Computational intelligence of Levenberg-Marquardt backpropagation neural networks to study the dynamics of expanding/contracting cylinder for Cross magneto-nanofluid flow model

Abstract

Abstract In the present investigation, design of integrated numerical computing through Levenberg-Marquardt backpropagation neural network (LMBNN) is presented to examine the fluid mechanics problems governing the dynamics of expanding and contracting cylinder for Cross magneto-nanofluid flow (ECCCMNF) model in the presence of time dependent non-uniform magnetic force and permeability of the cylinder. The original system model ECCCMNF in terms of PDEs is converted to nonlinear ODEs by introducing the similarity transformations. Reference dataset of the designed LMBNN methodology is formulated with Adam numerical technique for scenarios of ECCCMNF by variation of thermophoresis temperature ratio parameter, Brownian motion, suction parameters as well as Schmidt, Prandtl, local Weissenberg and Biot numbers. To calculate the approximate solution for ECCCMNF for different scenarios, the training, testing, and validation processes are conducted in parallel to adapt neural network by reducing the mean square error (MSE) function through Levenberg-Marquardt backpropagation. The comparative studies and performance analyses based on outcomes of MSE, error histograms, correlation and regression demonstrate the effectiveness of designed LMBNN technique.