<p>The work examines the magnetohydrodynamic (MHD) influence on heat and mass transmission across shrinking cylinders. Using similarity variables, the governing PDEs are converted into a system of linked ODEs. The first results are obtained by the use of a mathematical technique, which forms the basis for the artificial neural networking (ANN) study. 15% is put aside for validation, 15% for testing, and 70% of the ANN sample is used for training. The main goal is to investigate hidden layers that affect the error, dependability, and efficiency of ANNs. The ANN is trained using the Levenberg–Marquardt algorithm, yielding an error range of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14683_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">${10}^{-8}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>-</mo> <mn>8</mn> </mrow> </msup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14683_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">${10}^{-6}.$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> Findings indicate that when the magnetic force strength increases, the velocity curve lowers. The ideal number of hidden layers for a dataset with 70 data points is determined to be 9. After this, the model begins to produce inaccuracies and the outcomes become erroneous, suggesting that it has trouble identifying the deeper trends in the data. Selecting the right quantity of hidden layers is essential since it has a significant impact on the model's efficiency, precision, and error. While having insufficient layers may not adequately represent the intricacy of the issue, overly complicated the model having an excessive number of hidden layers might result in excessive fitting or insufficient generalization. For ANN models to produce accurate outcomes, an appropriate number of hidden layers must be balanced.</p>

Optimizing hidden layers for prediction of heat and mass transfer in steady two-dimensional flow over cylinder

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发表日期：

2025年9月19日

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Sohaib Abdal,
Talal Taha,
Liaqat Ali,
Rana Muhammad Zulqarnain,
Se-Jin Yook,
Zarwa Fatima

摘要

The work examines the magnetohydrodynamic (MHD) influence on heat and mass transmission across shrinking cylinders. Using similarity variables, the governing PDEs are converted into a system of linked ODEs. The first results are obtained by the use of a mathematical technique, which forms the basis for the artificial neural networking (ANN) study. 15% is put aside for validation, 15% for testing, and 70% of the ANN sample is used for training. The main goal is to investigate hidden layers that affect the error, dependability, and efficiency of ANNs. The ANN is trained using the Levenberg–Marquardt algorithm, yielding an error range of ${10}^{-8}$ $10^{- 8}$ and ${10}^{-6}.$ $10^{- 6} .$ Findings indicate that when the magnetic force strength increases, the velocity curve lowers. The ideal number of hidden layers for a dataset with 70 data points is determined to be 9. After this, the model begins to produce inaccuracies and the outcomes become erroneous, suggesting that it has trouble identifying the deeper trends in the data. Selecting the right quantity of hidden layers is essential since it has a significant impact on the model's efficiency, precision, and error. While having insufficient layers may not adequately represent the intricacy of the issue, overly complicated the model having an excessive number of hidden layers might result in excessive fitting or insufficient generalization. For ANN models to produce accurate outcomes, an appropriate number of hidden layers must be balanced.