Neural network approach to data-driven estimation of chemotactic sensitivity in the Keller-Segel model

We consider the mathematical model of chemotaxis introduced by Patlak, Keller, and Segel. Aggregation and progression waves are present everywhere in the population dynamics of chemotactic cells. Aggregation originates from the chemotaxis of mobile cells, where cells are attracted to migrate to high...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Sunwoo Hwang, Seongwon Lee, Hyung Ju Hwang
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	differential equation approximated solution artificial neural networks patlak-keller-segel equation Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/9602e92d47e646cc9d3ee6983704e602
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:9602e92d47e646cc9d3ee6983704e602
record_format	dspace
spelling	oai:doaj.org-article:9602e92d47e646cc9d3ee6983704e6022021-11-29T00:42:47ZNeural network approach to data-driven estimation of chemotactic sensitivity in the Keller-Segel model10.3934/mbe.20214211551-0018https://doaj.org/article/9602e92d47e646cc9d3ee6983704e6022021-09-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021421?viewType=HTMLhttps://doaj.org/toc/1551-0018We consider the mathematical model of chemotaxis introduced by Patlak, Keller, and Segel. Aggregation and progression waves are present everywhere in the population dynamics of chemotactic cells. Aggregation originates from the chemotaxis of mobile cells, where cells are attracted to migrate to higher concentrations of the chemical signal region produced by themselves. The neural net can be used to find the approximate solution of the PDE. We proved that the error, the difference between the actual value and the predicted value, is bound to a constant multiple of the loss we are learning. Also, the Neural Net approximation can be easily applied to the inverse problem. It was confirmed that even when the coefficient of the PDE equation was unknown, prediction with high accuracy was achieved.Sunwoo HwangSeongwon LeeHyung Ju HwangAIMS Pressarticledifferential equationapproximated solutionartificial neural networkspatlak-keller-segel equationBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 6, Pp 8524-8534 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	differential equation approximated solution artificial neural networks patlak-keller-segel equation Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	differential equation approximated solution artificial neural networks patlak-keller-segel equation Biotechnology TP248.13-248.65 Mathematics QA1-939 Sunwoo Hwang Seongwon Lee Hyung Ju Hwang Neural network approach to data-driven estimation of chemotactic sensitivity in the Keller-Segel model
description	We consider the mathematical model of chemotaxis introduced by Patlak, Keller, and Segel. Aggregation and progression waves are present everywhere in the population dynamics of chemotactic cells. Aggregation originates from the chemotaxis of mobile cells, where cells are attracted to migrate to higher concentrations of the chemical signal region produced by themselves. The neural net can be used to find the approximate solution of the PDE. We proved that the error, the difference between the actual value and the predicted value, is bound to a constant multiple of the loss we are learning. Also, the Neural Net approximation can be easily applied to the inverse problem. It was confirmed that even when the coefficient of the PDE equation was unknown, prediction with high accuracy was achieved.
format	article
author	Sunwoo Hwang Seongwon Lee Hyung Ju Hwang
author_facet	Sunwoo Hwang Seongwon Lee Hyung Ju Hwang
author_sort	Sunwoo Hwang
title	Neural network approach to data-driven estimation of chemotactic sensitivity in the Keller-Segel model
title_short	Neural network approach to data-driven estimation of chemotactic sensitivity in the Keller-Segel model
title_full	Neural network approach to data-driven estimation of chemotactic sensitivity in the Keller-Segel model
title_fullStr	Neural network approach to data-driven estimation of chemotactic sensitivity in the Keller-Segel model
title_full_unstemmed	Neural network approach to data-driven estimation of chemotactic sensitivity in the Keller-Segel model
title_sort	neural network approach to data-driven estimation of chemotactic sensitivity in the keller-segel model
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/9602e92d47e646cc9d3ee6983704e602
work_keys_str_mv	AT sunwoohwang neuralnetworkapproachtodatadrivenestimationofchemotacticsensitivityinthekellersegelmodel AT seongwonlee neuralnetworkapproachtodatadrivenestimationofchemotacticsensitivityinthekellersegelmodel AT hyungjuhwang neuralnetworkapproachtodatadrivenestimationofchemotacticsensitivityinthekellersegelmodel
_version_	1718407784724168704

Neural network approach to data-driven estimation of chemotactic sensitivity in the Keller-Segel model

Ejemplares similares