@inproceedings{LueckeKoltaiWinkelmannetal.2022, author = {L{\"u}cke, Marvin and Koltai, Peter and Winkelmann, Stefanie and Molkethin, Nora and Heitzig, Jobst}, title = {Discovering collective variable dynamics of agent-based models}, booktitle = {25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022}, doi = {https://doi.org/10.15495/EPub_UBT_00006809}, year = {2022}, abstract = {Analytical approximations of the macroscopic behavior of agent-based models (e.g. via mean-field theory) often introduce a significant error, especially in the transient phase. For an example model called continuous-time noisy voter model, we use two data-driven approaches to learn the evolution of collective variables instead. The first approach utilizes the SINDy method to approximate the macroscopic dynamics without prior knowledge, but has proven itself to be not particularly robust. The second approach employs an informed learning strategy which includes knowledge about the agent-based model. Both approaches exhibit a considerably smaller error than the conventional analytical approximation.}, language = {en} } @article{LueckeWinkelmannHeitzigetal.2024, author = {L{\"u}cke, Marvin and Winkelmann, Stefanie and Heitzig, Jobst and Molkenthin, Nora and Koltai, P{\´e}ter}, title = {Learning interpretable collective variables for spreading processes on networks}, volume = {109}, journal = {Physical Review E}, number = {2}, arxiv = {http://arxiv.org/abs/2307.03491}, doi = {10.1103/PhysRevE.109.L022301}, pages = {L022301}, year = {2024}, abstract = {Collective variables (CVs) are low-dimensional projections of high-dimensional system states. They are used to gain insights into complex emergent dynamical behaviors of processes on networks. The relation between CVs and network measures is not well understood and its derivation typically requires detailed knowledge of both the dynamical system and the network topology. In this Letter, we present a data-driven method for algorithmically learning and understanding CVs for binary-state spreading processes on networks of arbitrary topology. We demonstrate our method using four example networks: the stochastic block model, a ring-shaped graph, a random regular graph, and a scale-free network generated by the Albert-Barab{\´a}si model. Our results deliver evidence for the existence of low-dimensional CVs even in cases that are not yet understood theoretically.}, language = {en} } @article{HelfmannHeitzigKoltaietal.2021, author = {Helfmann, Luzie and Heitzig, Jobst and Koltai, P{\´e}ter and Kurths, J{\"u}rgen and Sch{\"u}tte, Christof}, title = {Statistical analysis of tipping pathways in agent-based models}, volume = {230}, journal = {Eur. Phys. J. Spec. Top.}, arxiv = {http://arxiv.org/abs/2103.02883}, doi = {10.1140/epjs/s11734-021-00191-0}, pages = {3249 -- 3271}, year = {2021}, abstract = {Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals on the microscopic scale can lead to emergent dynamics on the macroscopic scale, for instance a sudden shift of majority opinion or behavior. Here we are introducing a methodology for studying noise-induced tipping between relevant subsets of the agent state space representing characteristic configurations. Due to a large number of interacting individuals, agent-based models are high-dimensional, though usually a lower-dimensional structure of the emerging collective behaviour exists. We therefore apply Diffusion Maps, a non-linear dimension reduction technique, to reveal the intrinsic low-dimensional structure. We characterize the tipping behaviour by means of Transition Path Theory, which helps gaining a statistical understanding of the tipping paths such as their distribution, flux and rate. By systematically studying two agent-based models that exhibit a multitude of tipping pathways and cascading effects, we illustrate the practicability of our approach.}, language = {en} } @article{LueckeHeitzigKoltaietal.2023, author = {L{\"u}cke, Marvin and Heitzig, Jobst and Koltai, P{\´e}ter and Molkethin, Nora and Winkelmann, Stefanie}, title = {Large population limits of Markov processes on random networks}, volume = {166}, journal = {Stochastic Processes and their Applications}, arxiv = {http://arxiv.org/abs/2210.02934}, doi = {10.1016/j.spa.2023.09.007}, year = {2023}, abstract = {We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each discrete state in the system, or in certain subsystems, and general conditions for the convergence of the collective variable dynamics to a mean-field ordinary differential equation are proved. We discuss the convergence to this mean-field limit for a continuous-time noisy version of the so-called "voter model" on Erdős-R{\´e}nyi random graphs, on the stochastic block model, as well as on random regular graphs. Moreover, a heterogeneous population of agents is studied. For each of these types of interaction networks, we specify the convergence conditions in dependency on the corresponding model parameters.}, language = {en} }