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.

Original languageEnglish
Pages (from-to)899-913
Number of pages15
JournalJournal of Inverse and Ill-Posed Problems
Volume28
Issue number6
Early online date4 Sep 2020
DOIs
Publication statusPublished - 1 Dec 2020

Keywords

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

Fingerprint Dive into the research topics of 'Global and local optimization in identification of parabolic systems'. Together they form a unique fingerprint.

Cite this