Adaptive Refinement in Advection–Diffusion Problems by Anomaly Detection: A Numerical Study

We consider advection–diffusion–reaction problems, where the advective or the reactive term is dominating with respect to the diffusive term. The solutions of these problems are characterized by the so-called layers, which represent localized regions where the gradients of the solutions are rather l...

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Autores principales:	Antonella Falini, Maria Lucia Sampoli
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	advection–diffusion problems adaptive refinement a posteriori error estimates marking strategy anomaly detection Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/4c88a3a6be624b0fa90acc23bb3c1bd2
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spelling	oai:doaj.org-article:4c88a3a6be624b0fa90acc23bb3c1bd22021-11-25T16:13:15ZAdaptive Refinement in Advection–Diffusion Problems by Anomaly Detection: A Numerical Study10.3390/a141103281999-4893https://doaj.org/article/4c88a3a6be624b0fa90acc23bb3c1bd22021-11-01T00:00:00Zhttps://www.mdpi.com/1999-4893/14/11/328https://doaj.org/toc/1999-4893We consider advection–diffusion–reaction problems, where the advective or the reactive term is dominating with respect to the diffusive term. The solutions of these problems are characterized by the so-called layers, which represent localized regions where the gradients of the solutions are rather large or are subjected to abrupt changes. In order to improve the accuracy of the computed solution, it is fundamental to locally increase the number of degrees of freedom by limiting the computational costs. Thus, adaptive refinement, by a posteriori error estimators, is employed. The error estimators are then processed by an anomaly detection algorithm in order to identify those regions of the computational domain that should be marked and, hence, refined. The anomaly detection task is performed in an unsupervised fashion and the proposed strategy is tested on typical benchmarks. The present work shows a numerical study that highlights promising results obtained by bridging together standard techniques, i.e., the error estimators, and approaches typical of machine learning and artificial intelligence, such as the anomaly detection task.Antonella FaliniMaria Lucia SampoliMDPI AGarticleadvection–diffusion problemsadaptive refinementa posteriori error estimatesmarking strategyanomaly detectionIndustrial engineering. Management engineeringT55.4-60.8Electronic computers. Computer scienceQA75.5-76.95ENAlgorithms, Vol 14, Iss 328, p 328 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	advection–diffusion problems adaptive refinement a posteriori error estimates marking strategy anomaly detection Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
spellingShingle	advection–diffusion problems adaptive refinement a posteriori error estimates marking strategy anomaly detection Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95 Antonella Falini Maria Lucia Sampoli Adaptive Refinement in Advection–Diffusion Problems by Anomaly Detection: A Numerical Study
description	We consider advection–diffusion–reaction problems, where the advective or the reactive term is dominating with respect to the diffusive term. The solutions of these problems are characterized by the so-called layers, which represent localized regions where the gradients of the solutions are rather large or are subjected to abrupt changes. In order to improve the accuracy of the computed solution, it is fundamental to locally increase the number of degrees of freedom by limiting the computational costs. Thus, adaptive refinement, by a posteriori error estimators, is employed. The error estimators are then processed by an anomaly detection algorithm in order to identify those regions of the computational domain that should be marked and, hence, refined. The anomaly detection task is performed in an unsupervised fashion and the proposed strategy is tested on typical benchmarks. The present work shows a numerical study that highlights promising results obtained by bridging together standard techniques, i.e., the error estimators, and approaches typical of machine learning and artificial intelligence, such as the anomaly detection task.
format	article
author	Antonella Falini Maria Lucia Sampoli
author_facet	Antonella Falini Maria Lucia Sampoli
author_sort	Antonella Falini
title	Adaptive Refinement in Advection–Diffusion Problems by Anomaly Detection: A Numerical Study
title_short	Adaptive Refinement in Advection–Diffusion Problems by Anomaly Detection: A Numerical Study
title_full	Adaptive Refinement in Advection–Diffusion Problems by Anomaly Detection: A Numerical Study
title_fullStr	Adaptive Refinement in Advection–Diffusion Problems by Anomaly Detection: A Numerical Study
title_full_unstemmed	Adaptive Refinement in Advection–Diffusion Problems by Anomaly Detection: A Numerical Study
title_sort	adaptive refinement in advection–diffusion problems by anomaly detection: a numerical study
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/4c88a3a6be624b0fa90acc23bb3c1bd2
work_keys_str_mv	AT antonellafalini adaptiverefinementinadvectiondiffusionproblemsbyanomalydetectionanumericalstudy AT marialuciasampoli adaptiverefinementinadvectiondiffusionproblemsbyanomalydetectionanumericalstudy
_version_	1718413254552715264

Adaptive Refinement in Advection–Diffusion Problems by Anomaly Detection: A Numerical Study

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