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Global and local optimization in identification of parabolic systems. / Krivorotko, Olga; Kabanikhin, Sergey; Zhang, Shuhua et al.

In: Journal of Inverse and Ill-Posed Problems, Vol. 28, No. 6, 01.12.2020, p. 899-913.

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

Harvard

Krivorotko, O, Kabanikhin, S, Zhang, S & Kashtanova, V 2020, 'Global and local optimization in identification of parabolic systems', Journal of Inverse and Ill-Posed Problems, vol. 28, no. 6, pp. 899-913. https://doi.org/10.1515/jiip-2020-0083

APA

Krivorotko, O., Kabanikhin, S., Zhang, S., & Kashtanova, V. (2020). Global and local optimization in identification of parabolic systems. Journal of Inverse and Ill-Posed Problems, 28(6), 899-913. https://doi.org/10.1515/jiip-2020-0083

Vancouver

Krivorotko O, Kabanikhin S, Zhang S, Kashtanova V. Global and local optimization in identification of parabolic systems. Journal of Inverse and Ill-Posed Problems. 2020 Dec 1;28(6):899-913. Epub 2020 Sept 4. doi: 10.1515/jiip-2020-0083

Author

Krivorotko, Olga ; Kabanikhin, Sergey ; Zhang, Shuhua et al. / Global and local optimization in identification of parabolic systems. In: Journal of Inverse and Ill-Posed Problems. 2020 ; Vol. 28, No. 6. pp. 899-913.

BibTeX

@article{8d8e5240e1aa4fdc84276e647f25376b,
title = "Global and local optimization in identification of parabolic systems",
abstract = "The problem of identification of coefficients and initial conditions for a boundary value problem for parabolic equations that reduces to a minimization problem of a misfit function is investigated. Firstly, the tensor train decomposition approach is presented as a global convergence algorithm. The idea of the proposed method is to extract the tensor structure of the optimized functional and use it for multidimensional optimization problems. Secondly, for the refinement of the unknown parameters, three local optimization approaches are implemented and compared: Nelder-Mead simplex method, gradient method of minimum errors, adaptive gradient method. For gradient methods, the evident formula for the continuous gradient of the misfit function is obtained. The identification problem for the diffusive logistic mathematical model which can be applied to social sciences (online social networks), economy (spatial Solow model) and epidemiology (coronavirus COVID-19, HIV, etc.) is considered. The numerical results for information propagation in online social network are presented and discussed. ",
keywords = "gradient method, Inverse problem, optimization, parameter estimation, partial differential equations, regularization, social network, tensor train, tensor train decomposition",
author = "Olga Krivorotko and Sergey Kabanikhin and Shuhua Zhang and Victoriya Kashtanova",
year = "2020",
month = dec,
day = "1",
doi = "10.1515/jiip-2020-0083",
language = "English",
volume = "28",
pages = "899--913",
journal = "Journal of Inverse and Ill-Posed Problems",
issn = "0928-0219",
publisher = "Walter de Gruyter GmbH",
number = "6",

}

RIS

TY - JOUR

T1 - Global and local optimization in identification of parabolic systems

AU - Krivorotko, Olga

AU - Kabanikhin, Sergey

AU - Zhang, Shuhua

AU - Kashtanova, Victoriya

PY - 2020/12/1

Y1 - 2020/12/1

N2 - The problem of identification of coefficients and initial conditions for a boundary value problem for parabolic equations that reduces to a minimization problem of a misfit function is investigated. Firstly, the tensor train decomposition approach is presented as a global convergence algorithm. The idea of the proposed method is to extract the tensor structure of the optimized functional and use it for multidimensional optimization problems. Secondly, for the refinement of the unknown parameters, three local optimization approaches are implemented and compared: Nelder-Mead simplex method, gradient method of minimum errors, adaptive gradient method. For gradient methods, the evident formula for the continuous gradient of the misfit function is obtained. The identification problem for the diffusive logistic mathematical model which can be applied to social sciences (online social networks), economy (spatial Solow model) and epidemiology (coronavirus COVID-19, HIV, etc.) is considered. The numerical results for information propagation in online social network are presented and discussed.

AB - The problem of identification of coefficients and initial conditions for a boundary value problem for parabolic equations that reduces to a minimization problem of a misfit function is investigated. Firstly, the tensor train decomposition approach is presented as a global convergence algorithm. The idea of the proposed method is to extract the tensor structure of the optimized functional and use it for multidimensional optimization problems. Secondly, for the refinement of the unknown parameters, three local optimization approaches are implemented and compared: Nelder-Mead simplex method, gradient method of minimum errors, adaptive gradient method. For gradient methods, the evident formula for the continuous gradient of the misfit function is obtained. The identification problem for the diffusive logistic mathematical model which can be applied to social sciences (online social networks), economy (spatial Solow model) and epidemiology (coronavirus COVID-19, HIV, etc.) is considered. The numerical results for information propagation in online social network are presented and discussed.

KW - gradient method

KW - Inverse problem

KW - optimization

KW - parameter estimation

KW - partial differential equations

KW - regularization

KW - social network

KW - tensor train

KW - tensor train decomposition

UR - http://www.scopus.com/inward/record.url?scp=85092389472&partnerID=8YFLogxK

U2 - 10.1515/jiip-2020-0083

DO - 10.1515/jiip-2020-0083

M3 - Article

AN - SCOPUS:85092389472

VL - 28

SP - 899

EP - 913

JO - Journal of Inverse and Ill-Posed Problems

JF - Journal of Inverse and Ill-Posed Problems

SN - 0928-0219

IS - 6

ER -

ID: 25611212