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

Authors
  • Niemann, Jan-Hendrik1, 2
  • Klus, Stefan2, 3
  • Schütte, Christof1, 2
  • 1 Modeling and Simulation of Complex Processes, Zuse Institute Berlin, Berlin, Germany. , (Germany)
  • 2 Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany. , (Germany)
  • 3 Department of Mathematics, University of Surrey, Guildford, United Kingdom. , (United Kingdom)
Type
Published Article
Journal
PLoS ONE
Publisher
Public Library of Science
Publication Date
Jan 01, 2021
Volume
16
Issue
5
Identifiers
DOI: 10.1371/journal.pone.0250970
PMID: 33984008
Source
Medline
Language
English
License
Unknown

Abstract

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.

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