AN INVERSE BACKWARD PROBLEM FOR A HEAT EQUATION WITH A MEMORY TERM, SOLVED BY A DEEP LEARNING METHOD

被引：0

作者：

Abid, Soufiane ^{[1
]}

Atifi, Khalid ^{[1
]}

Essoufi, El -Hassan ^{[1
]}

机构：

[1] Univ Hassan 1, Lab Math Informat & Sci Ingn MISI, Settat 26000, Morocco

来源：

MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS | 2024年 / 91卷

关键词：

Inverse problem; memory term; optimization; deep learning; IDENTIFICATION; KERNEL;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our goal of this paper is the identification of an initial condition in a heat equation that contains a memory term from final data. To this aim, we first establish the well-posedness of the direct problem. Then we prove the continuity and the G -derivability of the cost function. Finally, we validate the results numerically by using a deep neural network. Our algorithm is meshfree.

引用

页码：1 / 20

页数：20

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