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.
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页码：1 / 20
页数：20
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