Numerical Algorithm for Source Determination in a Diffusion-Logistic Model from Integral Data Based on Tensor Optimization

被引：2

作者：

Zvonareva, T. A. ^{[1
,2
]}

Kabanikhin, S. I. ^{[2
,3
]}

Krivorotko, O. I. ^{[1
,2
,3
]}

机构：

[1] Russian Acad Sci, Siberian Branch, Inst Computat Math & Math Geophys, Novosibirsk 630090, Russia

[2] Novosibirsk State Univ, Novosibirsk 630090, Russia

[3] Russian Acad Sci, Siberian Branch, Sobolev Inst Math, Novosibirsk 630090, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2023年 / 63卷 / 09期

基金：

俄罗斯科学基金会;

关键词：

source determination problem; reaction-diffusion model; inverse problem; tensor optimization; regularization; gradient methods; INVERSE;

D O I：

10.1134/S0965542523090166

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An algorithm has been developed for numerically solving the source determination problem in the model of information dissemination in synthetic online social networks, described by reaction-diffusion-type equations, using additional information about the process at fixed time points. The degree of ill-posedness of the source determination problem for a parabolic equation is studied based on the analysis of singular values of the linearized operator of the inverse problem. The algorithm developed is based on a combination of the tensor optimization method and gradient descent supplemented with the A.N. Tikhonov regularization. Numerical calculations demonstrate the smallest relative error in the reconstructed source obtained by the developed algorithm in comparison with classical approaches

引用

页码：1654 / 1663

页数：10

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