Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
Inverse modeling of diffusion-reaction processes with image-type measurement data. / Penenko, Alexey; Mukatova, Zhadyra.
11th International Conference Bioinformatics of Genome Regulation and Structure\Systems Biology, BGRS\SB 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2018. стр. 39-43 8544885.Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
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TY - GEN
T1 - Inverse modeling of diffusion-reaction processes with image-type measurement data
AU - Penenko, Alexey
AU - Mukatova, Zhadyra
N1 - Publisher Copyright: © 2018 IEEE.
PY - 2018/11/26
Y1 - 2018/11/26
N2 - The inverse source problem for 1D diffusion-reaction model is considered. The measurement data is given as the images of the concentration fields dynamics for the subset of the interacting species. These inverse problems arise in the study of the growing tissues (morphogenes theory), in the development of the tissue engineering technologies and in the other fields of modern mathematical biology. The sensitivity operator, composed of the ensemble of the independent adjoint problem solutions allow to transform the inverse problem to the family of nonlinear ill-posed integral equations. Each member of the family correspond to the image to structure operator that extracts certain features of the image. An equation from the family is solved with the Newton-Kantorovich-type algorithm combining truncated SVD and iterative regularization. Due to the design with the adjoint problems ensemble, the algorithm can be efficiently parallelized. The algorithm's convergence and stability are illustrated numerically in Brusselator model case.
AB - The inverse source problem for 1D diffusion-reaction model is considered. The measurement data is given as the images of the concentration fields dynamics for the subset of the interacting species. These inverse problems arise in the study of the growing tissues (morphogenes theory), in the development of the tissue engineering technologies and in the other fields of modern mathematical biology. The sensitivity operator, composed of the ensemble of the independent adjoint problem solutions allow to transform the inverse problem to the family of nonlinear ill-posed integral equations. Each member of the family correspond to the image to structure operator that extracts certain features of the image. An equation from the family is solved with the Newton-Kantorovich-type algorithm combining truncated SVD and iterative regularization. Due to the design with the adjoint problems ensemble, the algorithm can be efficiently parallelized. The algorithm's convergence and stability are illustrated numerically in Brusselator model case.
KW - adjoint problems ensemble
KW - diffusion-reaction
KW - image data
KW - inverse problem
KW - iterative regularization
KW - Newton-Kantorovich method
KW - sensitivity operator
KW - truncated SVD
UR - http://www.scopus.com/inward/record.url?scp=85059743521&partnerID=8YFLogxK
U2 - 10.1109/CSGB.2018.8544885
DO - 10.1109/CSGB.2018.8544885
M3 - Conference contribution
AN - SCOPUS:85059743521
SP - 39
EP - 43
BT - 11th International Conference Bioinformatics of Genome Regulation and Structure\Systems Biology, BGRS\SB 2018 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 11th International Conference Bioinformatics of Genome Regulation and Structure\Systems Biology, BGRS\SB 2018
Y2 - 20 August 2018 through 25 August 2018
ER -
ID: 18119050