Comparative Analysis of Gradient Methods for Source Identification in a Diffusion-Logistic Model

Standard

Comparative Analysis of Gradient Methods for Source Identification in a Diffusion-Logistic Model. / Zvonareva, T. A.; Krivorot’ko, O. I.

In: Computational Mathematics and Mathematical Physics, Vol. 62, No. 4, 04.2022, p. 674-684.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{c37233326c8b4db59e29a4beff23149e,

title = "Comparative Analysis of Gradient Methods for Source Identification in a Diffusion-Logistic Model",

abstract = "The paper presents a comparative analysis of the numerical solution of the problem of source identification in the diffusion-logistics model from the data on the diffusion process at fixed points in time and space by gradient methods in continuous and discrete formulations. Expressions are obtained for calculating the gradient of the objective functional for two formulations related to the solution of the corresponding adjoint problems. It is shown that, if the discrete functions of the model are approximated by cubic splines, the accuracy of the solutions of the source identification problem has the same order in the case of continuous and discrete calculation of the gradient. Numerical experiments in solving the source identification problem for a discrete model of information dissemination in online social networks have shown that the use of the discrete approach significantly increases the computational time in comparison with the continuous approach.",

keywords = "adjoint problem, comparative analysis, diffusion-logistic model, gradient methods, inverse problem, optimization, regularization, social processes, source identification problem",

author = "Zvonareva, {T. A.} and Krivorot{\textquoteright}ko, {O. I.}",

note = "Funding Information: This work was financially supported by the Russian Science Foundation (project no. 18-71-10044-P). Publisher Copyright: {\textcopyright} 2022, Pleiades Publishing, Ltd.",

year = "2022",

month = apr,

doi = "10.1134/S0965542522040145",

language = "English",

volume = "62",

pages = "674--684",

journal = "Computational Mathematics and Mathematical Physics",

issn = "0965-5425",

publisher = "PLEIADES PUBLISHING INC",

number = "4",

}

RIS

TY - JOUR

T1 - Comparative Analysis of Gradient Methods for Source Identification in a Diffusion-Logistic Model

AU - Zvonareva, T. A.

AU - Krivorot’ko, O. I.

PY - 2022/4

Y1 - 2022/4

N2 - The paper presents a comparative analysis of the numerical solution of the problem of source identification in the diffusion-logistics model from the data on the diffusion process at fixed points in time and space by gradient methods in continuous and discrete formulations. Expressions are obtained for calculating the gradient of the objective functional for two formulations related to the solution of the corresponding adjoint problems. It is shown that, if the discrete functions of the model are approximated by cubic splines, the accuracy of the solutions of the source identification problem has the same order in the case of continuous and discrete calculation of the gradient. Numerical experiments in solving the source identification problem for a discrete model of information dissemination in online social networks have shown that the use of the discrete approach significantly increases the computational time in comparison with the continuous approach.

AB - The paper presents a comparative analysis of the numerical solution of the problem of source identification in the diffusion-logistics model from the data on the diffusion process at fixed points in time and space by gradient methods in continuous and discrete formulations. Expressions are obtained for calculating the gradient of the objective functional for two formulations related to the solution of the corresponding adjoint problems. It is shown that, if the discrete functions of the model are approximated by cubic splines, the accuracy of the solutions of the source identification problem has the same order in the case of continuous and discrete calculation of the gradient. Numerical experiments in solving the source identification problem for a discrete model of information dissemination in online social networks have shown that the use of the discrete approach significantly increases the computational time in comparison with the continuous approach.

KW - adjoint problem

KW - comparative analysis

KW - diffusion-logistic model

KW - gradient methods

KW - inverse problem

KW - optimization

KW - regularization

KW - social processes

KW - source identification problem

UR - http://www.scopus.com/inward/record.url?scp=85130713894&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/13f035b4-89b1-34b3-873c-367901268e4f/

U2 - 10.1134/S0965542522040145

DO - 10.1134/S0965542522040145

M3 - Article

AN - SCOPUS:85130713894

VL - 62

SP - 674

EP - 684

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 4

ER -

ID: 36188589