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

• URL: http://arxiv.org/abs/2012.07718v1
• Date: Mon, 14 Dec 2020 17:12:54 GMT
• Title: Data-driven model reduction of agent-based systems using the Koopman generator
• Authors: Jan-Hendrik Niemann, Stefan Klus, Christof Sch\"utte
• Abstract summary: We show how Koopman operator theory can be used to derive reduced models of agent-based systems. Our goal is to learn coarse-grained models and to represent the reduced dynamics by ordinary or differential equations.
• Score: 0.3867363075280544
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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