Speaker
Description
Particle-based models with pairwise interactions provide a natural framework to describe clustering phenomena in biological systems, but their simulation and analysis become computationally demanding at large scales. In this talk, I will present two complementary approaches for efficient coarse-grained modeling of particle clustering dynamics. First, I will show that stochastic partial differential equations (SPDEs) can accurately reproduce spatiotemporal clustering behavior, including cluster formation and merging, beyond the reach of deterministic mean-field models~\cite{wehlitz2025approximating}. Second, I will introduce a data-driven reduction of transfer operators, yielding low-dimensional Markov models that capture metastable cluster configurations and transition pathways~\cite{wehlitz2026data}. Together, these approaches provide interpretable and computationally efficient descriptions of clustering dynamics, enabling the analysis of large systems and long time scales.
Bibliography
@article{wehlitz2025approximating,
title={Approximating particle-based clustering dynamics by stochastic {PDEs}},
author={Wehlitz, Nathalie and Sadeghi, Mohsen and Montefusco, Alberto and Sch{\"u}tte, Christof and Pavliotis, Grigorios A and Winkelmann, Stefanie},
journal={SIAM Journal on Applied Dynamical Systems},
volume={24},
number={2},
pages={1231--1250},
year={2025},
publisher={SIAM}
}
@article{wehlitz2026data,
author = {Wehlitz, Nathalie and Pavliotis, Grigorios A and Sch{\"u}tte, Christof and Winkelmann, Stefanie},
title = {Data-driven Reduction of Transfer Operators for Particle Clustering Dynamics},
journal = {Communications in Applied Mathematics and Computational Science},
year = {2026},
note = {Accepted for publication. Available at arXiv:2601.02932}
}
