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<p>Artificial intelligence (AI)-based algorithm and methodologies are capable to improve dynamic characteristic of fluid mechanics problems by using sophisticated strategies to simulate complex interactions more efficiently and accurately for the system design in a variety of applications, including electronic cooling, magnetic separation, and biological therapies. The aim of this study is to use AI-based neuro-structures for novel implementation of cascade forward neural networks (CFNNs) to describe the behavioral dynamics for the MHD nanofluidic (MHD-NF) model in a porous convergent–divergent channels. The PDEs governing the mathematical structure of the model are transformed into the ODEs system by appropriate adjustments with transformations. The synthetic data are generated numerically using Adam’s method for MHD-NF by incorporating parameters, i.e., porosity, thermal diffusivity, and nanoparticle volume fraction as well as numbers, i.e., Hartmann, Reynold, Eckert, and Prandtl. The obtained datasets are fed to supervised computing paradigm of CFNNs to approximate the solutions of MHD-NF model in a porous convergent–divergent channels, and the results of CFNNs reliably align with numerical observations for each variant with negligible error magnitudes. The CFNNs performance on comprehensive experimentations is efficiently demonstrated through error histograms plots, iterative learning curves on mean squared error, time series responses, and regression analysis for the MHD-NF model in a porous convergent–divergent channels.</p>

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A novel design of cascade neural networks for magnetized nanofluidic model in porous convergent–divergent channels

  • 期刊论文

  • 发表日期：

    2025年7月24日

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  • Maryam Pervaiz Khan,
  • Chuan-Yu Chang,
  • Muhammad Asif Zahoor Raja,
  • Muhammad Shoaib,
  • Zeshan Aslam Khan,
  • Chi-Min Shu

摘要

Artificial intelligence (AI)-based algorithm and methodologies are capable to improve dynamic characteristic of fluid mechanics problems by using sophisticated strategies to simulate complex interactions more efficiently and accurately for the system design in a variety of applications, including electronic cooling, magnetic separation, and biological therapies. The aim of this study is to use AI-based neuro-structures for novel implementation of cascade forward neural networks (CFNNs) to describe the behavioral dynamics for the MHD nanofluidic (MHD-NF) model in a porous convergent–divergent channels. The PDEs governing the mathematical structure of the model are transformed into the ODEs system by appropriate adjustments with transformations. The synthetic data are generated numerically using Adam’s method for MHD-NF by incorporating parameters, i.e., porosity, thermal diffusivity, and nanoparticle volume fraction as well as numbers, i.e., Hartmann, Reynold, Eckert, and Prandtl. The obtained datasets are fed to supervised computing paradigm of CFNNs to approximate the solutions of MHD-NF model in a porous convergent–divergent channels, and the results of CFNNs reliably align with numerical observations for each variant with negligible error magnitudes. The CFNNs performance on comprehensive experimentations is efficiently demonstrated through error histograms plots, iterative learning curves on mean squared error, time series responses, and regression analysis for the MHD-NF model in a porous convergent–divergent channels.