Neural network method for solving fractional diffusion equations

作者：

Highlights：

• Neural networks based on Legendre polynomials are established to solve space and time fractional diffusion equations.

• The error functions containing adjustable parameters for the training sets are constructed.

• The range of learning rate is analyzed to ensure that the error decreases with respect to training times.

摘要

•Neural networks based on Legendre polynomials are established to solve space and time fractional diffusion equations.•The error functions containing adjustable parameters for the training sets are constructed.•The range of learning rate is analyzed to ensure that the error decreases with respect to training times.

论文关键词：Fractional diffusion equation,Neural network method,Time fractional derivative,Space fractional derivative,Time-space fractional derivative

论文评审过程：Received 16 April 2020, Revised 22 August 2020, Accepted 30 August 2020, Available online 11 September 2020, Version of Record 11 September 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125635