Memory-Based Reduced Modelling and Data-Based Estimation of Opinion Spreading

Wulkow, Niklas; Koltai, Péter; Schütte, Christof

doi:10.1007/s00332-020-09673-2

Cited by 3 publications

(2 citation statements)

References 72 publications

(86 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, it is shown that the learning rate is then independent of the dimension, making their approach suitable for large-scale systems. The data-driven approach described in [25] utilizes memory terms to improve the accuracy of the coarse-grained model.…”

Section: Introductionmentioning

confidence: 99%

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

2021

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…For a time-discrete ABM with a clustered interaction network it has recently been shown that the state of the system for future time steps depends not only on the present time step, but also on the past. A data-driven method involving memory terms is proposed to mitigate this issue [48].…”

Section: Introductionmentioning

confidence: 99%

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

Niemann,

Klus,

Schütte

2020

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract