Optimization through the Levenberg—Marquardt Backpropagation Method for a Magnetohydrodynamic Squeezing Flow System

Abstract

The present study introduced the unsteady squeezing flow of two-dimensional viscous fluid with nanoparticles between two disks by using the Levenberg–Marquardt backpropagated neural network (LMB-NN). Conversion of the partial differential equations (PDEs) into equivalent ordinary differential equations (ODEs) is performed by suitable similarity transformation. The data collection for suggested (LMB-NN) is made for various magnetohydrodynamic squeezing flow (MHDSF) scenarios in terms of the squeezing parameter, Prandtl number, Brownian motion parameter, and the thermophoresis parameter by employing the Runge–Kutta technique with the help of Mathematica software. The worth of the proposed methodology has been established for the proposed solver (LMB-NN) with different scenarios and cases, and the outcomes are compared through the effectiveness and reliability of mean square error (MSE) for the squeezing flow problem MHDSF. Moreover, the state transition, Fitness outline, histogram error, and regression presentation also endorse the strength and reliability of the solver LMB-NN. The high convergence between the reference solutions and the solutions obtained by incorporating the efficacy of a designed solver LMB-NN indicates the strength of the proposed methodology, where the accuracy level is achieved in the ranges from 10−6 to 10−12.

Numerical Computational Heuristic Through Morlet Wavelet Neural Network for Solving the Dynamics of Nonlinear SITR COVID-19

“…The authors are inspired to solve the nonlinear COVID-19 fractal model by applying the proposed method due to the immense applications of stochastic computing solvers. Few of them are nonlinear singular delay differential model [6,7], multi-fractional multi-singular differential models [8][9][10], fractionalorder pantograph Lane-Emden differential systems [11], prey-predator models [12], second grade nanofluidic system [13], heat transfer possessions in a Bodewadt flow [14], solution of functionally graded material of the porous fin model [15], HIV infection system [16], hybrid hydro-nanofluid Al 2 O 3 -Cu-H 2 O model [17], Ferrofluidic models [18], singular functional systems [19], magnetohydrodynamic squeezing flow model [20], Cattaneo-christov heat flux model [21], nonlinear optics [22], nonlinear Falkner-Skan systems [23], singular Thomas-Fermi system [24], thin-film flow of Maxwell nanofluidic model [25], mosquito dispersal nonlinear system [26], nonlinear corneal shape model [27], heat conduction based human head system [28], mathematical model for entropy generation system [29] and singular periodic models [30,31]. The novel features of the MWNN-GA-ASA are given as:…”

Intelligent computing paradigm for the Buongiorno model of nanofluid flow with partial slip and MHD effects over a rotating disk

“…The models of neural networks constructed on stochastic numerical calculation procedures by evolutionary/swamped metaheuristic methods are formulated for linear or non-linear weather differential system solutions that occur in different areas. These algorithms are widely used in a numerous field of science, including; bioinformatics [42,43], fluid dynamics [44][45][46][47][48], nonlinear multi-singular Emden-Fowler equation [49], dynamics of plant virus [50], dusty plasma system [51], astrophysics [52], COVID-19 virus spread models [53][54][55], magneto hydrodynamics models [56,57], finance [58,59], atomic physics [60,61], plasma physics [62,63], entropy generation fluid flow systems [64][65][66] and nonlinear circuits [67,68]. Similarly, stochastic approaches are used to solve stiff problems involving fractional order differential equations, such as the Riccati and Baglay-Torvik equations [69,70].…”