ratings (either low or high), a confidence value for each rating is required. Hence, an improved, confidence-integrated DAE is proposed to enhance the performance of the standard DAE for solving recommender systems problems. The correctness of the proposed method is authenticated using two standard MovieLens datasets such as ML-1M and ML-100K. The proposed study acts as a vital contribution for the design of an efficient, robust, and accurate algorithm by learning prominent latent features used for fast and accurate recommendations. The proposed model outperforms the state-of-the-art methods by achieving improved P@10, R@10, NDCG@10, and MAP scores.

Piezoelectric actuated models are promising high-performance precision positioning devices used for broad applications in the field of precision machines and nano/micro manufacturing. Piezoelectric actuators involve a nonlinear complex hysteresis that may cause degradation in performance. These hysteresis effects of piezoelectric actuators are mathematically represented as a second-order system using the Dahl hysteresis model. In this paper, artificial intelligence-based neurocomputing feedforward and backpropagation networks of the Levenberg–Marquardt method (LMM-NNs) and Bayesian Regularization method (BRM-NNs) are exploited to examine the numerical behavior of the Dahl hysteresis model representing a piezoelectric actuator, and the Adams numerical scheme is used to create datasets for various cases. The generated datasets were used as input target values to the neural network to obtain approximated solutions and optimize the values by using backpropagation neural networks of LMM-NNs and BRM-NNs. The performance analysis of LMM-NNs and BRM-NNs of the Dahl hysteresis model of the piezoelectric actuator is validated through convergence curves and accuracy measures via mean squared error and regression analysis.