A Levenberg–Marquardt Backpropagation Neural Network for the Numerical Treatment of Squeezing Flow With Heat Transfer Model
Maryam Mabrook Almalki, Eman Salem Alaidarous, Dalal Adnan Maturi, Muhammad Asif Zahoor Raja, Muhammad Shoaib
Abstract
In this paper, the computational strength in terms of soft computing neural networks backpropagated with the efficacy of Levenberg-Marquard training (NN-BLMT) is presented to study the squeezing flow with the heat transfer model (SF-HTM). The governing system of PDEs is reduced to an equivalent system of nonlinear ODEs using similarity transformations. NN-BLMT dataset for all problem scenarios progresses through the standard Adam numerical method by the influence of Prandtl number, Eckert number, and thermal slip. The processing of NN-BLMT training, testing, and validation, is employed for various scenarios and cases to find and compare approximation solutions with reference results. For the fluidic system SF-HTM, convergence analysis based on mean square errors, histogram presentations, and statistical regression plots is considered for the proposed computing infrastructure's performance in terms of NN-BLMT. Matching of the results for the fluid flow system SF-HTM based on proposed and reference results in terms of convergence up-to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-07</sup> to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-03</sup> proves the worth of proposed NN-BLMT.