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

@article{Niemann2021DatadrivenMR,
  title={Data-driven model reduction of agent-based systems using the Koopman generator},
  author={Jan-Hendrik Niemann and Stefan Klus and Christof Sch{\"u}tte},
  journal={PLoS ONE},
  year={2021},
  volume={16}
}
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… 
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References

SHOWING 1-10 OF 64 REFERENCES
Agent-based modeling: Population limits and large timescales.
TLDR
It is demonstrated that it is possible to reveal metastable structures and timescales of rare events of the ABM process by finite-length trajectories of the SDE process for large enough populations, which has the potential to drastically reduce computational effort for the analysis of ABMs.
From interacting agents to density-based modeling with stochastic PDEs
TLDR
A reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations and Finite Element discretization in space is presented which not only ensures efficient simulation but also serves as a regularization of the SPDE.
Equation-free Model Reduction in Agent-based Computations: Coarse-grained Bifurcation and Variable-free Rare Event Analysis
We study the coarse-grained, reduced dynamics of an agent-based market model due to Omurtag and Sirovich []. We first describe the large agent number, deterministic limit of the system dynamics by
Agent-Based Model Calibration using Machine Learning Surrogates
TLDR
The algorithm introduced in this paper merges model simulation and output analysis into a surrogate meta-model, which substantially ease ABM calibration and provides a fast and accurate approximation of model behaviour, dramatically reducing computation time.
Agent based models and opinion dynamics as Markov chains
TLDR
It is found that the Markov chain approach may be an attractive alternative to mean–field approaches and that this approach provides new perspectives on the modeling of opinion exchange dynamics, and more generally of other ABM.
Model reduction for agent-based social simulation: coarse-graining a civil violence model.
TLDR
This paper demonstrates a computer-assisted approach that bridges the significant gap between the single-agent microscopic level and the macroscopic population level, where fundamental questions must be rationally answered and policies guiding the emergent dynamics devised.
Koopman Mode Analysis of agent-based models of logistics processes
TLDR
This work applies Koopman Mode Analysis to two problems, both of which exhibit a bifurcation in dynamical behavior, but feature very different dynamics: Medical Treatment Facility (MTF) logistics and ship fueling (SF) logistics.
Nonparametric inference of interaction laws in systems of agents from trajectory data
TLDR
A nonparametric estimator for learning interaction kernels from trajectory data, scalable to large datasets, statistically optimal, avoiding the curse of dimensionality, and applicable to a wide variety of systems from Physics, Biology, Ecology, and Social Sciences is introduced.
Equation-Free Multiscale Computations in Social Networks: from Agent-Based Modeling to Coarse-Grained Stability and bifurcation Analysis
TLDR
This work addresses how the Equation-Free approach can be exploited to systematically extract coarse-grained, emergent dynamical information by bridging detailed, agent-based models of social interactions on networks, with macroscopic, systems-level, continuum numerical analysis tools.
Equation-free: The computer-aided analysis of complex multiscale systems
TLDR
Over the last few years with several collaborators, a mathematically inspired, computational enabling technology is developed and validated that allows the modeler to perform macroscopic tasks acting on the microscopic models directly, and can lead to experimental protocols for the equation-free exploration of complex system dynamics.
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