Global and local optimization in identification of parabolic systems

Global and local optimization in identification of parabolic systems Full article

Journal

Journal of Inverse and Ill-Posed Problems
ISSN: 0928-0219 , E-ISSN: 1569-3945

Output data

Year: 2020, Volume: 28, Number: 6, Pages: 899-913 Pages count : 15 DOI: 10.1515/jiip-2020-0083

Tags

gradient method; Inverse problem; optimization; parameter estimation; partial differential equations; regularization; social network; tensor train; tensor train decomposition

Authors

Krivorotko O. ^1,2 , Kabanikhin S. ^1,2,3 , Zhang S. ⁴ , Kashtanova V. ²

Affiliations

1	Institute of Computational Mathematics and Mathematical Geophysics of SB RAS
2	Novosibirsk State University, Novosibirsk, Russian Federation
3	Sobolev Institute of Mathematics of SB RAS, Novosibirsk, Russian Federation
4	Tianjin University of Finance and Economics, Tianjin, China

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. © 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.

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. V.28. N6. P.899-913. DOI: 10.1515/jiip-2020-0083 WOS Scopus OpenAlex

Web of science:	WOS:000594396300010
Scopus:	2-s2.0-85092389472
OpenAlex:	W3083776558

DB	Citing
Scopus	10
OpenAlex	8
Web of science	6