Data-driven model reduction of agent-based systems using the Koopman generator

TL;DR

This paper introduces a data-driven approach using Koopman operator theory to derive simplified, coarse-grained models of large agent-based social systems, enabling efficient analysis of complex dynamics.

Contribution

It presents a novel method to learn reduced models of agent-based systems directly from simulation data using Koopman generators, bridging detailed agent rules and aggregate behavior.

Findings

Reduced models closely match analytical results for large agent populations.

The approach effectively captures collective dynamics with fewer variables.

Demonstrated success on benchmark problems with known coarse-grained models.

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.