Adaptive Learning Neural Network Method for Solving Time-Fractional Diffusion Equations.

Journal: Neural computation
Published Date: Mar 23, 2022

Abstract

A neural network method for solving fractional diffusion equations is presented in this letter. An adaptive gradient descent method is proposed to minimize energy functions. Due to the memory effects of the fractional calculus, the gradient of energy function becomes much more complicated, and we suggest a simplified method. Numerical examples with one-layer and two-layer neurons show the effectiveness of the method.

Authors

  • Babak Shiri
    Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, PRC shiri@njtc.edu.cn.
  • Hua Kong
    Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, PRC konghua2008@126.com.
  • Guo-Cheng Wu
    Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, PRC wuguocheng@gmail.com.
  • Cheng Luo
    Department of Cardiology, Liuzhou Workers' Hospital, The Fourth Affiliated Hospital of Guangxi Medical University, Liuzhou, China.

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