In this study, a new computing model is developed using the strength of feed-forward neural networks with the Levenberg–Marquardt scheme-based backpropagation technique (NN-BLMS). It is used to find a solution for the nonlinear system obtained from the governing equations of the magnetohydrodyanmic (MHD) boundary layer flow over a stretching sheet. Moreover, the partial differential equations (PDEs) for the MHD boundary layer flow over a stretching sheet are converting into ordinary differential equations (ODEs) with the help of similarity transformation. A dataset for the proposed NN-BLMM-based model is generated at different scenarios by a variation of various embedding parameters: Deborah number and magnetic parameter (M). The training (TR), testing (TS), and validation (VD) of the NN-BLMS model are evaluated in the generated scenarios to compare the obtained results with the reference results. For the fluidic system convergence analysis, a number of metrics, such as the mean square error (MSE), error histogram (EH), and regression (RG) plots, are utilized for measuring the effectiveness and performance of the NN-BLMS infrastructure model. The experiments showed that comparisons between the results of proposed model and the reference results match in terms of convergence up to E-02 to E-10. This proves the validity of the NN-BLMS model. Furthermore, the results demonstrated that there is a decrease in the thickness of the boundary layer by increasing the Deborah number and magnetic parameter. The importance of the experiment can be seen due to its industrial applications such as MHD power generation, MHD generators, and MHD pumps.

中文翻译：

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拉伸片上的 MHD 边界层流：一种新的随机方法

在这项研究中，使用前馈神经网络的强度和基于 Levenberg-Marquardt 方案的反向传播技术 (NN-BLMS) 开发了一种新的计算模型。它用于找到非线性系统的解，该非线性系统从拉伸片上的磁流体动力学 (MHD) 边界层流的控制方程获得。此外，在相似变换的帮助下，MHD 边界层流在拉伸片上的偏微分方程 (PDE) 正在转换为常微分方程 (ODE)。所提出的基于 NN-BLMM 的模型的数据集是在不同场景下通过各种嵌入参数的变化生成的：德博拉数和磁参数 ( M）。NN-BLMS 模型的训练 (TR)、测试 (TS) 和验证 (VD) 在生成的场景中进行评估，以将获得的结果与参考结果进行比较。对于流体系统收敛分析，许多指标，例如均方误差 (MSE)、误差直方图 (EH) 和回归 (RG) 图，用于衡量 NN-BLMS 基础设施模型的有效性和性能. 实验表明，所提出模型的结果与参考结果之间的比较在收敛性方面匹配到 E-02 到 E-10。这证明了 NN-BLMS 模型的有效性。此外，结果表明，通过增加德博拉数和磁参数，边界层的厚度减小。