A Combined Artificial Neural Network Method for Solving Time Fractional Diffusion Equations

WANG Jiang; CHEN Wen

doi:10.21656/1000-0887.390288

Volume 40 Issue 7

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WANG Jiang, CHEN Wen. A Combined Artificial Neural Network Method for Solving Time Fractional Diffusion Equations[J]. Applied Mathematics and Mechanics, 2019, 40(7): 741-750. doi: 10.21656/1000-0887.390288

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A Combined Artificial Neural Network Method for Solving Time Fractional Diffusion Equations

doi: 10.21656/1000-0887.390288

Institute of Soft Matter Mechanics, College of Mechanics and Materials, Hohai University, Nanjing 211100, P.R.China

Received Date: 2018-11-16
Rev Recd Date: 2018-11-20
Publish Date: 2019-07-01

Abstract

Abstract

A combined artificial neural network method was proposed to solve 1D time fractional diffusion equations. The combined artificial neural network is a new network structure constructed through combination of the radial basis function (RBF) neural network and the power series feed-forward neural network. First, the proposed new model was applied to create a numerical solution conforming to the conditions of the time fractional diffusion equation. Meanwhile, an error function was defined and the original differential equation was transformed into a minimization problem. Afterwards, the gradient descent learning algorithm was used to obtain the optimal weights of the neural network and other optimal parameters. Finally, a numerical example was given to illustrate the validity of the proposed method. The work makes a new way to the solution of 1D time fractional diffusion equations.
- 1D time fractional diffusion equation,
- combined artificial neural network,
- error function,
- gradient descent learning algorithm

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References(15)

References

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