Project
EF4-8
Concentration Effects and Collective Variables in Agent-Based Systems
Project Heads
Jobst Heitzig, Péter Koltai, Nora Molkenthin, Stefanie Winkelmann
Project Members
Marvin Lücke
Project Duration
01.02.2021 − 31.01.2024
Located at
ZIB
Description
In this project, stochastic dynamics on networks of interacting agents and their projection onto low-dimensional collective variables were investigated. General conditions for the convergence in the large population limit to a mean-field ordinary differential equation have been proved. Moreover, data-driven methods for algorithmically learning and understanding collective variables for spreading processes on networks have been developed. The methods have been applied to famous types of networks, such as Erdős–Rényi random graphs, stochastic block models, and scale-free networks generated by the Albert–Barabási model.
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Publications
- Marvin Lücke, Stefanie Winkelmann, Jobst Heitzig, Nora Molkenthin, Péter Koltai. Learning interpretable collective variables for spreading processes on networks, Physical Review E, 109(2):L022301, 2024.
- Marvin Lücke, Jobst Heitzig, Péter Koltai, Nora Molkenthin and Stefanie Winkelmann. Large population limits of Markov processes on random networks, Stochastic Processes and their Applications, 166:104220, 2023.
- M. Lücke, P. Koltai, S. Winkelmann, N. Molkenthin, and J. Heitzig. Discovering collective variable dynamics of agent-based models. In Extended Abstracts presented at the 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022, pages 202–205. University of Bayreuth, 2022.
- Marvin Lücke and Felix Nüske. tgEDMD: Approximation of the Kolmogorov operator in tensor train format. Journal of Nonlinear Science, 32(4):44, 2022.