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The current investigative exploration exemplifies the conceptualization of a novel design intelligent computing paradigm based on artificial neural networks (ANNs) by utilizing radial basis function (RBF) to analyze magnetohydrodynamic (MHD) Williamson nanofluid two-dimensional flow along a stretchable sheet under the effect of chemical reaction as well as thermal radiation in a porous medium. This newly designed technique is an amalgam of a well-known reliable global solver named genetic algorithms (GAs) and a swift convergence generated local solver named sequential quadratic programming (SQP) used in ANNs by taking RBF as a kernel function i.e. ANNs-RBF-GASQP solver. The PDEs demonstrating the current nanofluid problem flow are transformed into the system of non-linear ODEs through a relevant similarity transformation and subsequently solved using ANNs-RBF-GASQP solver to investigate thermohydraulic properties by manipulating the values of various system parameters present in the ODEs. Moreover, the simulation results show that increasing the heat source parameter leads to a significant decrease in temperature. Additionally, an increase in the porosity parameter causes a decrease in the velocity of nanofluid, as a higher value of porosity increases fluid permeability and greater resistance to flow. The efficacy of the suggested solver is scrutinized through various statistical and convergence analyses.

Abstract The improvement of thermal exchange is of utmost interest in a wide range of engineering areas. The current study focuses on thermal evaluation involving natural radiation and convection in a fractionally arranged moving longitudinal fin model placed under a magnetic field. We implement the Levenberg Marquardt backpropagation (LMB) algorithm for investigating an innovative use of stochastic numerical computation for analyzing the efficiency of the temperature distribution in a porous moving longitudinal fin. The datasets for LMB have been created using a shooting approach for dynamic systems with varying ranges of different parameters. The validation, testing, and training processes are used to simulate networks using the LMB approach for diverse scenarios of moving porous fin models. The reliability of results is assessed based on the regression measures, absolute error, error histograms, mean square error, and other metrics for fuller numerical modeling of the suggested LMB to investigate the thermal efficiency and effectiveness of porous moving fin.

Abstract Background There are a variety of lethal infectious diseases that are seriously affecting people's lives worldwide, particularly in developing countries. Hepatitis B, a fatal liver disease, is a contagious disease spreading globally. In this paper, a new hybrid approach of feed forward neural networks is considered to investigate aspects of the SEACTR (susceptible, exposed, acutely infected, chronically infected, treated, and recovered) transmission model of hepatitis B virus disease (HBVD). The combination of genetic algorithms and sequential quadratic programming, namely CGASQP, is applied, where genetic algorithm (GA) is used as the main optimization algorithm and sequential quadratic programming (SQP) is used as a fast-searching algorithm to fine-tune the outcomes obtained by GA. Considering the nature of HBVD, the whole population is divided into six compartments. An activation function based on mean square errors (MSEs) is constructed for the best performance of CGASQP using proposed model. Results The solution's confidence is boosted through comparative analysis with reference to the Adam numerical approach. The results revealed that approximated results of CGASQP overlapped the reference approach up to 3–9 decimal places. The convergence, resilience, and stability characteristics are explored through mean absolute deviation (MAD), Theil’s coefficient (TIC), and root mean square error (RMSE), as well as minimum, semi-interquartile range, and median values with respect to time for the nonlinear proposed model. Most of these values lie around 10−10–10−4 for all classes of the model. Conclusion The results are extremely encouraging and indicate that the CGASQP framework is very effective and highly feasible for implementation. In addition to excellent reliability and level of precision, the developed CGASQP technique also stands out for its simplicity, wider applicability, and flexibility.

Our study delves into the dynamics of a convective Magneto-Hydrodynamic Bioconvective Nanofluid model (MHD-BCNFM) flowing over a convectively heated stretched sheet. To accomplish this, we utilize the distinctive capabilities of the Supervised Stochastic Approach for Computational Analysis (SSACA). By integrating similarity transformations, we convert the partial differential equations (PDEs) governing the system into coupled ordinary differential equations (ODEs). We generate the dataset for our approach using the Adam numerical technique specifically tailored for the (MHD-BCNFM). Achieving this involves systematic modulation of parameters such as λ, bioconvection Péclet number Pe, Bioconvection constant σ, Brownian motion parameter Nb, and thermophoresis parameter Nt. ''Moreover, we utilize a reference dataset to compute numerical values of various physical quantities in the (MHD-BCNFM) employing SSACA-based Artificial Intelligence methods. The effectiveness of our devised SSACA approach is demonstrated by a negligible mean squared error, ranging from approximately 10−8 to 10−10. Histograms exhibit a maximum error range of 10−5, closely aligning with optimal correlation/regression measures. Outstanding performance metrics in terms of Mean Squared Error (MSE) are attained at levels such as l 9.93E−12, 1.07E−11, 6.28E−10, 1.43E−11, 2.09E−09, 3.65E−11, 2.97E−11, and 2.80E−13 against 320, 430, 209, 85, 356, 295, 66, and 136 epochs. A comparative study between the proposed and reference datasets underscores the authenticity and precision of SSACA, supported by error analyses ranging from E-05 to E-09 across all scenarios.

This research implements an evolutionary optimized finite differences scheme (FDS) for nonlinear electrohydrodynamics ion drag flow dynamics in a cylindrical conduit (EHD-IDFCC). In the scheme, finite differences are exploited to discretize governing expressions of EHD-IDFCC, represented with a nonlinear singular seconder order differential equation, into a nonlinear equations-based system. The fitness function based on residual error is constructed for the FDS-based discretized EHD-IDFCC model. Its optimization is conducted with the global search capability of genetic algorithms (GAs) aided by the local search efficacy of the interior-point method (IPM), i.e., FDS-GA-IPM. The performance of the designed stochastic numerical solver FDS-GA-IPM is evaluated for a variant of the EHD-IDFCC model for different scenarios to measure the effect of axial flow velocity by varying the electric Hartmann numbers, as well as the nonlinearity factor. Statistical interpretations based on histogram illustrations, probability plots, and boxplots in terms of the cost function, mean absolute error (MAE), Thai inequality coefficients (TIC), and coefficient of determination metrics (R2) are used to endorse the accuracy, convergence, stability, and strength of the FDS-GA-IPM.

Recurrent Neural Networks (RNNs), a type of machine learning technique, have recently drawn a lot of interest in numerous fields, including epidemiology. Implementing public health interventions in the field of epidemiology depends on efficient modeling and outbreak prediction. Because RNNs can capture sequential dependencies in data, they have become highly effective tools in this field. In this paper, the use of RNNs in epidemic modeling is examined, with a focus on the extent to which they can handle the inherent temporal dynamics in the spread of diseases. The mathematical representation of epidemics requires taking time-dependent variables into account, such as the rate at which infections spread and the long-term effects of interventions. The goal of this study is to use an intelligent computing solution based on RNNs to provide numerical performances and interpretations for the SEIR nonlinear system based on the propagation of the Zika virus (SEIRS-PZV) model. The four patient dynamics, namely susceptible patients S(y), exposed patients admitted in a hospital E(y), the fraction of infective individuals I(y), and recovered patients R(y), are represented by the epidemic version of the nonlinear system, or the SEIR model. SEIRS-PZV is represented by ordinary differential equations (ODEs), which are then solved by the Adams method using the Mathematica software to generate a dataset. The dataset was used as an output for the RNN to train the model and examine results such as regressions, correlations, error histograms, etc. For RNN, we used 100% to train the model with 15 hidden layers and a delay of 2 seconds. The input for the RNN is a time series sequence from 0 to 5, with a step size of 0.05. In the end, we compared the approximated solution with the exact solution by plotting them on the same graph and generating the absolute error plot for each of the 4 cases of SEIRS-PZV. Predictions made by the model appeared to be become more accurate when the mean squared error (MSE) decreased. An increased fit to the observed data was suggested by this decrease in the MSE, which suggested that the variance between the model's predicted values and the actual values was dropping. A minimal absolute error almost equal to zero was obtained, which further supports the usefulness of the suggested strategy. A small absolute error shows the degree to which the model's predictions matches the ground truth values, thus indicating the level of accuracy and precision for the model's output.

The power system incorporates renewable energy resources into the main utility grid, which possesses low or no inertia, and these systems generate harmonics due to the utilization of power electronic equipment. The precise and effective assessment of harmonic characteristics is necessary for maintaining power quality in distributed power systems. In this paper, the Marine Predator Algorithm (MPA) that mimics the hunting behavior of predators is exploited for harmonics estimation. The MPA utilizes the concepts of Levy and Brownian motions to replicate the movement of predators as they search for prey. The identification model for parameter estimation of harmonics is presented, and an objective function is developed that minimizes the difference between the real and predicted harmonic signals. The efficacy of the MPA is assessed for different levels of noise, population sizes, and iterations. Further, the comparison of the MPA is conducted with a recent metaheuristic of the Reptile Search Algorithm (RSA). The statistical analyses through sufficient autonomous executions established the accurate, stable, reliable and robust behavior of MPA for all variations. The substantial enhancement in estimation accuracy indicates that MPA holds great potential as a strategy for estimating harmonic parameters in distributed power systems.

The current investigation formulated an efficient computing technique by incorporating the algorithm of Artificial Neural Network Levenberg Marquardt Method (ANNLMM) to approximate Soret and Dufour effects on Magnetohydrodynamic squeezing flow of Jeffrey fluid (MHDSFJF) in MATLAB environment. Due to its efficiency and flexibility, the applied neural network model can accurately predict the output results. In the ANNLMM, 80% of the data is used for training and 10% is set for both the testing and validation processes. The flow under consideration is mathematically formulated with the help of Navier Stokes Equations. The partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) by similarity variables. The effects of the physical parameters are discussed briefly. When the Hartmann number and Jeffrey fluid parameter increase, the concentration, temperature, and velocity profiles decreases. The temperature profile and heat transfer rate are improved by the effects of joule dissipation, Dufour numbers, and heat generation/absorption. On the other hand, as thermal radiation rises, the temperature profile decreases and the heat transfer rate increases. With an augment in Soret number, the mass transfer rate increases and the concentration profile slows down. Additionally, increasing chemical reactions, the mass transfer rate increases, but in convective chemical reactions, the contradiction is observed.

This article explores the enhancement of thermal exchange in a dissipative Triple-nanoparticle (Al2O3+CuO+Cu) hybrid fluid over a stretchable wavy cylindrical surface with slip effect, incorporating Python bvp algorithm with artificial intelligence AI analysis of numerical results. The stochastic AI analysis gives the enhanced and optimized results with predictive modeling, incorporating randomness of influencing parameters and nonlinear turbulent behavior of model. The model has significant importance and application in noise reducing and drag reduction devices or structures. Moreover, the presented geometrical structure is useful in enhancing thermal conduction characteristic. The intricate interplay of constituent nanoparticles and their effect on complex heat transfer in drag optimization devices is the main focus of this study. Mathematical Model of PDEs of this flow problem is converted into system of ODEs by similarity transformations with introducing dimensionless parameters. Numerical solutions of the emerged system are obtained by Python bvp solver algorithm and graphical solutions by Python are presented. To expedite the solution process and enhance the accuracy of prediction, advanced AI algorithm, such as neural network and machine learning technique is adopted. Numerical dataset obtained from Python is embedded for further AI analysis by using Levenberg Marquardt Feed-forward Algorithm (LMFA) with 10 computing neurons and 4 output layers representing results for 4 parametric variations.A rise in the fluid flow speed is observed with higher of value yield stress or Newtonian-behavior i.e. of Casson parameter a1 and stretching parameter λ for the sheet, but shows a decline with enhancing turbulence s2. Temperature profile show a descending behavior with inclination of Eckert ratio Ec, and Prandtl ratio of momentum-thermal diffusivity.

Studying compressible inviscid flow over symmetric and supercritical airfoils is important because it is useful to understand and maximize aerodynamic performance in a range of industrial contexts. This study addresses the analysis of symmetric and supercritical airfoils for compressible inviscid flow for both time-dependent and stationary scenarios. The primary goal of these simulations’ is to look at how different velocity variations affected certain airfoil parameters. Air is utilized as the material above airfoils. The best fit for these simulations is the Spalart-Allmaras Turbulence model, which shows good agreement over a wider velocity range with published experimental data from other studies. The COMSOL Multiphysics software is used for all the analysis, for angle of attack 0°, temperature 288K, pressure 1bar and the airfoils that are constructed by importing airfoil data file in COMSOL in the form of excel file. On the comparison of compressible inviscid flow, the supercritical airfoil has better results on the basis of velocity magnitude, pressure, vorticity magnitude, shear rate and rotation rate. The results are converging faster in supercritical airfoil than symmetric airfoil. At a zero-degree angle of attack, velocity increases more on the suction side while decreases on the pressure side (bottom). The final solution error for supercritical airfoil is 1.6E-05, while final residual error for “velocity u pressure p” is 1.2E-05. For symmetric airfoil, final solution error is 0.15, although final residual error is 2.6. Based on the error plot, it decreases rapidly in case of supercritical with a range from 100 to 10-4. Additionally, the wall resolution is constructed for both cases i.e., symmetric airfoil and supercritical airfoil. The main result is that ,with the passage of time, the flow is becoming to stationary state. In the end, model validation via comparison with experimental data highlights the validity and applicability of the results.

Artificial neural networks (ANNs) have transformed machine learning and computational intelligence by providing unprecedented powers in modeling complicated data and addressing a wide range of challenges. In the field of ANNs, back propagation is a key approach for training neural networks. However, obtaining optimum network efficiency while tackling over fitting and controlling uncertainty is a difficult task. The present study employs the Bayesian Regularization Method with Neural Network Backpropagation (BRM-NNB) technique to investigate the rumors spreading delay model. With their rapid spread, rumors have the potential to cause fear and even financial loss. Thus, we must take decisive actions to stop the rumor from spreading. Nowadays, rumors can spread through instant messaging, emails, or publishing, thanks to the development of the internet. In this research, an XY-SIR rumors spreading delay model (XY-SIR-RS-DM) is investigated in relation to the novel spreading pattern. Media networks can be categorized into susceptible and infected media, while friendship networks can be categorized into three groups: spreaders (S, I, and R), who actively disseminate rumors, those who are ignorant and those who have no desire to do so. To estimate the solution of the suggested model, the Bayesian regularization method with neural network back propagation (BRM-NNB) is used. The data set is generated by applying the explicit Runge-Kutta method. The computing BRM-NNB strategy is implemented for three different performances, where the training, testing, and verification data are reported as 80%, 15%, and 5%, respectively, with 10 hidden neurons. To verify the validity of the developed artificial intelligence (AI) approach represented by the BRM-NNB, outcome comparisons are presented. The result is compatible with obtaining a minimal absolute error that is nearly equal to zero, thereby proving the efficacy of the proposed method.

Artificial neural networks (ANNs) have brought a huge transformation to the machine learning regime by furnishing unparalleled abilities for modeling intricate phenomena and coping with a variety of challenges. In the oneiric field of ANNs, the essential approach for training ANNs is backpropagation. However, optimization is crucial when handling the complex fluid flow phenomenon through backpropagation. The current article implements the Levenberg Marquardt Technique with ANN backpropagation (LMT-BP-ANN) to investigate the radiative flow of a hybrid nanofluid (RHNF) addressing a Cattaneo-Christov flux system past a stretching sheet (SS). Fe2O3 with single-walled carbon nanotubes (SWCNT) and multi-walled carbon nanotubes (MWCNT) hybrid nanofluid is considered. The base fluid is ethylene glycol. Physical parameters of nanofluidic system, including the magnetic parameter M, the solid volume fractions φ1 and φ2, the velocity slip parameter λ, the relaxation time parameter Ω, the Biot number ϒ, and the thermal radiation parameter Gr are evaluated through appropriate variations that effectively accomplish the dynamics of the fluid model. These are utilized to create the dataset for LMT-BP-ANNs using the renowned deterministic Adam's numerical technique in Mathematica software. In MATLAB software, 70 % of data is kept for preparing, 15 % for checking, and 15 % for validating the neural network. The performance plot, regression graphs, and error histograms are constructed to demonstrate the suggested LMT-BP neural network scheme's high efficiency, efficacy, and exactness. When ANN performs, a mean squared error (MSE) of order 10−11 is observed. The observed R squared value is 1. As the magnetic parameter estimate grows, the fluid velocity declines, although the thermal profile shows increasing behavior. As the velocity slip parameter increases, the velocity of the fluid drops. Key findings of this study are anticipated to have a noteworthy bearing on sectors that require local refrigeration and heating by contravention.

Angle estimation of signals received by antenna arrays is a key step in adaptive beamforming, used to detect and locate targets in space. It is desirable to reduce costs by employing a smaller number of antennas while maintaining efficiency and degrees of freedom (DOF) of the system at the same time. Co-prime antenna arrays not only circumvent the operational constraints of cost and hardware complexity, but also boost the DOF by utilizing far fewer antennas as compared to traditional uniform linear arrays. In this paper, meta-heuristic computing paradigm for estimating arrival angle of targets with co-prime arrays incorporated in monostatic radar is proposed. The system's autocorrelation and Mean Square Error (MSE) are used for fitness function optimized by global/local search with Genetic Algorithm (GA) and Pattern Search (PS). Monte Carlo simulations are performed to evaluate the performance via estimation accuracy, MSE, and computational cost for varying numbers of impinging waves.

The current research work focuses on the thermal effectiveness and distribution of an internal heat-generating longitudinal rectangular fin that is dependent on temperature thermal conductivity that varies exponentially. Additionally, the thermal dispersion of a longitudinal fin is studied for thermal conductivities that vary exponentially with temperature and linearly with temperature. With the use of dimensionless terms, the considered problem's governing equation is transformed into a non-linear ordinary differential equation. Using the shooting method in Mathematica software, the dataset for the Levenberg Marquardt Backpropagation based on artificial neural network is created by varying different parameters, including the thermogeometric parameter, the parameter of internal heat generation, the parameter of heat transfer, and the parameter of thermal conductivity parameter. For network modeling using the Levenberg Marquardt Backpropagation approach for various longitudinal fin model scenarios, the testing, training, and validation process is used. Error histogram, regression, training state and fitness, and mean square error are used to analyze the accuracy of the outcome. This study shows that the temperature gradient increases for larger values of the parameter of thermal conductivity but decreases for different thermogeometric parametric values. Additionally, the temperature distribution is improved by higher numbers of heat transfer and heat generation parameters.

The growing attractiveness of Artificial Neural Networks (ANNs) derives from their exceptional effectiveness in handling difficult and exceptionally nonlinear mathematical ideas. In complicated disciplines such as fluid mechanics, biological computation, and the field of biotechnology ANNs provide a diverse computing framework that is extremely valuable. This article's major aim is to harness the capabilities of the Levenberg-Marquardt technique with backpropagation intelligent neural networks (LM- BPINNs) to study there is still a lack of clarity regarding the mechanics underlying the increased heat transfer caused by dispersed nanoparticles. The using proposed LM-BPINNs to improve the heat transmission use activation energy and Hall current phenomena in nanofluid (HTAHCNF). The data set is obtained by using Lobatto-III. A method and then ANNs is applied. The LM- BPINNs technique is applied by utilizing reference datasets, with 80% of the dataset devoted to training, 10% to testing, and 10% to verification. The precision/accuracy and converging of developed LM- BPINNs are validated based on the obtained reliability via efficient fitness achieved on mean squared error (MSE), comprehensive regression analysis, and appropriate error histogram visualizations. A diminished MSE indicates that the model's predictions are more reliable. The outcome is consistent with getting a minimal absolute error close to zero, exhibiting the effectiveness of the proposed approach.

Fractional order algorithms demonstrate superior efficacy in signal processing while retaining the same level of implementation simplicity as traditional algorithms. The self-adjusting dual-stage fractional order least mean square algorithm, denoted as LFLMS, is developed to expedite convergence, improve precision, and incurring only a slight increase in computational complexity. The initial segment employs the least mean square (LMS), succeeded by the fractional LMS (FLMS) approach in the subsequent stage. The latter multiplies the LMS output, with a replica of the steering vector (Ŕ) of the intended signal. Mathematical convergence analysis and the mathematical derivation of the proposed approach are provided. Its weight adjustment integrates the conventional integer ordered gradient with a fractional-ordered. Its effectiveness is gauged through the minimization of mean square error (MSE), and thorough comparisons with alternative methods are conducted across various parameters in simulations. Simulation results underscore the superior performance of LFLMS. Notably, the convergence rate of LFLMS surpasses that of LMS by 59%, accompanied by a 49% improvement in MSE relative to LMS. So it is concluded that the LFLMS approach is a suitable choice for next generation wireless networks, including Internet of Things, 6G, radars and satellite communication.

The paper presents an innovative computational framework for predictive solutions for simulating the spread of malaria. The structure incorporates sophisticated computing methods to improve the reliability of predicting malaria outbreaks. The study strives to provide a strong and effective tool for forecasting the propagation of malaria via the use of an AI-based recurrent neural network (RNN). The model is classified into two groups, consisting of humans and mosquitoes. To develop the model, the traditional Ross-Macdonald model is expanded upon, allowing for a more comprehensive analysis of the intricate dynamics at play. To gain a deeper understanding of the extended Ross model, we employ RNN, treating it as an initial value problem involving a system of first-order ordinary differential equations, each representing one of the seven profiles. This method enables us to obtain valuable insights and elucidate the complexities inherent in the propagation of malaria. Mosquitoes and humans constitute the two cohorts encompassed within the exposition of the mathematical dynamical model. Human dynamics are comprised of individuals who are susceptible, exposed, infectious, and in recovery. The mosquito population, on the other hand, is divided into three categories: susceptible, exposed, and infected. For RNN, we used the input of 0 to 300 days with an interval length of 3 days. The evaluation of the precision and accuracy of the methodology is conducted by superimposing the estimated solution onto the numerical solution. In addition, the outcomes obtained from the RNN are examined, including regression analysis, assessment of error autocorrelation, examination of time series response plots, mean square error, error histogram, and absolute error. A reduced mean square error signifies that the model's estimates are more accurate. The result is consistent with acquiring an approximate absolute error close to zero, revealing the efficacy of the suggested strategy. This research presents a novel approach to solving the malaria propagation model using recurrent neural networks. Additionally, it examines the behavior of various profiles under varying initial conditions of the malaria propagation model, which consists of a system of ordinary differential equations.

The use of artificial neural networks (ANNs) to solve complex fluid dynamics problems has revolutionized computational approaches. This article explores novel ANN solutions for fluid problems. ANNs have demonstrated unmatched effectiveness in comprehending and forecasting fluidic behaviors, from mimicking complex fluid flow trends to optimizing structures for dynamics. This study emphasizes the significance of neural networks in revolutionizing our understanding and control of fluidic systems by using ANNs and Bayesian Regularization. This study examined the 3D Darcy-Forchheimer stretching flow (TDDFSF) of nanofluid under convective conditions along with homogeneous and heterogeneous reactions by employing the scheme of Bayesian Regularization with the procedure of backpropagation in neural networks (SBR-BNNs). The flow is influenced by Brownian diffusion, thermophoresis and zero nanoparticles mass flux condition. The PDEs given in this model are converted into nonlinear ODEs. Results from MSE, regression analysis, and error histogram are used to verify the performance of SBR-BNNs. The absolute errors lie in the ranges up to 10−9, which depict the worth of the solver SBR-BNNs. The absolute error measures the discrepancy between the values actually observed and those predicted by the SBR-BNNs model. SBR-BNNs' high precision in TDDFSF models can lead to more effective and reliable solutions.

The non-linear ordinary differential equations (NODEs) in this article are estimated and analyzed numerically using the capability of the Quartic Splines Method (QSM) for mathematical modeling of the Falkner-Skan fluidic system and its optimization through global search Genetic Algorithms (GAs) and local search Active-Set (AS) techniques. The concept of hybridization is used to optimize the obtained results and provide a boost to the suggested method, QSM, which allows for rapid iteration. Falkner-Skan fluid model (FSFM) is solved by the proposed technique QSM-GAs-AS. The FSFM is solved for three, seven, and twelve splines successfully. The problem is analyzed for three scenarios, in which each scenario is based on the variation of a parameter out of the three involved parameters, namely the wall mass transfer parameter (γ), the wall movement parameter (λ), and the stream-wise pressure gradient parameter (β), appearing in FSFM. The QSM-GAs-AS produces an interpolated function that is continuous up to its fourth derivative. The solution outcomes of FSFM, treated by the designed scheme QSM-GAs-AS, are presented graphically. The evaluation of the planned solution is done with a deterministic numerical solver, the Homotopy Analysis Method (HAM). Statistical analysis for multiple runs is used to examine the proposed scheme's convergence, exactness, and accuracy.

Smoking has emerged as one of the leading global factors that is the source of health issues. It damages almost all of the body's organs. It damages various muscles and causes lung cancer. Additionally, it causes ulcers, pulmonary disease, and vascular deterioration. Except for the financial benefit to tobacco companies, manufacturers, and marketing companies, smoking has no advantages. Due to these factors, the present study exploited a feed forward neural networking based global optimization procedure with a local scheme to solve a mathematical model of smoking. A genetic based algorithm and sequential quadratic programming (GA-SQP) are utilized as hybridized global and local strategies. The model is categorized into five classes: potential smokers, occasional smokers, smokers, temporary quit, and permanent quit smokers. An objective optimization function is constructed to minimize the mean square error using the designed smoking model in form of feed forward neural networking. The comparative evaluation of hybrid GA-SQP and Adam numerical scheme is also assessed to authenticate the precision and correctness of the solution of the smoking model. The robustness, perfection, and convergence stability of GA-SQP are verified by establishing various statistical performance indicators. The quantitative analysis provides the minimum, mean, and semi-inter quartile range values for absolute errors up to 6 to 13 decimal places, demonstrating the worthiness and precision of the proposed GA-SQP.

Applications of artificial intelligence (AI) via soft computing procedures have attracted the attention of researchers due to their effective modeling, simulation procedures, and detailed analysis. In this article, the designing of intelligence computing through a neural network that is backpropagated with the Levenberg-Marquardt method (NN-BLMM) to study the Cattaneo-Christov heat flow model at the mixed impulse stagnation point (CCHFM-MISP) past a Riga plate is investigated. The original model CCHFM-MISP in terms of PDEs is converted into non-linear ODEs through suitable similarity variables. A data set is generated for all scenarios of CCHFM-MISP through Lobatto IIIA numerical solver by varying Hartman number, velocity ratio parameter, inverse Darcy number, mixed impulse variable, non-dimensional constraint, Eckert number, heat generation variable, Prandtl number, thermal relaxation variable. To find the physical impacts of parameters of interest associated with the presented fluidic system CCHFM-MISP, the approximate solution of NN-BLMM is carried out by performing training (80 %), testing (10 %), and validation (10 %), and then the results are equated with the reference data to ensure the perfection of the proposed model. Through MSE, state transition, error histogram, and regression analysis, the outcomes of NN-BLMM are presented and analyzed. The graphical illustration and numerical outcomes confirm the authentication and effectiveness of the solver. Moreover, mean square errors for validation, training and testing data points along with performance measures lie around 10−10 and the solution plots generated through deterministic (Lobatto IIIA) approach and stochastic numerical solver are matching up to 10−6, which surely validate the solver NN-BLMM. The outcomes of M and B on velocity present the similar impacts. The velocity of material particles decreases under Da while, it increases through velocity ratio and magnetic parameters.

Abstract A complete shape factor investigation of water‐based mixture type hybrid nanofluid in a permeable boundary with the impact of magnetic field, thick dissemination, and warm radiation is presented in this article. A computational convection analysis of an inverted semi vertical cone with a porous surface in the form of SiO2/water nanofluid and MoS2‐SiO2/water hybrid nanofluid transport is developed. The system of differential equations is presented and solved numerically by the Lobatto IIIA method. The temperature distributions and fluid velocity are studied along with the coefficient of skin friction and the Nusselt number, taking into account the form of distinct nano‐particles. The flow problem's results are approximated by using several embedding variables. Tables and graphs are constructed for a variety of scenarios including maximum residual error, mesh points, and Nusselt numbers. We conclude that boundary film thickness reduces and the fluid flow is resisted by magnetic field presence. Fluid flow slows down as λ increases, and this reduction is more evident in nanofluids than in hybrid nanofluids. With an increment in S, velocity drops. A detailed analysis of the proposed ordinary differential equations, boundary conditions, and numerical data of skin friction is given both in tabular and graphical forms. Additionally, it is observed that the fluid flow slows down more for the hybrid nanofluid than for the SiO2/water nanofluid. Moreover, it is clear that the temperature increase for the SiO2/water nanofluid is substantially greater. The authors deduce that the existence of a magnetic field resists fluid flow for hybrid nanofluid forms and decreases the thickness of the viscous boundary layer.

The impact of activation energy in chemical processes, heat radiations, and temperature gradients on non-Darcian steady MHD convective Casson nanofluid flows (NMHD-CCNF) over a radial elongated circular cylinder is investigated in this study. The network of partial differential equations (PDEs) for NMHD-CCNF is developed using the modified Buongiorno framework, and the network of controlling PDEs is then transformed into ordinary differential equations (ODEs) utilizing the Von Karman method. Finally, the resulting non-linear ODEs are computed using the ND-solve approach to produce sets of data to assess the proposed model's skills, which can then be handled using the Bayesian Regularization technique of artificial neural networks (BRT-ANN). A novel stochastic computing-based application is being developed to evaluate the importance of NMHD-CCNF across a spinning disc that is radially stretched. The novelty and significance of results for better understanding, clarity, and highlighting the innovative contributions and significance of the proposed scheme. Further, to check the validity of the defined results for NMHD-CCNF, error charts, validation, and mean squared error suggestions are employed. The impact of multiple physical parameters on concentration, radial and tangential velocities, and temperature profiles is shown via tables and figures. Additionally, the results demonstrate that as the Forchheimer number, Casson nanofluid parameter, magnetic parameter, and porosity parameter are strengthened, the radial and rotational nanofluid mobility drops dramatically. The stretching parameter, on the other hand, has a parallel developmental trend. The heat generation parameter, the thermophoresis process, the thermal radiation parameter, and the Brownian motion of nanoparticles can all be increased to give thermal enhancement. On the other side, with larger estimates in thermophoresis parameters and the activation energy, there is a noticeable increase in the concentration profile.

The present study aims to design a Levenberg-Marquardt backpropagation neural network (LMB-NN) integrated numerical computing to investigate the problem of fluid mechanics governing the flow of magnetohydrodynamics micro-polar nanofluid flow over a rotating disk (MHD-MNRD) model along with the partial slip condition. In terms of PDEs, the basic system model MHD-MNRD is transformed into a system of non-linear ODEs by applying the similarity of transformations. For MHD-MNRD scenarios, the comparative dataset of the built LMB-NN procedure is formulated with the technique of Adams numerical by variation of micro-polar parameters, Brownian motion, Lewis number, magnetic parameter, velocity slip parameter and thermophoresis parameter. To compute the approximate solution for MHD-MNRD for various scenarios, validation, testing and training procedures are carried out in accordance to adjust the networks under the backpropagation procedure in terms of the mean square error (MSE). The efficiency of the designed LMB-NN methodology is highlighted by comparative study and performance analysis based on error histograms, MSE analysis, regression and correlation.

The present communication examines the unsteady-two-dimensional (2-D) squeezing flow of magnetohydrodynamic (MHD) Jeffrey fluid between two parallel plates (HT2DUSMHDJF). In its own plane, the bottom channel plate is extended while the upper plate squeezes towards the lower plate. The complete structure is takan is a rotating frame. Cattaneo-Christov heat flux model (CCHFM) is forced to explore the features of heat transfer. Distinct the conventional position, Instead of the Fourier heat conduction law, the heat flux is implemented by the Cattaneo-Christov theory. The resultant systems are computed through Artificial Neural Network (ANN). The behaviors of a number of relevant parameters are analyzed through graphs and numerical data. The velocity profile increases for Deborah number β and squeezing parameter sq and decreases for rotation, magnetic and relaxation time parameter ω, M, and λ1 respectively. Also the Skin friction coefficient decreases for λ1 and Sq and increases for high value of Deborah numbers β, ω and M.

The purpose of this investigation is to provide the numerical study based on the fractional order (FO) economic and environmental mathematical model (EEMM) called as FO-EEMM. The motive of this work is to find more realistic results of the EEMM of the non-integer and FO derivatives. The structure of the FO-EEMM is categorized into three dynamics, control accomplishment cost, capability of the manufacturing elements and the diagnostics cost of the technical exclusion. The solution of the FO-EEMM is numerically presented by using the scaled conjugate gradient neural networks (SCGNNs). Three cases based on the FO-EEMM have been scrutinized to indicate the numerical performances along with the selection of the statics as 76% for training, 13% for testing and 11% for certification. The correctness of the designed SCGNNs is authenticated by using the matching of the achieved and the reference solutions (Adams-Bashforth-Moulton). The validity, exactness, dependability, and competence of the SCGNNs is observed through the performances of the mean square error, regression, state transitions, error histograms and correlation.

The research groups in engineering and technological fields are becoming increasingly interested in the investigations into and utilization of artificial intelligence techniques in order to offer enhanced productivity gains and amplified human capabilities in day-to-day activities, business strategies and societal development. In the present study, the hydromagnetic second-order velocity slip nanofluid flow of a viscous material with nonlinear mixed convection over a stretching and rotating disk is numerically investigated by employing the approach of Levenberg-Marquardt back-propagated artificial neural networks. Heat transport properties are examined from the perspectives of thermal radiation, Joule heating and dissipation. The activation energy of chemical processes is also taken into account. A system of ordinary differential equations (ODEs) is created from the partial differential equations (PDEs), indicating the velocity slip nanofluid flow. To resolve the ODEs and assess the reference dataset for the intelligent network, Lobatto IIIA is deployed. The reference dataset makes it easier to compute the approximate solution of the velocity slip nanofluid flow in the MATLAB programming environment. A comparison of the results is presented with a state-of-the-art Lobatto IIIA analysis method in terms of absolute error, regression studies, error histogram analysis, mu, gradients and mean square error, which validate the performance of the proposed neural networks. Further, the impacts of thermal, axial, radial and tangential velocities on the stretching parameter, magnetic variable, Eckert number, thermal Biot numbers and second-order slip parameters are also examined in this article. With an increase in the stretching parameter's values, the speed increases. In contrast, the temperature profile drops as the magnetic variable's value increases. The technique's worthiness and effectiveness are confirmed by the absolute error range of 10-7 to 10-4. The proposed system is stable, convergent and precise according to the performance validation up to E-10. The outcomes demonstrate that artificial neural networks are capable of highly accurate predictions and optimizations.

Introduction: Knacks of evolutionary computing paradigm-based heuristics has been exploited exhaustively for system modeling and parameter estimation of complex nonlinear systems due to their legacy of reliable convergence, accurate performance, simple conceptual design ease implementation ease and wider applicability. Objectives: The aim of the presented study is to investigate in evolutionary heuristics of weighted differential evolution (WDE) to estimate the parameters of Hammerstein-Wiener model (HWM) along with comparative evaluation from state-of-the-art counterparts. The objective function of the HWM for controlled autoregressive systems is efficaciously formulated by approximating error in mean square sense by computing difference between true and estimated parameters. Methods: The adjustable parameters of HWM are estimated through heuristics of WDE and genetic algorithms (GAs) for different degrees of freedom and noise levels for exhaustive, comprehensive, and robust analysis on multiple autonomous trials. Results: Comparison through sufficient large number of graphical and numerical illustrations of outcomes for single and multiple execution of WDE and GAs through different performance measuring metrics of precision, convergence and complexity proves the worth and value of the designed WDE algorithm. Statistical assessment studies further prove the efficacy of the proposed scheme. Conclusion: Extensive simulation based experimentations on measure of central tendency and variance authenticate the effectiveness of the designed methodology WDE as precise, efficient, stable, and robust computing platform for system identification of HWM for controlled autoregressive scenarios.

The current research work is related to present the numerical solutions of three-species food chain model (TS-FCM) by exploiting the strength of Meyer wavelet neural networks (MWNNs) along with the global and local search competencies. The particle swarm optimization technique works as a global operator, while the sequential quadratic programming scheme is applied as a local operator for the TS-FCM. The nonlinear TS-FCM is dependent upon three categories, called consistent of prey populations, specialist predator and top predator. The optimization of an error-based fitness function is presented by using the hybrid computing efficiency of the global and local search schemes, which is designed through the differential form of the designed ordinary differential model and its initial conditions. The proposed results of the TS-FCM are calculated through the stochastic numerical techniques and further comparison is performed by the Adams method to check the exactness of the scheme. The absolute error in good ranges is performed, which shows the competency of the proposed solver. Moreover, different statistical procedures have also been used to check the reliability of the proposed stochastic procedure along with forty numbers of independent trials and 10 numbers of neurons.

The most important factor for increasing crop production is pest and pathogen resistance, which has a major impact on global food security. Pest management also emphasizes the need for farming awareness. A high crop yield is ultimately achieved by protecting crops from pests and raising public awareness of the devastation caused by pests. In this research, we aim to investigate the intricate impacts of nonlinear delayed systems for managing crop pest management (CPM) supervised by Ordinary Differential Equations (ODEs). Our focus will be on highlighting the intricate and often unpredictable relationships that occur over time among crops, pests, strategies for rehabilitation, and environmental factors. The nonlinear delayed CPM model incorporated the four compartments: crop biomass density [B(t)], susceptible pest density [S(t)], infected pest density [I(t)], and population awareness level [A(t)]. The approximate solutions for the four compartments B(t), S(t), I(t), and A(t) are determined by the implementation of sundry scenarios generated with the variation in crop biomass growth rate, rate of pest attacks, pest natural death rate, disease associated death rate and memory loss of aware people, by means of exploiting the strength of the Adams (ADS) and explicit Runge-Kutta (ERK) numerical solvers. Comparative analysis of the designed approach is carried out for the dynamic impacts of the nonlinear delayed CPM model in terms of numerical outcomes and simulations based on sundry scenarios.

The aim of such work is to design a Meyer wavelet neural network (WNN) for solving the mathematical form of the Leptospirosis disease model (LDM). The global and local search optimization schemes based on the genetic algorithm (GA) and active-set algorithm (ASA) are used in this study. Leptospirosis is an infection spread by rodents, which is found in the world and causes fatalities in humans. The mathematical LDM model form consists of susceptible-infected-recovered (SIR), which is based on the disease spread processes. A fitness function is designed by using the mathematical LMD and then optimized by the hybridization of the GAASA. For the correctness, and capability of the Meyer WNN along with the procedures of GAASA, the comparison of the obtained and reference results is provided. Moreover, the reducible absolute error provides the efficiency of the proposed Meyer WNN along with the procedures of GAASA. The statistical observations are also provided to authenticate the convergence of the stochastic Meyer WNN along with the procedures of GAASA.

Scraped surface heat exchanger (SSHE) is vibrantly utilized in various industries. The heat exchanger devices play pivotal role in the energy transfer phenomenon between the fluids, and it improves the efficient use of energy. The steady isothermal flow of a rheological aqueous ionic solution in a narrow gap scraped surface heat exchanger is explored. The mathematical model is established with the aid of lubrication approximation theory and extracted analytical solution. Exact analytical expressions are gathered for velocities, volume fluxes, pressure gradients, pressure at the edges of the blades and stream functions in the various stations of SSHE. Strength of significant flow parameters on the velocities, volume fluxes, pressure gradients, pressure at the edges of the blades and stream functions is revealed with aid of various plots. Significant enhancement in the velocity profile is observed in main domain of the flow with increasing ratio of relaxation to retardation time parameter and Helmholtz Smoluchowski velocity. While, it is observed that electro-osmotic parameter creates impediments to the flow.

A new model of fractional for the influence of consciousness initiatives on epidemic incidences (ICIEI) is described in this research. The fractional Caputo operator (FCO) is used to expand this system to the typical awareness program model (ICIEI-FCO). Analytically and quantitatively, the properties of the new system are investigated. This article presents an artificial neural network-based fractional model (ANN-FM) for estimating the efficacy of epidemic outbreak awareness initiatives. The reliability, resolution, durability, and robustness of the proposed model are examined using the suggested ANN-BLM approach for five distinct situations. The population of the model is created by utilizing the power of the explicit Runge-Kutta numerical approach, and it is represented by a system of nonlinear ordinary differential equations. The Grunwald–Letnikov (GL) technique is used to numerically evaluate the modeled differential system of the physical issue for multiple scenarios to anticipate numerical data, and these results are utilized as a reference dataset of the networks. The data needed to answer the fractional model's questions on how awareness campaigns affect epidemic outbreaks is broken down as follows: training takes up 80% of the time, testing 10%, and authorization 10%. There are two aspects to the strategy: First, the fundamental ANN-BLM operator performances are displayed. In the meantime, the ANN-BLM execution approach is used to address the fractional-order problem. The GL-mathematical system was used to compare the numerical findings. The TSs, regression, correlation, EHs, and MSE are used to demonstrate the dependability and competency of ANN-BLM as well as their numerical performances in the presented numerical findings, which were developed using ANN-BLM to lower the MSE. The Levenberg-Marquart training (LMT) algorithm is used to optimize network results in terms of mean-square errors, training states graphs, errors of the histogram, recession analysis, auto-correlation and time series responses, which demonstrates the system's accurate and proficient trend acknowledgment. The mean-square error fitness analysis in the ranges of 10-6 to 10-11 validates the authenticity and effectiveness of the designed solver. The suggested AI-based study is expected to pave the way for new, creative approaches to fractional order modeling and analysis of naturally unpredictable dynamic systems.

In this work, the influence of thermal energy in term of heat source, thermal radiation and chemical reaction on magneto hydrodynamic Casson fluid flow model (MHD-CFM) over a nonlinear slanted extending surface with slip velocity in a Forchheimer permeable medium is numerically studied using the Levenberg Marquardt methodology with backpropagated learning mechanism. It is valuable to evaluate the flow of Cason fluids based on materials (such as drilling muds, clay coatings, various suspensions and certain lubricating oils, polymeric melts, and a wide range of colloids) in the occurrence of heat transfer. Using efficient data, PDEs of (MHD-CFM) were converted to ordinary differential equations. These obtained non-linear ODEs are then rectified using the computational power of the Lobatto IIIA approach to obtain a dataset of Levenberg Marquardt algorithm based trained neural networks (LMA-TNN) for six scenarios of this presented model, which were graphically represented using nftool to obtain regression, efficiency, fit curve, error bars, and trained state analysis. The velocity, temperature, and concentration profiles were computed, and the findings were presented. Additionally, the skin friction coefficient, Nusselt number, & local Sherwood number are explored. The graphs show that when values of radiation parameter and the Forchheimer porous media parameter increase, the temperature of the plate drops. In the existence of a chemical process and a high Schmidt number, the concentration drops. The accuracy achieved in terms of relative error demonstrates the validity and significance of the solution process.

The aim of this work is to present the numerical simulations of the novel designed fractional order Leptospirosis model (FOLM) by using the strength of stochastic numerical supervised neural networks. This novel work provides the numerical study of the Leptospirosis model, which is classified into five dynamics. Different values of the fractional order derivatives have been provided to solve the biological FOLM. The numerical formulations of the FOLM are obtained through the supervised neural networks (SNNs) along with the computational performances of the Levenberg-Marquardt backpropagation (LVMBP), i.e., SNNs-LVMBP. The correctness of the procedure is observed by using the comparative performances of the obtained and reference solutions. The statics are performed for these investigations as 74% and 13% for both certification and learning. The process of error histograms (EHs), recurrence, MSE, correlation, and state transitions (STs) will be performed to authenticate the capability, steadiness, accuracy, reliability, and fitness of the proposed procedure.

The purpose of this research work is to present a numerical study through artificial neural networks (ANNs) to solve a SIQ-based COVID-19 mathematical model using the effects of lockdown. The effects of lockdown are considered to the three-dimensional mathematical model, “susceptible”, “infective” and “quarantined”, i.e. the SIQ system. ANNs and Levenberg–Marquardt backpropagation (LMB) are used to present the numerical analyses of the SIQ system-based COVID-19. Three different types of authentications, testing and training as sample data are applied to solve the SIQ system. Statistical ratios for the SIQ-based COVID-19 mathematical model are selected – 80% for training and 10% for both testing and authentication. The obtained numerical results of the SIQ mathematical system have been compared with the reference dataset, which is constructed through Adams solutions. The obtained numerical performances of the nonlinear SIQ dynamical model are testified with a reduction of the error in mean square sense in the range of 10−9 to 10−12.

Abstract Numerical treatment of the COVID-19 transposition and severity in Romania and Pakistan has been presented in this study, i.e., ANN-GA-SQP through artificial neural network genetic algorithms (ANN-GA) and sequential quadratic programming (SQP), a design of an integrated computational intelligent paradigm, COVID-19 is widely considered to be the greatest health threat humanity has ever faced. In terms of both health and economics, COVID-19 is a huge disaster. Many academics have looked at the COVID-19 model in their research papers, although they use different traditional techniques to represent it. The use of hybrid suggested solutions to solve this issue in the present article is significant, demonstrating the study's novelty. The SIR model of COVID-19 consists of a susceptible, infectious, and recovered class of population. The activation function for the construction of functions based on fitness in mean squared error sense is developed using nonlinear equations of the COVID-19 SIR model for the best performance of ANN-GA-SQP with the combined potential of GA and SQP of a network. While detailed refining is done with efficient local search with SQP, GAs operates as a global search. In addition, a neuron analysis will be presented to verify the effectiveness and complexity of the proposed method. Adam’s numerical methodology is applied to compare the sustainability and efficacy of the presented paradigm. Analytical evaluations of mean, median, and semi-interquartile range values, as well as Theil’s inequality coefficients, root mean squared error, and mean of absolute deviation) values have been observed. The convergence and correctness of the ANN-GA-SQP approach are further validated by statistical analyses.

The purpose of this work is to present the stochastic computing study based on the artificial neural networks (ANNs) along with the scaled conjugate gradient (SCG), ANNs-SCG for solving the predator-prey delay differential system of Holling form-III. The mathematical form of the predator-prey delay differential system of Holling form-III is categorized into prey class, predator category and the recent past effects. Three variations of the predator-prey delay differential system of Holling form-III have been numerical stimulated by using the stochastic ANNs-SCG procedure. The selection of the data to solve the predator-prey delay differential system of Holling form-III is provided as 13%, 12% and 75% for testing, training, and substantiation together with 15 neurons. The correctness and exactness of the stochastic ANNs-SCG method is provided by using the comparison of the obtained and data-based reference solutions. The constancy, authentication, soundness, competence, and precision of the stochastic ANNs-SCG technique is performed through the analysis of the correlation measures, state transitions (STs), regression analysis, correlation, error histograms (EHs) and MSE.

A repeatedly infected person is one of the most important barriers to malaria disease eradication in the population. In this article, the effects of recurring malaria re-infection and decline in the spread dynamics of the disease are investigated through a supervised learning based neural networks model for the system of non-linear ordinary differential equations that explains the mathematical form of the malaria disease model which representing malaria disease spread, is divided into two types of systems: Autonomous and non-autonomous, furthermore, it involves the parameters of interest in terms of Susceptible people, Infectious people, Pseudo recovered people, recovered people prone to re-infection, Susceptible mosquito, Infectious mosquito. The purpose of this work is to discuss the dynamics of malaria spread where the problem is solved with the help of Levenberg-Marquardt artificial neural networks (LMANNs). Moreover, the malaria model reference datasets are created by using the strength of the Adams numerical method to utilize the capability and worth of the solver LMANNs for better prediction and analysis. The generated datasets are arbitrarily used in the Levenberg-Marquardt back-propagation for the testing, training, and validation process for the numerical treatment of the malaria model to update each cycle. On the basis of an evaluation of the accuracy achieved in terms of regression analysis, error histograms, mean square error based merit functions, where the reliable performance, convergence and efficacy of design LMANNs is endorsed through fitness plot, auto-correlation and training state.

The current study provides the solutions of the mathematical model based on the coronavirus including the effects of vaccination and quarantine. The numerical stochastic process relying on Levenberg-Marquardt backpropagation technique (L-MB) neural networks (NN), i.e., L-MBNNs, is presented to solve the model. The entire dynamics of the proposed model depends upon the human population, which is represented by N and is further divided into multiple subgroups. The detail of these subgroups is presented in the form of susceptible population (S), exposed population (E), and infected people (I). Likewise, Q represents the quarantined and R shows the recovered or deceased individuals. Those who have been immunized are symbolized by V. All these categories make the model SEIQRV, that is based on a system of nonlinear differential equations. The statistics that is used to provide the numerical solutions of the SEIQRV model is 76% for training, 10% for testing and 14% for authorization. The correctness of the L-MBNNs is tested by using the comparison of the proposed and reference solutions (Adam method). The statistical representations are provided in order to check the reliability, competence and validity of L-MBNNs using the procedures of error histograms (EH), state transitions (ST), regression and correlation.

A novel theoretical model is devised for electro osmotic flow of Williamson fluid model by incorporating heat transfer phenomena in a micro ciliated channel. The physical fluid model is designed by exploiting the renowned Debye–Huckel, long wavelength small Reynolds number approximation. The exact expression for Poisson–Boltzmann equation is obtained to find the analytical solution for axial velocity, pressure gradient, temperature and stream functions comprehensively by using perturbation technique. Whereas, transverse velocity and pressure rise profile are explored numerically through the MATHEMATICA software infrastructure. The variations of paramount significant parameters on the velocity distribution, temperature, pressure gradient and pressure rise per wavelength are demonstrated graphically. It has been investigated that axial velocity profiles escalates with enhancing Weissenberg, electro-osmotic, mobility of medium parameter, while dual behavior is recorded for the case of traverse component of velocity. Cilia plays a crucial role in ductus efferentes and assumed to transfer sperm through the rete testis to the epididymis. Besides above mentioned application cilia like actuators serve in micro-mixers to regulate the flow in bio-sensors and in various drug-delivery mechanism.

In recent years, hybrid genetic algorithms have attracted a lot of attention and are being utilized more frequently to address real-world issues. A genetic algorithm can combine multiple approaches within its framework to create a hybrid that benefits the most from the combination. In this article, a new methodology of hybrid genetic algorithm using sequential quadratic programming (HGASQP) is presented to optimize the transmission dynamics of the Ebola virus disease model (EVDM) by implementing the intelligent paradigm of feed-forward neural networks. The Ebola virus, also known as Ebola haemorrhagic, is a transmitter virus that was initially transferred to humans by wild and domestic animals, and then it spread from human to human. To control this spread, a mathematical model is proposed consist of susceptible-S, exposed-E, infected-I, quarantined-Q and recovered-R classes. Coupling GA with local search SQP take the advantages of both for determining the global optimum as well as local optimum while at the same time also providing fast convergence. The mean squared error (MSE) is minimized as fitness objective function to optimize HGASQP. The optimized solutions of HGASQP are compared with the numerical results of the Adam approach in order to validate the effectiveness and robustness of the proposed algorithm. Furthermore, statistical and quantitative analysis are also established to authenticate the performance of HGASQP. It has been demonstrated that the suggested optimization approach is precise and can boost optimization effectiveness.

The artificial intelligence based neural networking with Back Propagated Levenberg-Marquardt method (NN-BPLMM) is developed to explore the modeling of double‐diffusive free convection nanofluid flow considering suction/injection, Brownian motion and thermophoresis effects past an inclined permeable sheet implanted in a porous medium. By applying suitable transformations, the PDEs presenting the proposed problem are transformed into ordinary ones. A reference dataset of NN-BPLMM is fabricated for multiple influential variants of the model representing scenarios by applying Lobatto III-A numerical technique. The reference data is trained through testing, training and validation operations to optimize and compare the approximated solution with desired (standard) results. The reliability, steadiness, capability and robustness of NN-BPLMM is authenticated through MSE based fitness curves, error through histograms, regression illustrations and absolute errors. The investigations suggest that the temperature enhances with the upsurge in thermophoresis impact during suction and decays for injection, whereas increasing Brownian effect decreases the temperature in the presence of wall suction and reverse behavior is seen for injection. The best measures of performance in form of mean square errors are attained as 7.1058×10−10,2.9262×10−10,1.1652×10−08,1.5657×10−10 and 5.5652×10−10 against 969, 824, 467, 277 and 650 iterations. The comparative study signifies the authenticity of proposed solver with the absolute errors about 10−7 to 10−3 for all influential parameters results.

This article aims to investigate the analytical nature and approximate solution of the radiated flow of electrically conductive viscous fluid into a porous medium with slip effects (RFECVF). In order to build acceptable accurate solutions for RFECVF, this study presented an efficient Levenberg-Marquardt technique of artificial neural networks (LMT-ANNs) approach. One of its fastest back-propagation algorithms for nonlinear lowest latency is the LMT. To turn a quasi-network of PDEs expressing RFECVF into a set of standards, the appropriate adjustments are required. During the flow, the boundary is assumed to be convective. The flow and heat transfer are governed by partial differential equations, and similarity transform is the main tool to convert it into a coupled nonlinear system of ODEs. The usefulness of the constructed LMT-ANNs for such a modelled issue is demonstrated by the best promising algebraic outputs in the E−03 to E−08 range, as well as error histogram and regression analysis measures. Mu is a controller that oversees the entire training procedure. The LMT-ANNs mainly focuses on the higher accuracy of nonlinear systems. Analytical results for the improved boundary layer ODEs are produced using the Variational Iteration Method, a tried-and-true method (VIM). The Lagrange Multiplier is a powerful tool in the suggested method for reducing the amount of computing required. Further, a tabular comparison is provided to demonstrate the usefulness of this study. The final results of the Variational Iteration Method (VIM) in MATLAB have accurately depicted the physical characteristics of a number of parameters, including Eckert, Prandtl, Magnetic, and Thermal radiation parameters.

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.

Whereas computer viruses (CVs) are a terrible threat to individual and corporate computer structures. A considerable attempt has been made to research ways to prevent their negative consequences, to develop anti-virus software that behave as vaccines in desktop computers or strategic network nodes. A further method for combating viral transmission is to develop preventative strategies associated with a given performance of a network that may be described using population models compared to the few employed with epidemiological analyses. An updated variation of such $SIR$ (Susceptible-Infected-Removed) framework is offered here, along with an explanation of whether these parameters correspond to network properties. The novel formed $SAIR$ model is then numerically treated, employing the qualities of stochastic procedure-based numerical computation approaches that use neural networks (NNs). In this research study, we suggest novel fractional-order SAIR (FO-SAIR) differential model that has not previously been published. This study’s aim appeared to be to demonstrate the effects and applicability of such FO-SAIR differential scheme. An FO-SAIR problem is examined using stochastic solvers relyed upon Levenberg-Marquardt backpropagation approach (L-MB) and NNs, specifically L-MBNNs. For solve the FO-SAIR system, three examples with different values under the same fractional order are presented. The statistical methods used to generate numerical answers for the FO-SAIR system are categorised thus obeys: 75% for training, 13% for testing, and 12% for permission. By using Adams-Bashforth-Moulton, the numerical results were contrasted with the reference solutions to determine the accuracy of such L-MBNNs. To confirm overall capability, competence, validity, consistency, and exactness, the numerical performances of these L-MBNNs using error histograms (EHs), state transitions (STs), regression, correlation, and mean square error (MSE) are also shown.

These investigations are to find the numerical solutions of the nonlinear smoke model to exploit a stochastic framework called gudermannian neural works (GNNs) along with the optimization procedures of global/local search terminologies based genetic algorithm (GA) and interior-point algorithm (IPA), i.e., GNNs-GA-IPA. The nonlinear smoke system depends upon four groups, temporary smokers, potential smokers, permanent smokers and smokers. In order to solve the model, the design of fitness function is presented based on the differential system and the initial conditions of the nonlinear smoke system. To check the correctness of the GNNs-GA-IPA, the obtained results are compared with the Runge-Kutta method. The plots of the weight vectors, absolute error and comparison of the results are provided for each group of the nonlinear smoke model. Furthermore, statistical performances are provided using the single and multiple trial to authenticate the stability and reliability of the GNNs-GA-IPA for solving the nonlinear smoke system.

Abstract In current study, analysis is presented for peristaltic motion of applied magnetic field and entropy generation within couple stress (Cu/H2O) nanofluid through an endoscope. An endoscope contains two coaxial cylindrical tubes in which the internal tube is nonflexible while the external tube has sinusoidal wave passing through the boundary. Influences of mixed convection along with applied magnetic field are encountered as well. Formulated governing model is fabricated introducing long wavelength and creeping Stokesian flow approximation which are then analyzed numerically by utilizing Adams Bashforth method. For a physical insight, results are demonstrated to examine the behaviors of flow profiles and entropy generation number for emerging flow parameters with the help of graphs, bar-charts and tables.

In this study, it is indicated that the world can get rid of the dengue virus by using vaccines and Wolbachia. In many findings, it is observed that Wolbachia therapy is efficacious in those regions that display the minimal to moderate the transmission level. On the contrary, vaccination is highly successful when used in serologically persons and places with large transmission levels. The resilience of stochastic methodology based on the numerical computing schemes will be used to exploit the artificial neural networks (ANNs) modelling legacy, as well as the metaheuristic intelligence using the hybrid of global and local search schemes thru genetic algorithms (GAs) and active-set method (ASA). The combination of both strategies is used to manage the numerical therapies of the mathematical form of the dengue model. The optimal control results through GA-ASA can be retrieved by offering an error-based fitness function generated for dengue model represented via nonlinear systems of equations. The acquired findings are compared to the Adams numerical results to ensure that the suggested stochastic system is accurate. For determining convergence, the training contours are based on various contact rate values. Furthermore, the statistical achievements of the suggested stochastic scheme to solve the novel developed dengue model, which demonstrate the stability and dependability of the dynamical system scheme.

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.