Integrated intelligent computing paradigm for nonlinear multi-singular third-order Emden–Fowler equation

Abstract The presented research work articulates a new design of heuristic computing platform with artificial intelligence algorithm by exploitation of modeling with feed-forward Gudermannian neural networks (FFGNN) trained with global search viability of genetic algorithms (GA) hybrid with speedy local convergence ability of sequential quadratic programing (SQP) approach, i.e., FFGNN-GASQP for solving the singular nonlinear third order Emden-Fowler (SNEF) models. The proposed FFGNN-GASQP intelligent computing solver Gudermannian kernel unified in the hidden layer structure of FFGNN systems of differential operators based on the SNEF that are arbitrary connected to represent the error-based merit function. The optimization objective function is performed with hybrid heuristics of GASQP. Three problems of the third order SNEF are used to evaluate the correctness, robustness and effectiveness of the designed FFGNN-GASQP scheme. Statistical assessments of the performance of FFGNN-GASQP are used to validate the consistent accuracy, convergence and stability.

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Intelligent computing for the dynamics of entropy optimized nanofluidic system under impacts of MHD along thick surface

International Journal of Modern Physics B ◽

10.1142/s0217979221502696 ◽

2021 ◽

pp. 2150269

Author(s):

M. Asif Zahoor Raja ◽

M. Shoaib ◽

Rafia Tabassum ◽

M. Ijaz Khan ◽

R. J. Punith Gowda ◽

...

Keyword(s):

Mean Squared Error ◽

Fluid Motion ◽

Lewis Number ◽

Index Formula ◽

Brownian Diffusion ◽

Intelligent Computing ◽

Similarity Transformations ◽

Computing Paradigm ◽

Numerical Solver ◽

Nanofluidic System

This article examines entropy production (EP) of magneto-hydrodynamics viscous fluid flow model (MHD-VFFM) subject to a variable thickness surface with heat sink/source effect by utilizing the intelligent computing paradigm via artificial Levenberg–Marquardt back propagated neural networks (ALM-BPNNs). The governing partial differential equations (PDEs) of MHD-VFFM are transformed into ODEs by applying suitable similarity transformations. The reference dataset is obtained from Adam numerical solver by the variation of Hartmann number (Ha), thickness parameter [Formula: see text], power index ([Formula: see text], thermophoresis parameter (Nt), Brinkman number (Br), Lewis number (Le) and Brownian diffusion parameter (Nb) for all scenarios of proposed ALM-BPNN. The reference data samples arbitrary selected for training/testing/validation are used to find and analyze the approximated solutions of proposed ALM-BPNNs as well as comparison with reference results. The excellent performance of ALM-BPNN is consistently endorsed by Mean Squared Error (MSE) convergence curves, regression index and error histogram analysis. Intelligent computing based investigation suggests that the rise in values of Ha declines the velocity of the fluid motion but converse trend is seen for growing values of [Formula: see text]. The rising values of Ha, Nt and Br improve the heat transfer but converse trend is seen for growing values of [Formula: see text]. The inclining values of Nt incline the mass transfer but it shows reverse behavior for escalating values of Le. The inclining values of Br incline the EP.

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