Optimization through the Levenberg—Marquardt Backpropagation Method for a Magnetohydrodynamic Squeezing Flow System
Maryam Mabrook Almalki, Eman Salem Alaidarous, Muhammad Asif Zahoor Raja, Dalal Adnan Maturi, Muhammad Shoaib
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.