Integrated computational intelligent paradigm for nonlinear electric circuit models using neural networks, genetic algorithms and sequential quadratic programming

Cattaneo-Christov heat flow model at mixed impulse stagnation point past a Riga plate: Levenberg-Marquardt backpropagation method

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 D a while, it increases through velocity ratio and magnetic parameters.

Intelligent Predictive Solution Dynamics for Dahl Hysteresis Model of Piezoelectric Actuator

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.

Analysis of MHD Falkner–Skan Boundary Layer Flow and Heat Transfer Due to Symmetric Dynamic Wedge: A Numerical Study via the SCA-SQP-ANN Technique

This article considers Falkner–Skan flow over a dynamic and symmetric wedge under the influence of a magnetic field. The Hall effect on a magnetic field is negligible for small magnetic Reynolds numbers. The magnetic field B(x) is considered over x-axis, which is in line with the wedge i.e., parallel, while the flow is transverse over the y-axis. This study has numerous device-centric applications in engineering, such as power generators, cooling reactor and heat exchanger design, and MHD accelerators. The Third and second-ordered ordinary differential equations characterize the system. A novel hybrid computational technique is designed for the surrogate solutions of the Falkner–Skan flow system. The designed technique is based on the sine–cosine optimization algorithm and sequential quadratic programming. Reference solutions are calculated by using the Runge–Kutta numerical technique. Performance matrices evaluate the accuracy and stability of our surrogate solutions, mean-absolute deviation (MAD), root-mean-square error (RMSE), and error in Nash-–Sutcliffe efficiency (ENSE). Furthermore, graphical representations in terms of convergence graphs, mesh graphs, stem graphs, stairs plots, and boxplots are presented to establish the symmetry, reliability, and validity of our solutions.

Neuro-swarm computational heuristic for solving a nonlinear second-order coupled Emden–Fowler model

The aim of the current study is to present the numerical solutions of a nonlinear second-order coupled Emden–Fowler equation by developing a neuro-swarming-based computing intelligent solver. The feedforward artificial neural networks (ANNs) are used for modelling, and optimization is carried out by the local/global search competences of particle swarm optimization (PSO) aided with capability of interior-point method (IPM), i.e., ANNs-PSO-IPM. In ANNs-PSO-IPM, a mean square error-based objective function is designed for nonlinear second-order coupled Emden–Fowler (EF) equations and then optimized using the combination of PSO-IPM. The inspiration to present the ANNs-PSO-IPM comes with a motive to depict a viable, detailed and consistent framework to tackle with such stiff/nonlinear second-order coupled EF system. The ANNs-PSO-IP scheme is verified for different examples of the second-order nonlinear-coupled EF equations. The achieved numerical outcomes for single as well as multiple trials of ANNs-PSO-IPM are incorporated to validate the reliability, viability and accuracy.

Improved Interactive Genetic Algorithm for Three-Dimensional Vase Modeling Design

Interactive genetic algorithm (IGA) is an effective way to help users with product design optimization. However, in this process, users need to evaluate the fitness of all individuals in each generation. It will cause users' fatigue when users cannot find satisfactory products after multi-generation evaluations. To solve this problem, an improved interactive genetic algorithm (IGA-KDTGIM) is proposed, which combines K-dimensional tree surrogate model and a graphic interaction mechanism. In this algorithm, the K-dimensional tree surrogate model is built on the basis of users' historical evaluation information to assist the user's evaluation, so as to reduce the times of users' evaluation. At the same time, users are allowed to interact with the graphic interface to adjust the shape of the individual, so as to increase users' creation fun and to make the evolution direction of the population conform to users' expectations. The IGA-KDTGIM is applied to the 3D vase design system and independently experimented with IGA, IGA-KDT, and IGA-GIM, respectively. The average fitness, maximum average fitness, and evaluation times of statistical data were compared and analyzed. Compared with traditional IGA, the number of evaluations required by users decreased by 60.0%, and the average fitness of the population increased by 15.0%. The results show that this method can reduce the users' operation fatigue and improve the ability of finding satisfactory solutions to a certain extent.

The Influence of Genetic Algorithms on Learning Possibilities of Artificial Neural Networks

The presented research study focuses on demonstrating the learning ability of a neural network using a genetic algorithm and finding the most suitable neural network topology for solving a demonstration problem. The network topology is significantly dependent on the level of generalization. More robust topology of a neural network is usually more suitable for particular details in the training set and it loses the ability to abstract general information. Therefore, we often design the network topology by taking into the account the required generalization, rather than the aspect of theoretical calculations. The next part of the article presents research whether a modification of the parameters of the genetic algorithm can achieve optimization and acceleration of the neural network learning process. The function of the neural network and its learning by using the genetic algorithm is demonstrated in a program for solving a computer game. The research focuses mainly on the assessment of the influence of changes in neural networks’ topology and changes in parameters in genetic algorithm on the achieved results and speed of neural network training. The achieved results are statistically presented and compared depending on the network topology and changes in the learning algorithm.

A bio-mathematical approach to control the Anopheles mosquito using sterile males technology

Initiative for this study is taken to solve the mathematical model which is base-forming with population dynamics of the Anopheles mosquito using an advanced computational intelligence scheme named as genetic algorithm (GA), artificial neural network (ANN). This ANN is a famous global search method, active set (AS) scheme known as a quick local refinement, i.e. ANN-GA-AS. An error-based fitness function is optimized which is made by using the sense of the differential system and boundary conditions for solving the Anopheles mosquito control model. The ability of the stochastic ANN-GA-AS approach to solve the population dynamics of the Anopheles mosquito is examined to check the exactness, efficiency, precision, and consistency of the scheme. The numerical outcomes of the Anopheles mosquito control model through the ANN-GA-AS approach are compared with the reference Adams numerical results to show the significance of the designed scheme. Moreover, statistical considerations using the “semi-interquartile range”, “Theil’s inequality coefficient”, and “mean absolute deviation” have been applied to validate the precision and accuracy of the obtained results.

A computational framework to solve the nonlinear dengue fever SIR system

This study is relevant to present the numerical form of the nonlinear dengue fever SIR system are presented using the artificial neural networks along with the Levenberg-Marquardt backpropagation technique, i.e. ANNs-LMB. The procedures of ANNs-LMB are applied with three different sample data scales based on testing, training and authentication. The statistics to solve three cases of the nonlinear dengue fever based on susceptible, infected and recovered system are selected with 75%, 15% and 10% for training, validation and testing, respectively. To find the numerical results of the nonlinear dengue fever system, the reference dataset is designed on the basis of Adams scheme for the numerical solution. The numerical results based on the nonlinear dengue fever system are obtained through the ANNs-LMB to reduce the mean square error. In order to check the exactness, reliability, effectiveness and competence of the proposed ANNs-LMB, the numerical outcomes are proficient to the proportional measures using the topographies of the fitness attained in mean squared error sense, correlation, error histograms and regression.

Design of neuro-swarming computational solver for the fractional Bagley-Torvik mathematical model

This study is to introduce a novel design and implementation of a neuro-swarming computational numerical procedure for numerical treatment of the fractional Bagley-Torvik mathematical model (FBTMM). The optimization procedures based on the global search with particle swarm optimization (PSO) and local search via active-set approach (ASA), while Mayer wavelet kernel-based activation function used in neural network (MWNNs) modeling, i.e., MWNN-PSOASA, to solve the FBTMM. The efficiency of the proposed stochastic solver MWNN-GAASA is utilized to solve three different variants based on the fractional order of the FBTMM. For the meticulousness of the stochastic solver MWNN-PSOASA, the obtained and exact solutions are compared for each variant of the FBTMM with reasonable accuracy. For the reliability of the stochastic solver MWNN-PSOASA, the statistical investigations are provided based on the stability, robustness, accuracy and convergence metrics.

Artificial intelligence knacks-based stochastic paradigm to study the dynamics of plant virus propagation model with impact of seasonality and delays

The presented study deals with the exploitation of the artificial intelligence knacks-based stochastic paradigm for the numerical treatment of the nonlinear delay differential system for dynamics of plant virus propagation with the impact of seasonality and delays (PVP-SD) model by implementing neural networks backpropagation with Bayesian regularization scheme (NNs-BBRS). The PVP-SD model is represented with five classes-based ODEs systems for the interaction between insects and plants. The nonlinear PVP-SD model governs with five populations: S(t) susceptible plants, I(t) infected plants, X(t) susceptible insect vectors, Y(t) infected insect vectors and P(t) predators. Adams numerical procedure is adopted to generate the reference solutions of the nonlinear PVP-SD model based on the variety of cases by varying the plants bite rate due to vectors, vector bite rate due to plants, plant's recovery rate, predator contact rate with healthy insects, predator contact rate with infected insects and death rate caused by insecticides. The approximate solutions of the nonlinear PVP-SD model are determined by executing the designed NNs-BBRS through different target and inputs arbitrary selected samples for the training and testing data. Validation of the consistent precision and convergence of the designed NNs-BBRS is efficaciously substantiated through exhaustive simulations and analyses on mean square error-based merit function, index of regression and error histogram illustrations.

Gudermannian neural networks using the optimization procedures of genetic algorithm and active set approach for the three-species food chain nonlinear model

The present study is to investigate the Gudermannian neural networks (GNNs) using the optimization procedures of genetic algorithm and active-set approach (GA-ASA) to solve the three-species food chain nonlinear model. The three-species food chain nonlinear model is dependent upon the prey populations, top-predator, and specialist predator. The design of an error-based fitness function is presented using the sense of the three-species food chain nonlinear model and its initial conditions. The numerical results of the model have been obtained by exploiting the GNN-GA-ASA. The obtained results through the GNN-GA-ASA have been compared with the Runge-Kutta method to substantiate the correctness of the designed approach. The reliability, efficacy and authenticity of the proposed GNN-GA-ASA are examined through different statistical measures based on single and multiple neurons for solving the three-species food chain nonlinear model.

Predictive Control for Small Unmanned Ground Vehicles via a Multi-Dimensional Taylor Network

Tracking control of Small Unmanned Ground Vehicles (SUGVs) is easily affected by the nonlinearity and time-varying characteristics. An improved predictive control scheme based on the multi-dimensional Taylor network (MTN) is proposed for tracking control of SUGVs. First, a MTN model is used as a predictive model to construct a SUGV model and back propagation (BP) is taken as its learning algorithm. Second, the predictive control law is designed and the traditional objective function is improved to obtain a predictive objective function with a differential term. The optimal control quantity is given in real time through iterative optimization. Meanwhile, the stability of the closed-loop system is proved by the Lyapunov stability theorem. Finally, a tracking control experiment on the SUGV model is used to verify the effectiveness of the proposed scheme. For comparison, traditional MTN and Radial Basis Function (RBF) predictive control schemes are introduced. Moreover, a noise disturbance is considered. Experimental results show that the proposed scheme is effective, which ensures that the vehicle can quickly and accurately track the desired yaw velocity signal with good real-time, robustness, and convergence performance, and is superior to other comparison schemes.

A Novel Design of Morlet Wavelet to Solve the Dynamics of Nervous Stomach Nonlinear Model

The present study introduces a novel design of Morlet wavelet neural network (MWNN) models to solve a class of a nonlinear nervous stomach system represented with governing ODEs systems via three categories, tension, food and medicine, i.e., TFM model. The comprehensive detail of each category is designated together with the sleep factor, food rate, tension rate, medicine factor and death rate are also provided. The computational structure of MWNNs along with the global search ability of genetic algorithm (GA) and local search competence of active-set algorithms (ASAs), i.e., MWNN-GA-ASAs is applied to solve the TFM model. The optimization of an error function, for nonlinear TFM model and its related boundary conditions, is performed using the hybrid heuristics of GA-ASAs. The performance of the obtained outcomes through MWNN-GA-ASAs for solving the nonlinear TFM model is compared with the results of state of the article numerical computing paradigm via Adams methods to validate the precision of the MWNN-GA-ASAs. Moreover, statistical assessments studies for 50 independent trials with 10 neuron-based networks further authenticate the efficacy, reliability and consistent convergence of the proposed MWNN-GA-ASAs.

Designing of Morlet wavelet as a neural network for a novel prevention category in the HIV system

The aim of this work is to present a design of Morlet wavelet neural network (MWNN) for solving a novel prevention category (P) in the HIV system, known as HIPV mathematical model. The numerical performance of the novel HIPV mathematical model will be observed by exploiting the MWNN that works through the optimization procedures of global/local via “genetic algorithm (GA)” and local search “interior-point algorithm (IPA)”, i.e. MWNN-GA-IPA. An error function using the differential HIPV mathematical model and its initial conditions is presented and optimized by the MWNN-GA-IPA. The obtained results have been compared with the Adams method to check the competence of the MWNN-GA-IPA. For the reliability and stability of the scheme, the performance using different statistical operators has been performed based on the multiple independent trials to solve the novel HIPV mathematical model.

A Hybrid Metaheuristic Based on Neurocomputing for Analysis of Unipolar Electrohydrodynamic Pump Flow

A unipolar electrohydrodynamic (UP-EHD) pump flow is studied with known electric potential at the emitter and zero electric potential at the collector. The model is designed for electric potential, charge density, and electric field. The dimensionless parameters, namely the electrical source number (Es), the electrical Reynolds number (ReE), and electrical slip number (Esl), are considered with wide ranges of variation to analyze the UP-EHD pump flow. To interpret the pump flow of the UP-EHD model, a hybrid metaheuristic solver is designed, consisting of the recently developed technique sine-cosine algorithm (SCA) and sequential quadratic programming (SQP) under the influence of an artificial neural network. The method is abbreviated as ANN-SCA-SQP. The superiority of the technique is shown by comparing the solution with reference solutions. For a large data set, the technique is executed for one hundred independent experiments. The performance is evaluated through performance operators and convergence plots.

Design of Gudermannian Neuroswarming to solve the singular Emden-Fowler nonlinear model numerically

The current investigation is related to the design of novel integrated neuroswarming heuristic paradigm using Gudermannian artificial neural networks (GANNs) optimized with particle swarm optimization (PSO) aid with active-set (AS) algorithm, i.e., GANN-PSOAS, for solving the nonlinear third-order Emden-Fowler model (NTO-EFM) involving single as well as multiple singularities. The Gudermannian activation function is exploited to construct the GANNs-based differential mapping for NTO-EFMs, and these networks are arbitrary integrated to formulate the fitness function of the system. An objective function is optimized using hybrid heuristics of PSO with AS, i.e., PSOAS, for finding the weights of GANN. The correctness, effectiveness and robustness of the designed GANN-PSOAS are verified through comparison with the exact solutions on three problems of NTO-EFMs. The assessments on statistical observations demonstrate the performance on different measures for the accuracy, consistency and stability of the proposed GANN-PSOAS solver.

A fractional-order model of COVID-19 considering the fear effect of the media and social networks on the community

Since December 2019, the world has experienced from a virus, known as Covid-19, that is highly transmittable and is now spread worldwide. Many mathematical models and studies have been implemented to work on the infection and transmission risks. Besides the virus's transmission effect, another discussion appears in the community: the fear effect. People who have never heard about coronavirus, face every day uncertain and different information regarding the effect of the virus and the daily death rates from sources like the media, the medical institutions or organizations. Thus, the fear of the virus in the community can possibly reach the point that people become scared and confused about information polluted from different networks with long-term trend discussions. In this work, we use the Routh-Hurwitz Criteria to analyze the local stability of two essential critical points: the disease-free and the co-existing critical point. Using the discretization process, our analysis have shown that one should distinguish between the spread of "awareness" or "fear" in the community through the media and others to control the virus's transmission. Finally, we conclude our theoretical findings with numerical simulations.

Falkner-Skan Flow with Stream-Wise Pressure Gradient and Transfer of Mass over a Dynamic Wall

In this work, an important model in fluid dynamics is analyzed by a new hybrid neurocomputing algorithm. We have considered the Falkner-Skan (FS) with the stream-wise pressure gradient transfer of mass over a dynamic wall. To analyze the boundary flow of the FS model, we have utilized the global search characteristic of a recently developed heuristic, the Sine Cosine Algorithm (SCA), and the local search characteristic of Sequential Quadratic Programming (SQP). Artificial neural network (ANN) architecture is utilized to construct a series solution of the mathematical model. We have called our technique the ANN-SCA-SQP algorithm. The dynamic of the FS system is observed by varying stream-wise pressure gradient mass transfer and dynamic wall. To validate the effectiveness of ANN-SCA-SQP algorithm, our solutions are compared with state-of-the-art reference solutions. We have repeated a hundred experiments to establish the robustness of our approach. Our experimental outcome validates the superiority of the ANN-SCA-SQP algorithm.

State Estimation of an Underwater Markov Chain Maneuvering Target Using Intelligent Computing

In this study, an application of deep learning-based neural computing is proposed for efficient real-time state estimation of the Markov chain underwater maneuvering object. The designed intelligent strategy is exploiting the strength of nonlinear autoregressive with an exogenous input (NARX) network model, which has the capability for estimating the dynamics of the systems that follow the discrete-time Markov chain. Nonlinear Bayesian filtering techniques are often applied for underwater maneuvering state estimation applications by following state-space methodology. The robustness and precision of NARX neural network are efficiently investigated for accurate state prediction of the passive Markov chain highly maneuvering underwater target. A continuous coordinated turning trajectory of an underwater maneuvering object is modeled for analyzing the performance of the neural computing paradigm. State estimation modeling is developed in the context of bearings only tracking technology in which the efficiency of the NARX neural network is investigated for ideal and complex ocean environments. Real-time position and velocity of maneuvering object are computed for five different cases by varying standard deviations of white Gaussian measured noise. Sufficient Monte Carlo simulation results validate the competence of NARX neural computing over conventional generalized pseudo-Bayesian filtering algorithms like an interacting multiple model extended Kalman filter and an interacting multiple model unscented Kalman filter.

Computational Intelligent Paradigms to Solve the Nonlinear SIR System for Spreading Infection and Treatment Using Levenberg–Marquardt Backpropagation

The current study aims to design an integrated numerical computing-based scheme by applying the Levenberg–Marquardt backpropagation (LMB) neural network to solve the nonlinear susceptible (S), infected (I) and recovered (R) (SIR) system of differential equations, representing the spreading of infection along with its treatment. The solutions of both the categories of spreading infection and its treatment are presented by taking six different cases of SIR models using the designed LMB neural network. A reference dataset of the designed LMB neural network is established with the Adam numerical scheme for each case of the spreading infection and its treatment. The approximate outcomes of the SIR system based on the spreading infection and its treatment are presented in the training, authentication and testing procedures to adapt the neural network by reducing the mean square error (MSE) function using the LMB. Studies based on the proportional performance and inquiries based on correlation, error histograms, regression and MSE results establish the efficiency, correctness and effectiveness of the proposed LMB neural network scheme.

Intelligent computing with Levenberg-Marquardt artificial neural networks for nonlinear system of COVID-19 epidemic model for future generation disease control

The aim of this work is to design an intelligent computing paradigm through Levenberg-Marquardt artificial neural networks (LMANNs) for solving the mathematical model of Corona virus disease 19 (COVID-19) propagation via human to human interaction. The model is represented with systems of nonlinear ordinary differential equations represented with susceptible, exposed, symptomatic and infectious, super spreaders, infection but asymptomatic, hospitalized, recovery and fatality classes, and reference dataset of the COVID-19 model is generated by exploiting the strength of explicit Runge-Kutta numerical method for metropolitans of China and Pakistan including Wuhan, Karachi, Lahore, Rawalpindi and Faisalabad. The created dataset is arbitrary used for training, validation and testing processes for each cyclic update in Levenberg-Marquardt backpropagation for numerical treatment of the dynamics of COVID-19 model. The effectiveness and reliable performance of the design LMANNs are endorsed on the basis of assessments of achieved accuracy in terms of mean squared error based merit functions, error histograms and regression studies.

A Stochastic Intelligent Computing with Neuro-Evolution Heuristics for Nonlinear SITR System of Novel COVID-19 Dynamics

The present study aims to design stochastic intelligent computational heuristics for the numerical treatment of a nonlinear SITR system representing the dynamics of novel coronavirus disease 2019 (COVID-19). The mathematical SITR system using fractal parameters for COVID-19 dynamics is divided into four classes; that is, susceptible (S), infected (I), treatment (T), and recovered (R). The comprehensive details of each class along with the explanation of every parameter are provided, and the dynamics of novel COVID-19 are represented by calculating the solution of the mathematical SITR system using feed-forward artificial neural networks (FF-ANNs) trained with global search genetic algorithms (GAs) and speedy fine tuning by sequential quadratic programming (SQP)—that is, an FF-ANN-GASQP scheme. In the proposed FF-ANN-GASQP method, the objective function is formulated in the mean squared error sense using the approximate differential mapping of FF-ANNs for the SITR model, and learning of the networks is proficiently conducted with the integrated capabilities of GA and SQP. The correctness, stability, and potential of the proposed FF-ANN-GASQP scheme for the four different cases are established through comparative assessment study from the results of numerical computing with Adams solver for single as well as multiple autonomous trials. The results of statistical evaluations further authenticate the convergence and prospective accuracy of the FF-ANN-GASQP method.