Data-driven model reduction of agent-based systems using the Koopman generator
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.
Cite
@article{arxiv.2012.07718,
title = {Data-driven model reduction of agent-based systems using the Koopman generator},
author = {Jan-Hendrik Niemann and Stefan Klus and Christof Schütte},
journal= {arXiv preprint arXiv:2012.07718},
year = {2022}
}