Data-driven model reduction of agent-based systems using the Koopman generator
- 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.
Author: | Jan-Hendrik NiemannORCiD, Stefan Klus, Christof Schütte |
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Document Type: | Article |
Parent Title (English): | PLOS ONE |
Volume: | 16 |
Issue: | 5 |
Date of first Publication: | 2021/05/13 |
ArXiv Id: | http://arxiv.org/abs/2012.07718 |
DOI: | https://doi.org/10.1371/journal.pone.0250970 |