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<p>In this work, we introduce a new numerical framework for addressing both homogeneous and nonhomogeneous gas dynamics equations by combining the extreme learning machine technique with a nonlinear least squares perturbation strategy. The approach employs a single-layer feedforward neural network to construct a trial solution within the ELM structure, where the output weights are obtained by minimizing the residuals of the governing differential equation together with the prescribed initial condition, thereby eliminating the need for iterative optimization. The algorithm and computational complexity of the proposed method are discussed. A comprehensive convergence study is carried out, and the stability of the method is examined under small perturbations in the training data and model parameters. The effectiveness, reliability and validity of the proposed scheme are illustrated through a series of numerical examples.</p>

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Numerical approximation to fractional gas dynamics model based on extreme learning machine approach

  • 期刊论文

  • 发表日期：

    2026年3月5日

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  • M. Fathima,
  • S. Raja Balachandar,
  • S.G. Venkatesh

摘要

In this work, we introduce a new numerical framework for addressing both homogeneous and nonhomogeneous gas dynamics equations by combining the extreme learning machine technique with a nonlinear least squares perturbation strategy. The approach employs a single-layer feedforward neural network to construct a trial solution within the ELM structure, where the output weights are obtained by minimizing the residuals of the governing differential equation together with the prescribed initial condition, thereby eliminating the need for iterative optimization. The algorithm and computational complexity of the proposed method are discussed. A comprehensive convergence study is carried out, and the stability of the method is examined under small perturbations in the training data and model parameters. The effectiveness, reliability and validity of the proposed scheme are illustrated through a series of numerical examples.