Publication Date:
2022-07-15
Description:
Modeling social systems and studying their dynamical behavior plays an important role in many fields of research. Agent-based modeling provides a high degree of detail into artificial societies by describing the model from the perspective of the agents. The interactions of agents, often characterized by simple rules, lead to complex, time-evolving patterns. Their understanding is of great importance, e.g., for predicting and influencing epidemics. Analysis and simulation, however, often becomes prohibitively time-consuming when the number of agents or the time scale of interest is large. Therefore, this thesis is devoted to learn significantly reduced models of large-scale agent-based systems from simulation data. We show how data-driven methods based on transfer operators can be used to find reduced models represented by ordinary or stochastic differential equations that describe the dynamical behavior of larger groups or entire populations and thus enable the analysis and prediction of agent-based systems. To this end, we first present an extension of EDMD (extended dynamic mode decomposition) called gEDMD to approximate the Koopman generator from data. This method can be used to compute eigenfunctions, eigenvalues, and modes of the generator, as well as for system identification and model reduction of both deterministic and non-deterministic dynamical systems. Secondly, we analyze the long-term behavior of certain agent-based models and their pathwise approximations by stochastic differential equations for large numbers of agents using transfer operators. We show that, under certain conditions, the transfer operator approach connects the pathwise approximations on finite time scales with methods for describing the behavior on possibly exponentially long time scales. As a consequence, we can use the finite-time, pathwise approximations to characterize metastable behavior on long time scales using transfer operators. This can significantly reduce the computational cost. The third part addresses the data-driven model reduction since in many cases no analytical limit models are known or existent. We show how the Koopman operator theory can be used to infer the governing equations of agent-based systems directly from simulation data. Using benchmark problems, we demonstrate that for sufficiently large population sizes the data-driven models agree well with analytical limit equations and, moreover, that the reduced models allow predictions even in cases far from the limit or when no limit equations are known. Lastly, we demonstrate the potential of the presented approach. We present an ansatz for the multi-objective optimization of agent-based systems with the help of data-driven surrogate models based on the Koopman generator. In particular, when limit models are unknown or non-existent, this approach makes multi-objective optimization problems solvable that would otherwise be computationally infeasible due to very expensive objective functions.
Language:
English
Type:
doctoralthesis
,
doc-type:doctoralThesis
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