Datadriven model reduction of agentbased systems using the Koopman generator
Abstract
The dynamical behavior of social systems can be described by agentbased models. Although single agents follow easily explainable rules, complex timeevolving patterns emerge due to their interaction. The simulation and analysis of such agentbased models, however, is often prohibitively timeconsuming if the number of agents is large. In this paper, we show how Koopman operator theory can be used to derive reduced models of agentbased systems using only simulation data. Our goal is to learn coarsegrained models and to represent the reduced dynamics by ordinary or stochastic differential equations. The new variables are, for instance, aggregated state variables of the agentbased model, modeling the collective behavior of larger groups or the entire population. Using benchmark problems with known coarsegrained 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.
 Publication:

PLoS ONE
 Pub Date:
 May 2021
 DOI:
 10.1371/journal.pone.0250970
 arXiv:
 arXiv:2012.07718
 Bibcode:
 2021PLoSO..1650970N
 Keywords:

 Mathematics  Dynamical Systems;
 Statistics  Machine Learning
 EPrint:
 doi:10.1371/journal.pone.0250970