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(AOAWCA)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ANNAOA-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。
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.
