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Abstract：
In the present work, a simple intelligence-based computation of artificial neural networks with the Levenberg-Marquardt backpropagation algorithm is developed to analyze the new ferromagnetic hybrid nanofluid flow model in the presence of a magnetic dipole within the context of flow over a stretching sheet. A combination of cobalt and iron (III) oxide (Co-Fe2O3) is strategically selected as ferromagnetic hybrid nanoparticles within the base fluid, water. The initial representation of the developed ferromagnetic hybrid nanofluid flow model, which is a system of highly nonlinear partial differential equations, is transformed into a system of nonlinear ordinary differential equations using appropriate similarity transformations. The reference data set of the possible outcomes is obtained from bvp4c for varying the parameters of the ferromagnetic hybrid nanofluid flow model. The estimated solutions of the proposed model are described during the testing, training, and validation phases of the backpropagated neural network. The performance evaluation and comparative study of the algorithm are carried out by regression analysis, error histograms, function fitting graphs, and mean squared error results. The findings of our study analyze the increasing effect of the ferrohydrodynamic interaction parameter β to enhance the temperature and velocity profiles, while increasing the thermal relaxation parameter α decreases the temperature profile. The performance on MSE was shown for the temperature and velocity profiles of the developed model about 9.1703e-10, 7.1313ee-10, 3.1462e-10, and 4.8747e-10. The accuracy of the artificial neural networks with the Levenberg-Marquardt algorithm method is confirmed through various analyses and comparative results with the reference data. The purpose of this study is to enhance understanding of ferromagnetic hybrid nanofluid flow models using artificial neural networks with the Levenberg-Marquardt algorithm, offering precise analysis of key parameter effects on temperature and velocity profiles. Future studies will provide novel soft computing methods that leverage artificial neural networks to effectively solve problems in fluid mechanics and expand to engineering applications, improving their usefulness in tackling real-world problems.
摘要：
在目前的工作中,开发了一种基于Levenberg-Marquardt反向传播算法的简单的基于智能的人工神经网络计算，以分析在拉伸片上流动的情况下存在磁偶极子的情况下的新的铁磁混合纳米流体流动模型。策略性地选择钴和氧化铁（III）（Co-Fe2O3）的组合作为基础流体中的铁磁混合纳米颗粒，水。开发的铁磁混合纳米流体流动模型的初始表示，这是一个高度非线性的偏微分方程系统，使用适当的相似性变换将其转换为非线性常微分方程组。从bvp4c获得可能结果的参考数据集，用于改变铁磁混合纳米流体流动模型的参数。在测试过程中描述了所提出模型的估计解，培训,和反向传播神经网络的验证阶段。通过回归分析对算法进行性能评估和对比研究,误差直方图,函数拟合图，和均方误差结果。我们的研究结果分析了铁磁流体动力学相互作用参数β的增加效应，以增强温度和速度分布，而增加热弛豫参数α会降低温度曲线。已开发模型的温度和速度曲线显示了MSE的性能，约为9.1703e-10，7.1313ee-10，3.1462e-10和4.8747e-10。通过各种分析并将结果与参考数据进行比较，证实了使用Levenberg-Marquardt算法方法的人工神经网络的准确性。这项研究的目的是使用带有Levenberg-Marquardt算法的人工神经网络来增强对铁磁混合纳米流体流动模型的理解，提供对温度和速度曲线的关键参数影响的精确分析。未来的研究将提供新的软计算方法，利用人工神经网络有效地解决流体力学中的问题，并扩展到工程应用，提高他们在解决现实问题方面的有用性。
