Data-driven model reduction of agent-based systems using the Koopman generator.

The dynamical behavior of social systems can be described by agent-based models. Although single agents follow easily explainable rules, complex time-evolving patterns emerge due to their interaction. The simulation and analysis of such agent-based models, however, is often prohibitively time-consum...

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Autores principales:	Jan-Hendrik Niemann, Stefan Klus, Christof Schütte
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/56efccd71c4e41818ecbb788e28b63fe
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id	oai:doaj.org-article:56efccd71c4e41818ecbb788e28b63fe
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spelling	oai:doaj.org-article:56efccd71c4e41818ecbb788e28b63fe2021-12-02T20:05:34ZData-driven model reduction of agent-based systems using the Koopman generator.1932-620310.1371/journal.pone.0250970https://doaj.org/article/56efccd71c4e41818ecbb788e28b63fe2021-01-01T00:00:00Zhttps://doi.org/10.1371/journal.pone.0250970https://doaj.org/toc/1932-6203The dynamical behavior of social systems can be described by agent-based models. Although single agents follow easily explainable rules, complex time-evolving patterns emerge due to their interaction. The simulation and analysis of such agent-based models, however, is often prohibitively time-consuming if the number of agents is large. In this paper, we show how Koopman operator theory can be used to derive reduced models of agent-based systems using only simulation data. Our goal is to learn coarse-grained models and to represent the reduced dynamics by ordinary or stochastic differential equations. The new variables are, for instance, aggregated state variables of the agent-based model, modeling the collective behavior of larger groups or the entire population. Using benchmark problems with known coarse-grained models, we demonstrate that the obtained reduced systems are in good agreement with the analytical results, provided that the numbers of agents is sufficiently large.Jan-Hendrik NiemannStefan KlusChristof SchüttePublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 16, Iss 5, p e0250970 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Jan-Hendrik Niemann Stefan Klus Christof Schütte Data-driven model reduction of agent-based systems using the Koopman generator.
description	The dynamical behavior of social systems can be described by agent-based models. Although single agents follow easily explainable rules, complex time-evolving patterns emerge due to their interaction. The simulation and analysis of such agent-based models, however, is often prohibitively time-consuming if the number of agents is large. In this paper, we show how Koopman operator theory can be used to derive reduced models of agent-based systems using only simulation data. Our goal is to learn coarse-grained models and to represent the reduced dynamics by ordinary or stochastic differential equations. The new variables are, for instance, aggregated state variables of the agent-based model, modeling the collective behavior of larger groups or the entire population. Using benchmark problems with known coarse-grained models, we demonstrate that the obtained reduced systems are in good agreement with the analytical results, provided that the numbers of agents is sufficiently large.
format	article
author	Jan-Hendrik Niemann Stefan Klus Christof Schütte
author_facet	Jan-Hendrik Niemann Stefan Klus Christof Schütte
author_sort	Jan-Hendrik Niemann
title	Data-driven model reduction of agent-based systems using the Koopman generator.
title_short	Data-driven model reduction of agent-based systems using the Koopman generator.
title_full	Data-driven model reduction of agent-based systems using the Koopman generator.
title_fullStr	Data-driven model reduction of agent-based systems using the Koopman generator.
title_full_unstemmed	Data-driven model reduction of agent-based systems using the Koopman generator.
title_sort	data-driven model reduction of agent-based systems using the koopman generator.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/56efccd71c4e41818ecbb788e28b63fe
work_keys_str_mv	AT janhendrikniemann datadrivenmodelreductionofagentbasedsystemsusingthekoopmangenerator AT stefanklus datadrivenmodelreductionofagentbasedsystemsusingthekoopmangenerator AT christofschutte datadrivenmodelreductionofagentbasedsystemsusingthekoopmangenerator
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Data-driven model reduction of agent-based systems using the Koopman generator.

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