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Analysis of incompressible viscous fluid flow in convergent and divergent channels with a hybrid meta-heuristic optimization techniques in ANN: An intelligent approach

用人工神经网络混合元启发式优化技术分析不可压缩黏性流体在收敛和发散通道中的流动:一种智能方法

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Abstract

In this research article, we introduce a numerical investigation through artificial neural networks (ANN) integrated with evolutionary algorithm especially Archimedean optimization algorithm (AOA) hybrid with the water cycle algorithm (WCA) to address and enhance the analysis of the non-linear magneto-hydrodynamic (MHD) Jeffery-Hamel problem, especially stretching/shrinking in convergent and divergent channel. This combined technique is referred to as ANN-AOA-WCA. The complex nonlinear magneto-hydrodynamic Jeffery-Hamel problem based partial differential equations are transformed into non-linear system of ordinary differential equations for velocity and temperature. We formulate the ANN based fitness function to find the solution of non-linear differential. Subsequently, we employ a novel hybridization of AOA and WCA (AOA-WCA) to optimize the ANN based fitness function and identify the best optimal weights and biases for ANN. To demonstrate the effectiveness and versatility of our proposed hybrid method, we explore MHD models across a range of Reynolds numbers, channel angles and stretchable boundary value leading to the development of two distinct cases. ANN-AOA-WCA numerical results closely align with reference solutions (NDSOLVE) and the absolute error between NDSOLVE and ANN-AOA-WCA is up to 3.35 × 10−8, particularly critical to the understanding of stretchable convergent and divergent channel. Furthermore, to validate the ANN-AOA-WCA technique, we conducted a statistical analysis over 150 independence runs to find the fitness value.

摘要

本文采用人工神经网络(ANN)与进化算法(特别是阿基米德优化算法(AOA)和水循环算法(WCA)相结合的方法)对非线性磁流体动力学(MHD)的Jeffery-Hamel 问题, 特别是收敛和发散通道中的拉伸/收缩问题进行了数值研究。这种组合技术被称为ANN-AOA-WCA。将基于复杂非线性磁流体动力学Jeffery-Hamel 问题的偏微分方程转化为速度和温度的非线性常微分方程系统, 我们建立了基于人工神经网络的适应度函数来求解非线性微分问题。随后, 采用了一种新的AOA 和WCA 结合方法(AOA-WCA)来优化基于神经网络的适应度函数, 并确定了神经网络的最优权值和偏差。为了证明提出混合方法的有效性和多功能性, 探索了一系列雷诺数、通道角和可拉伸边界值的MHD 模型, 从而开发了两种不同的情况。ANN-AOA-WCA 的数值结果与参考解(NDSOLVE)非常接近, NDSOLVE 与ANN-AOA-WCA 的绝对误差约为3.35×10−8, 对可拉伸收敛和发散通道的理解特别关键。此外, 为了验证ANN-AOA-WCA 技术, 我们对150 多个独立运行进行了统计分析, 以获得适应度值。

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Authors and Affiliations

  1. Department of Physics and Applied Mathematics (DPAM), Pakistan Institute of Engineering & Applied Sciences, Nilore, 45650, Islamabad, Pakistan

    Muhammad Naeem Aslam & Nadeem Shaukat

  2. Center for Mathematical Sciences (CMS), Pakistan Institute of Engineering & Applied Sciences, Nilore, 45650, Islamabad, Pakistan

    Muhammad Naeem Aslam & Nadeem Shaukat

  3. Department of Mathematics, Division of Science and Technology, University of Education, Lahore, 54770, Pakistan

    Arshad Riaz

  4. School of Mathematics, Minhaj University, Lahore, Pakistan

    Shahzad Ali

  5. MCS, National University of Sciences and Technology, Islamabad, Pakistan

    Safia Akram

  6. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    M. M. Bhatti

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  1. Muhammad Naeem Aslam
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Contributions

ASLAM Muhammad Naeem, RIAZ Arshad, SHAUKAT Nadeem, and ALI Shahzad provided the concept and edited the draft of manuscript. AKRAM Safia, and BHATTI M. M. conducted the literature review and wrote the first draft of the manuscript. Safia AKRAM, and M. M. BHATTI edited the draft of the manuscript.

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Correspondence to M. M. Bhatti.

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ASLAM Muhammad Naeem, RIAZ Arshad, SHAUKAT Nadeem, ALI Shahzad, AKRAM Safia, BHATTI M. M. declare that they have no conflict of interest.

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Aslam, M.N., Riaz, A., Shaukat, N. et al. Analysis of incompressible viscous fluid flow in convergent and divergent channels with a hybrid meta-heuristic optimization techniques in ANN: An intelligent approach. J. Cent. South Univ. 30, 4149–4167 (2023). https://doi.org/10.1007/s11771-023-5514-2

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