Adaptive Learning Neural Network Method for Solving Time–Fractional Diffusion Equations-Reference-Cited by-同舟云学术

Adaptive Learning Neural Network Method for Solving Time–Fractional Diffusion Equations

Published:2022-03-23 Issue:4 Volume:34 Page:971-990
ISSN:0899-7667
Container-title:Neural Computation
language:en
Short-container-title:

Author:

Shiri Babak¹,Kong Hua²,Wu Guo-Cheng³,Luo Cheng⁴

Affiliation:

1. Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, PRC shiri@njtc.edu.cn

2. Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, PRC konghua2008@126.com

3. Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, PRC wuguocheng@gmail.com

4. School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, Jiangsu, PR China mathluo@yeah.net

Abstract

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.

Publisher

MIT Press - Journals

Subject

Cognitive Neuroscience,Arts and Humanities (miscellaneous)

Link

https://direct.mit.edu/neco/article-pdf/34/4/971/2003093/neco_a_01482.pdf

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