An artificial neural network-based method for the optimal control problem governed by the fractional parabolic equation

Authors

Majid Darehmiraki, Behbahan Khatam Alanbia University of Technology
Arezou Rezazadeh, University of Qom
Ali Ahmadian, Universiti Kebangsaan Malaysia

Document Type

Article

Publication Date

5-1-2021

Abstract

In this paper, we propose an artificial neural network model (ANN) to solve a partial differential equation (PDE) constrained optimization problem. Here, the discretize then optimize approach is used. At first, the Legendre polynomials are used to discretize the optimization problem and transform it into a quadratic optimization problem with linear constraint. Then an ANN model is proposed to solve the obtained quadratic optimization problem. Finally, several examples are presented to illustrate the abilities and efficiency of the proposed approach.

Publication Title

Numerical Methods for Partial Differential Equations

First Page Number

2296

Last Page Number

2316

DOI

10.1002/num.22710

Recommended Citation

Darehmiraki, Majid; Rezazadeh, Arezou; and Ahmadian, Ali, "An artificial neural network-based method for the optimal control problem governed by the fractional parabolic equation" (2021). Kean Publications. 982.
https://digitalcommons.kean.edu/keanpublications/982