  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 or real-world 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.
