Inverse modeling of diffusion-reaction processes with image-type measurement data

Alexey Penenko, Zhadyra Mukatova

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаярецензирование

Аннотация

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.

Язык оригиналаанглийский
Название основной публикации11th International Conference Bioinformatics of Genome Regulation and Structure\Systems Biology, BGRS\SB 2018 - Proceedings
ИздательInstitute of Electrical and Electronics Engineers Inc.
Страницы39-43
Число страниц5
ISBN (электронное издание)9781538668504
DOI
СостояниеОпубликовано - 26 ноя 2018
Событие11th International Conference Bioinformatics of Genome Regulation and Structure\Systems Biology, BGRS\SB 2018 - Novosibirsk, Российская Федерация
Продолжительность: 20 авг 201825 авг 2018

Конференция

Конференция11th International Conference Bioinformatics of Genome Regulation and Structure\Systems Biology, BGRS\SB 2018
СтранаРоссийская Федерация
ГородNovosibirsk
Период20.08.201825.08.2018

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    Penenko, A., & Mukatova, Z. (2018). Inverse modeling of diffusion-reaction processes with image-type measurement data. В 11th International Conference Bioinformatics of Genome Regulation and Structure\Systems Biology, BGRS\SB 2018 - Proceedings (стр. 39-43). [8544885] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CSGB.2018.8544885