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<p>Aiming at solving the initial value problem of nonlinear dynamic system, a neural network method based on Lie symmetry theory of differential equation is proposed. Because the Lie series representation of the solution of the problem to be solved provides the prior knowledge of the solution for the network training, the structure of the neural network is simple, and the network solution is more effective to approximate the true solution. Theoretical analysis and numerical examples demonstrate the reliability and effectiveness of the proposed algorithm.</p>

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A Lie Series-Based Neural Network Method to Solve Initial Value Problem of a Nonlinear Dynamical System

  • 期刊论文

  • 发表日期：

    2025年9月26日

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  • Sulifu Bao,
  • Ying Wen,
  • Chaolu Temuer

摘要

Aiming at solving the initial value problem of nonlinear dynamic system, a neural network method based on Lie symmetry theory of differential equation is proposed. Because the Lie series representation of the solution of the problem to be solved provides the prior knowledge of the solution for the network training, the structure of the neural network is simple, and the network solution is more effective to approximate the true solution. Theoretical analysis and numerical examples demonstrate the reliability and effectiveness of the proposed algorithm.