Journal of East China Normal University(Natural Science) ›› 2022, Vol. 2022 ›› Issue (2): 34-44.doi: 10.3969/j.issn.1000-5641.2022.02.005

• Mathematics • Previous Articles     Next Articles

Determination of convergence control parameters in homotopy analysis solutions based on machine learning technique

Tonghui ZHOU1, Yinping LIU2,3,*()   

  1. 1. School of Computer Science and Technology, East China Normal University, Shanghai 200062, China
    2. School of Mathematical Sciences, East China Normal University, Shanghai 200241, China
    3. Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, China
  • Received:2020-11-25 Online:2022-03-25 Published:2022-03-28
  • Contact: Yinping LIU


Homotopy analysis method is an effective method for constructing approximate analytical solutions to strongly nonlinear problems. The technique has been widely applied to solve important problems in scientific research and engineering technology. Compared with other existing techniques, this method leverages auxiliary parameters and functions to adjust and control the convergence region and convergence speed of approximate analytical solutions. In this paper, we present a parameter selection algorithm based on machine learning techniques to determine the optimal values of convergence control parameters for homotopy analysis solutions. This marks the first time that homotopy analysis method and machine learning techniques have been combined to obtain approximate analytical method with better convergence for strongly nonlinear mathematical and physical equations. By applying the method to several examples, we show that the convergence of solutions using the proposed method is better than those obtained from existing homotopy analysis methods. In addition, our algorithm is both more universal and flexible.

Key words: homotopy analysis method, auxiliary function, control parameter, machine learning

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