Almalki Maryam Mabrook, Alaidarous Eman Salem, Maturi Dalal Adnan, Raja Muhammad Asif Zahoor, Shoaib Muhammad
Department of Mathematics, Faculty of Science, Umm Al-Qura University, Makkah, 24211, Saudi Arabia.
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia.
Sci Rep. 2021 Oct 1;11(1):19597. doi: 10.1038/s41598-021-99108-z.
In this study, the unsteady squeezing flow between circular parallel plates (USF-CPP) is investigated through the intelligent computing paradigm of Levenberg-Marquard backpropagation neural networks (LMBNN). Similarity transformation introduces the fluidic system of the governing partial differential equations into nonlinear ordinary differential equations. A dataset is generated based on squeezing fluid flow system USF-CPP for the LMBNN through the Runge-Kutta method by the suitable variations of Reynolds number and volume flow rate. To attain approximation solutions for USF-CPP to different scenarios and cases of LMBNN, the operations of training, testing, and validation are prepared and then the outcomes are compared with the reference data set to ensure the suggested model's accuracy. The output of LMBNN is discussed by the mean square error, dynamics of state transition, analysis of error histograms, and regression illustrations.
在本研究中,通过Levenberg-Marquard反向传播神经网络(LMBNN)的智能计算范式,对圆形平行板间的非定常挤压流动(USF-CPP)进行了研究。相似变换将控制偏微分方程的流体系统转化为非线性常微分方程。通过Runge-Kutta方法,对雷诺数和体积流量进行适当变化,为LMBNN生成了基于挤压流体流动系统USF-CPP的数据集。为了获得针对USF-CPP不同场景和情况的LMBNN近似解,准备了训练、测试和验证操作,然后将结果与参考数据集进行比较,以确保所提模型的准确性。通过均方误差、状态转移动态、误差直方图分析和回归图对LMBNN的输出进行了讨论。