Design of Mexican Hat Wavelet neural networks for solving Bratu type nonlinear systems

Design of stochastic computational Levenberg Marquardt backpropagation-based technique to investigate temperature distribution of longitudinal moving porous fin

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.

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.

Intelligent computing through neural networks for numerical treatment of non-Newtonian wire coating analysis model

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

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.

Investigation of singular ordinary differential equations by a neuroevolutionary approach

In this research, we have investigated doubly singular ordinary differential equations and a real application problem of studying the temperature profile in a porous fin model. We have suggested a novel soft computing strategy for the training of unknown weights involved in the feed-forward artificial neural networks (ANNs). Our neuroevolutionary approach is used to suggest approximate solutions to a highly nonlinear doubly singular type of differential equations. We have considered a real application from thermodynamics, which analyses the temperature profile in porous fins. For this purpose, we have used the optimizer, namely, the fractional-order particle swarm optimization technique (FO-DPSO), to minimize errors in solutions through fitness functions. ANNs are used to design the approximate series of solutions to problems considered in this paper. We find the values of unknown weights such that the approximate solutions to these problems have a minimum residual error. For global search in the domain, we have initialized FO-DPSO with random solutions, and it collects best so far solutions in each generation/ iteration. In the second phase, we have fine-tuned our algorithm by initializing FO-DPSO with the collection of best so far solutions. It is graphically illustrated that this strategy is very efficient in terms of convergence and minimum mean squared error in its best solutions. We can use this strategy for the higher-order system of differential equations modeling different important real applications.

Backtracking search optimization heuristics for nonlinear Hammerstein controlled auto regressive auto regressive systems

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