  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.
