Model-reduction techniques for PDE models with Turing type electrochemical phase formation dynamics

Next-generation battery research will heavily rely on physico-chemical models, combined with deep learning methods and high-throughput and quantitative analysis of experimental datasets, encoding spectral information in space and time. These tasks will require highly efficient computational approach...

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Autores principales:	Benedetto Bozzini, Angela Monti, Ivonne Sgura
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Model Order Reduction (MOR) POD-Galerkin Dynamic Mode Decomposition Turing patterns Reaction–diffusion PDE systems Battery modelling Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/7d8a538b64ed421fb92591f3a4eb242d
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spelling	oai:doaj.org-article:7d8a538b64ed421fb92591f3a4eb242d2021-12-04T04:36:03ZModel-reduction techniques for PDE models with Turing type electrochemical phase formation dynamics2666-496810.1016/j.apples.2021.100074https://doaj.org/article/7d8a538b64ed421fb92591f3a4eb242d2021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666496821000388https://doaj.org/toc/2666-4968Next-generation battery research will heavily rely on physico-chemical models, combined with deep learning methods and high-throughput and quantitative analysis of experimental datasets, encoding spectral information in space and time. These tasks will require highly efficient computational approaches, to yield rapidly accurate approximations of the models. This paper explores the capabilities of a representative range of model reduction techniques to face this problem in the case of a well-assessed electrochemical phase-formation model. We consider the Proper Orthogonal Decomposition (POD) with a Galerkin projection and the Dynamic Mode Decomposition (DMD) techniques to deal first of all with a semi-linear heat equation 2D in space as a test problem. As an application, we show that it is possible to save computational time by applying POD-Galerkin for different choices of the parameters without recalculating the snapshot matrix. Finally, we consider two reaction–diffusion (RD) PDE systems with Turing-type dynamics: the well-known Schnackenberg model and the DIB model for electrochemical phase formation. We show that their reduced models obtained by POD and DMD with suitable low-dimensional projections are able to approximate carefully both the Turing patterns at the steady state and the reactivity dynamics in the transient regime. Finally, for the DIB model we show that POD-Galerkin applied for different choices of parameters, by calculating once the snapshot matrices, is able to find reduced Turing patterns of different morphology.Benedetto BozziniAngela MontiIvonne SguraElsevierarticleModel Order Reduction (MOR)POD-GalerkinDynamic Mode DecompositionTuring patternsReaction–diffusion PDE systemsBattery modellingEngineering (General). Civil engineering (General)TA1-2040ENApplications in Engineering Science, Vol 8, Iss , Pp 100074- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Model Order Reduction (MOR) POD-Galerkin Dynamic Mode Decomposition Turing patterns Reaction–diffusion PDE systems Battery modelling Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	Model Order Reduction (MOR) POD-Galerkin Dynamic Mode Decomposition Turing patterns Reaction–diffusion PDE systems Battery modelling Engineering (General). Civil engineering (General) TA1-2040 Benedetto Bozzini Angela Monti Ivonne Sgura Model-reduction techniques for PDE models with Turing type electrochemical phase formation dynamics
description	Next-generation battery research will heavily rely on physico-chemical models, combined with deep learning methods and high-throughput and quantitative analysis of experimental datasets, encoding spectral information in space and time. These tasks will require highly efficient computational approaches, to yield rapidly accurate approximations of the models. This paper explores the capabilities of a representative range of model reduction techniques to face this problem in the case of a well-assessed electrochemical phase-formation model. We consider the Proper Orthogonal Decomposition (POD) with a Galerkin projection and the Dynamic Mode Decomposition (DMD) techniques to deal first of all with a semi-linear heat equation 2D in space as a test problem. As an application, we show that it is possible to save computational time by applying POD-Galerkin for different choices of the parameters without recalculating the snapshot matrix. Finally, we consider two reaction–diffusion (RD) PDE systems with Turing-type dynamics: the well-known Schnackenberg model and the DIB model for electrochemical phase formation. We show that their reduced models obtained by POD and DMD with suitable low-dimensional projections are able to approximate carefully both the Turing patterns at the steady state and the reactivity dynamics in the transient regime. Finally, for the DIB model we show that POD-Galerkin applied for different choices of parameters, by calculating once the snapshot matrices, is able to find reduced Turing patterns of different morphology.
format	article
author	Benedetto Bozzini Angela Monti Ivonne Sgura
author_facet	Benedetto Bozzini Angela Monti Ivonne Sgura
author_sort	Benedetto Bozzini
title	Model-reduction techniques for PDE models with Turing type electrochemical phase formation dynamics
title_short	Model-reduction techniques for PDE models with Turing type electrochemical phase formation dynamics
title_full	Model-reduction techniques for PDE models with Turing type electrochemical phase formation dynamics
title_fullStr	Model-reduction techniques for PDE models with Turing type electrochemical phase formation dynamics
title_full_unstemmed	Model-reduction techniques for PDE models with Turing type electrochemical phase formation dynamics
title_sort	model-reduction techniques for pde models with turing type electrochemical phase formation dynamics
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/7d8a538b64ed421fb92591f3a4eb242d
work_keys_str_mv	AT benedettobozzini modelreductiontechniquesforpdemodelswithturingtypeelectrochemicalphaseformationdynamics AT angelamonti modelreductiontechniquesforpdemodelswithturingtypeelectrochemicalphaseformationdynamics AT ivonnesgura modelreductiontechniquesforpdemodelswithturingtypeelectrochemicalphaseformationdynamics
_version_	1718372921504694272

Model-reduction techniques for PDE models with Turing type electrochemical phase formation dynamics

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