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<p>In the present work, a detailed study is provided for the error analysis of one-dimensional coupled Burgers’ equation through a novel Neural network-based regime named as Radial Basis Function Neural Network approach. For this purpose, six types of Radial basis functions are utilized such as; quintic radial basis, Linear radial basis, Cubic radial basis, Gaussian radial basis, Multiquadric radial basis, and thin plate radial basis. By the means of three examples a detailed analysis of the work is provided. <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:{L}_{\infty\:}\)</EquationSource> </InlineEquation> error and MSE are tested to check the validity. A good compatibility of the approx. and exact results is also verified via the graphs. The statistical notion is also verified among the effectiveness of errors via the Correlation matrix. The present neural network-based approach will surely be helpful to deal with complex natured differential equations.</p>

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A robust study of radial basis function neural network approach for coupled one-dimensional Burgers’ equation with statistical validation

  • 期刊论文

  • 发表日期：

    2026年7月8日

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  • Kirti Rawal

摘要

In the present work, a detailed study is provided for the error analysis of one-dimensional coupled Burgers’ equation through a novel Neural network-based regime named as Radial Basis Function Neural Network approach. For this purpose, six types of Radial basis functions are utilized such as; quintic radial basis, Linear radial basis, Cubic radial basis, Gaussian radial basis, Multiquadric radial basis, and thin plate radial basis. By the means of three examples a detailed analysis of the work is provided. \(\:{L}_{\infty\:}\) error and MSE are tested to check the validity. A good compatibility of the approx. and exact results is also verified via the graphs. The statistical notion is also verified among the effectiveness of errors via the Correlation matrix. The present neural network-based approach will surely be helpful to deal with complex natured differential equations.