Integrated neuro-evolution-based computing solver for dynamics of nonlinear corneal shape model numerically

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.

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.

Further analysis of double-diffusive flow of nanofluid through a porous medium situated on an inclined plane: AI-based Levenberg–Marquardt scheme with backpropagated neural network

The present article exploits a novel application of AI-based Levenberg–Marquardt scheme with backpropagated neural network (LMS–BPNN) to analyze the double-diffusive free convection nanofluid flow model (DDFC-NFM) over an inclined plate in the existence of Brownian motion and thermophoresis properties embedded in a porous medium. The governing PDEs representing DDFC-NFM are transformed into system of nonlinear ODEs by applying suitable transformation. The reference data set is generated from Lobatto III-A numerical solver by variation of magnetic field parameter (M), thermal Grashof number (Gr), angle of inclination (α), Brownian motion parameter (Nb), Dufour-solutal Lewis number (Ld), modified Dufour parameter (Nd) and thermophoresis parameter (Nt) for all scenarios of the designed LMS–BPNN. The approximate solution and its comparison with standard solution are analyzed by execution of training, testing and validation procedure of the designed LMS–BPNN. The effectiveness and reliable performance of LMS–BPNN are endorsed with MSE-based fitness curve, regression analysis, error histogram analysis and correlation index. Results reveal that velocity increases with the rise in Gr, whereas reverse trend has been noticed for angle of inclination and magnetic field parameter and the temperature profile increases with the increase in Nb, Nd and Nt. The solutal concentration profile increases with the increment in Ld, while an increase in Nd causes a decrease in it. When Nt increases, the enhancement in the nanoparticle volume frictions occurs, but an opposite behavior is depicted for Brownian motion parameter.

Heat Transfer Impacts on Maxwell Nanofluid Flow over a Vertical Moving Surface with MHD Using Stochastic Numerical Technique via Artificial Neural Networks

The technique of Levenberg–Marquardt back propagation with neural networks (TLMB-NN) was used in this research article to investigate the heat transfer of Maxwell base fluid flow of nanomaterials (HTM-BFN) with MHD over vertical moving surfaces. In this study, the effects of thermal energy, concentration, and Brownian motion are also employed. Moreover, the impacts of a heat-absorbing fluid with viscous dissipation and radiation have been explored. To simplify the governing equations from a stiff to a simple system of non-linear ODEs, we exploited the efficacy of suitable similarity transformation mechanism. Through applicability of state-of-the-art Adams numerical technique, a set of data for suggested (TLMB-NN) is generated for several situations (scenarios) by changing parameters, such as the Thermophoresis factor Nt, Hartmann number M, Eckert number Ec, concentration Grashoff parameter Gc, Prandtl number Pr, Lewis number Le, thermal Grashof number GT, and Brownian motion factor Nb. The estimate solution of different instances has validated using the (TLMB-NN) training, testing, and validation method, and the recommended model was compared for excellence. Following that, regression analysis, mean square error, and histogram explorations are used to validate the suggested (TLMB-NN). The proposed technique is distinguished based on the proximity of the proposed and reference findings, with an accuracy level ranging from 10−9 to 10−10.

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.

Intelligent computing technique based supervised learning for squeezing flow model

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

Intelligent Computing with Levenberg-Marquardt Backpropagation Neural Networks for Third-Grade Nanofluid Over a Stretched Sheet with Convective Conditions

This article discussed the influence of activation energy on MHD flow of third-grade nanofluid model (MHD-TGNFM) along with the convective conditions and used the technique of backpropagation in artificial neural network using Levenberg–Marquardt technique (BANN-LMT). The PDEs representing (MHD-TGNFM) transformed into the system of ODEs. The dataset for BANN-LMT is computed for the six scenarios by using the Adam numerical method by varying the local Hartman number (Ha), Prandtl number (Pr), local chemical reaction parameter (σ), Schmidt number (Sc), concentration Biot number (γ₂) and thermal Biot number (γ₁). By testing, validation and training process of (BANN-LMT), the estimated solutions are interpreted for (MHD-TGNFM). The validation of the performance of (BANN-LMT) is done through the MSE, error histogram and regression analysis. The concentration profile increases when there is an increase in Biot number and the local Hartmann number; meanwhile, it decreases for the higher values of Schmidt number and the local chemical reaction parameter.

Supervised Learning Algorithm to Study the Magnetohydrodynamic Flow of a Third Grade Fluid for the Analysis of Wire Coating

In the present study, modeling of intelligent numerical computing through Levenberg-Marquardt back propagation-based supervised neural network (LMB-SNN) is incorporated to analyze the magnetohydrodynamic flow of a third grade fluid for wire coating analysis (MHD-TGFWCA). The original mathematical formulations in terms of partial differential equations for MHD-TGFWCA are converted into a system of ordinary differential equations through dimensionless parameters and a suitable transformation mechanism. A reference dataset for the LMB-SNNs scheme is created with Adam's numerical technique for various scenarios by variation of different physical quantities such as third grade fluid parameter, magnetic parameter, and the velocity ratio parameter. To compute the approximate solution for MHD-TGFWCA in terms of various scenarios, the training, testing, and validation operations are carried out in parallel to adjust neural networks by developing the mean square error function (MSEF) through Levenberg-Marquardt back-propagation. The comparative analyses and performance studies through outputs of MSEF, regression illustrations, and error histograms validate the effectiveness of the suggested solver LMB-SNNs. The method's precision is verified by the closest numerical outputs of both built and dataset values with similar levels 10 - 5 to 10 - 9 .

A novel application of Lobatto IIIA solver for numerical treatment of mixed convection nanofluidic model

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

Design of Spline-Evolutionary Computing Paradigm for Nonlinear Thin Film Flow Model

A novel design of stochastic numerical computing method is introduced for computational fluid dynamics problem governed with nonlinear thin film flow (TFF) system by exploiting the competency of polynomial splines for discretization and optimization with evolutionary computing aided with brilliance of local search. The TFF model of second grade fluid is represented with nonlinear second-order differential system. The aim of the present work is to exploit the cubic spline approach (CSA) to transform the differential equations for TFF model into an equivalent set of nonlinear equations. The approximation in mean squared error sense is introduced for the formulation of cost function for solving the nonlinear system of equations representing TFF model. The optimization of the decision variables of the cost function is carried out with global search efficacy of evolution by genetic algorithms (GAs) integrated with sequential quadratic programming (SQP) for speedy adjustments. The designed spline-evolutionary computing paradigm, CSA-GA-SQP, is evaluated for different scenarios of TFF model by variation of second grade and magnetic parameters, as well as variation in the length of splines. Results endorsed the worth of CSA-GA-SQP solver as an efficient alternative, reliable, stable, and accurate framework for the variants of nonlinear TFF systems on the basis of multiple autonomous executions. The design computing spline paradigm CSA-GA-SQP is a promising alternative numerical solver to be implemented for the solution of stiff nonlinear systems representing the complex scenarios of computational fluid dynamics problems.