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An artificial neural network‐based method for the optimal control problem governed by the fractional parabolic equation
Numerical Methods for Partial Differential Equations ( IF 3.9 ) Pub Date : 2020-12-17 , DOI: 10.1002/num.22710
Majid Darehmiraki 1 , Arezou Rezazadeh 2 , Ali Ahmadian 3, 4
Affiliation  

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.

中文翻译:

基于分数阶抛物线方程的最优控制问题的基于人工神经网络的方法

在本文中,我们提出了一种人工神经网络模型(ANN)来解决偏微分方程(PDE)约束优化问题。在这里,使用了先离散后优化的方法。首先,使用勒让德多项式离散化优化问题,并将其转化为具有线性约束的二次优化问题。然后提出了一个人工神经网络模型来解决所获得的二次优化问题。最后,给出了几个例子来说明所提出方法的能力和效率。
更新日期:2020-12-17
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