Data-driven model reduction of agent-based systems using the Koopman generator
This work provides a method for researchers and practitioners to efficiently simulate and analyze large-scale agent-based social systems, which are often prohibitively time-consuming.
This paper tackles the problem of computationally expensive agent-based models by using Koopman operator theory to derive reduced models from simulation data. The resulting coarse-grained models, represented by ordinary or stochastic differential equations, show good agreement with analytical results for benchmark problems when the number of agents is sufficiently large.
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.