Soft computing through supervised neural network based on Levenberg–Marquardt back propagation for numerical treatment of steady flow of Oldroyd 4-constant fluid between two rolls

Muhammad Usman (), Yanren Hou (), Muhammad Zahid (), Fateh Ali and Muhammad Afzal Rana ()
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Muhammad Usman: School of Mathematics & Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, P. R. China
Yanren Hou: School of Mathematics & Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, P. R. China
Muhammad Zahid: Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Khyber Pakhtunkhwa, Pakistan
Fateh Ali: College of Mathematics and System Sciences, Xinjiang University, Ürümqi, Xinjiang Uyghur Autonomous, Region 830046, P. R. China
Muhammad Afzal Rana: Department of Mathematics & Statistics, Riphah International University, Sector I-14, Islamabad 44000, Islamabad Capital Territory, Pakistan

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 06, 1-33

Abstract: This study presents a new intelligent computing method based on the Levenberg–Marquardt back-propagation-based supervised neural network (LMB-SNN) for the flow of Oldroyd 4-constant fluid in the forward roll coating process (OFC-FRCP). The mathematical formulations for OFC-FRCP are converted into ordinary differential equations using lubrication approximation theory (LAT) and suitable dimensionless parameters. The analytic expressions for velocity distribution, pressure and pressure gradients have been obtained using Adomian’s Decomposition Method (ADM) for several situations. The fluid’s separation point and coating thickness are then calculated using integration. The reference dataset for LMB-SNN has been obtained by ADM for multiple scenarios by adjusting various physical variables. The neural network’s training, testing and validation are carried out in parallel to minimize the mean-squared error function (MSEF). The proposed LMB-SNN’s effectiveness was confirmed by analyzing the MSEF, error histograms and regression plots. The precision of the method is verified by the close agreement between numerical outputs and dataset values. The intelligent numerical results computed using ADM and LMB-SNN are presented in various graphs and tables. The method’s accuracy is demonstrated by the numerical outputs closest to the built and dataset values at levels between 10−9 and 10−12.

Keywords: Viscoelastic fluid; Oldroyd 4-constant fluid; forward roll coating; Levenberg–Marquardt method; Adomian’s decomposition method (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0129183124500712

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