论文标题
使用Koopman Generator，数据驱动的模型减少基于代理的系统
Data-driven model reduction of agent-based systems using the Koopman generator
论文作者
论文摘要
社会系统的动态行为可以通过基于代理的模型来描述。尽管单个代理遵循易于解释的规则，但由于其相互作用而出现了复杂的随时间不断发展的模式。但是，如果代理的数量较大，则对基于代理的模型的仿真和分析通常会非常耗时。在本文中，我们展示了如何使用仅使用仿真数据来推导基于代理系统的模型的模型。我们的目标是学习粗粒模型，并通过普通或随机微分方程表示减少的动态。例如，新变量是基于代理的模型的汇总状态变量，对较大组或整个人群的集体行为进行建模。使用已知的粗粒模型的基准问题，我们证明所获得的还原系统与分析结果非常吻合，前提是代理的数量足够大。
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.
