TY - JOUR A1 - Niemann, Jan-Hendrik A1 - Winkelmann, Stefanie A1 - Wolf, Sarah A1 - Schütte, Christof T1 - Agent-based modeling: Population limits and large timescales JF - Chaos: An Interdisciplinary Journal of Nonlinear Science N2 - Modeling, simulation and analysis of interacting agent systems is a broad field of research, with existing approaches reaching from informal descriptions of interaction dynamics to more formal, mathematical models. In this paper, we study agent-based models (ABMs) given as continuous-time stochastic processes and their pathwise approximation by ordinary and stochastic differential equations (ODEs and SDEs, respectively) for medium to large populations. By means of an appropriately adapted transfer operator approach we study the behavior of the ABM process on long time scales. We show that, under certain conditions, the transfer operator approach allows to bridge the gap between the pathwise results for large populations on finite timescales, i.e., the SDE limit model, and approaches built to study dynamical behavior on long time scales like large deviation theory. The latter provides a rigorous analysis of rare events including the associated asymptotic rates on timescales that scale exponentially with the population size. We demonstrate 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. This approach has the potential to drastically reduce computational effort for the analysis of ABMs. Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-77309 SN - 1438-0064 VL - 31 IS - 3 ER - TY - JOUR A1 - Niemann, Jan-Hendrik A1 - Klus, Stefan A1 - Schütte, Christof T1 - Data-driven model reduction of agent-based systems using the Koopman generator JF - PLOS ONE N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1371/journal.pone.0250970 VL - 16 IS - 5 ER - TY - JOUR A1 - Carderera, Alejandro A1 - Pokutta, Sebastian A1 - Schütte, Christof A1 - Weiser, Martin T1 - An efficient first-order conditional gradient algorithm in data-driven sparse identification of nonlinear dynamics to solve sparse recovery problems under noise JF - Journal of Computational and Applied Mathematics N2 - Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the potential to transform data-rich fields where well-established dynamical models remain unknown. This work contributes to the recent trend in data-driven sparse identification of nonlinear dynamics of finding the best sparse fit to observational data in a large library of potential nonlinear models. We propose an efficient first-order Conditional Gradient algorithm for solving the underlying optimization problem. In comparison to the most prominent alternative algorithms, the new algorithm shows significantly improved performance on several essential issues like sparsity-induction, structure-preservation, noise robustness, and sample efficiency. We demonstrate these advantages on several dynamics from the field of synchronization, particle dynamics, and enzyme chemistry. Y1 - 2021 ER -