Novel Adaptive Bayesian Regularization Networks for Peristaltic Motion of a Third-Grade Fluid in a Planar Channel

Tariq Mahmood,Nasir Ali,Naveed Ishtiaq Chaudhary,Muhammad Asif Zahoor Raja,Ahmad H Milyani,Khalid Mehmood Cheema

doi:10.3390/math10030358

Abstract

In this presented communication, a novel design of intelligent Bayesian regularization backpropagation networks (IBRBNs) based on stochastic numerical computing is presented. The dynamics of peristaltic motion of a third-grade fluid in a planar channel is examined by IBRBNs using multilayer structure modeling competency of neural networks trained with efficient optimization ability of Bayesian regularization method. The reference dataset used as inputs and targets parameters of IBRBN has been obtained via the state-of-the-art Adams numerical method. The data of solution dynamics is created for multiple scenarios of the peristaltic transport model by varying the volume flow rate, material parametric of a third-grade fluid model, wave amplitude, and inclination angles. The designed integrated IBRBNs are constructed by exploiting training, testing, and validation operations at each epoch via optimization of a figure of merit on mean square error sense. Exhaustive simulation of IBRBNs with comparison on mean square error, histograms, and regression index substantiated the precision, stability, and reliability to solve the peristaltic transport model.

Highlights

Peristaltic transport systems of fluid dynamics studies have utmost interest in the research community due to occurrence in the esophagus, the ureter, and the lower intestine models
The reference datasets used as inputs and targets parameters of intelligent Bayesian regularization backpropagation networks (IBRBNs) have been obtained via the state-of-the-art Adams numerical method for multiple scenarios of peristaltic transport model by varying the volume flow rate, material parametric of a third-grade fluid model, wave amplitude, and inclination angles
Comparative analysis on exhaustive numerical experimentation studies of presented computing platform IBRBNs with standard numerical solutions on mean square error, histograms and regression index substantiated the precision, stability, reliability, and robustness to solve a variant of peristaltic motion of a third-grade fluid in a planar channel

Summary

Introduction

Peristaltic transport systems of fluid dynamics studies have utmost interest in the research community due to occurrence in the esophagus, the ureter, and the lower intestine models. AI-based networks using Bayesian neural networks are exploited in different applications such as optimization of fluid flow processes [55,56], modeling of the explosion risk of the fixed offshore platforms [57], reliable optimization of complex equipment in automotive manufacturing [58], and solution dynamics of bioconvective nanofluidic models [59]. All this reported literature-inspired authors to examine the AI-based computing methodologies using Bayesian neural networks to solve the nonlinear differential systems governing the peristaltic flows of Newtonian and non-Newtonian fluidic models

Methods

Results

Conclusion