EF45 – Multi-Agent Social Systems

Project

EF45-1

Informing Opinion Dynamics Models with Online Social Network Data

Project Heads

Nataša Djurdjevac Conrad, Ana Djurdjevac, Christof Schütte, Carsten Hartmann, Philipp Lorenz-Spreen

Close Collaborators

Camille Roth, Sebastian Pokutta

Project Members

Sebastian Zimper

Project Duration

01.04.2023 – 31.03.2026

Located at

ZIB

Description

A wide range of fundamental models for the evolution of opinions are formulated as agent-based models (ABMs). While these models provide a detailed description of individual interactions, they become increasingly difficult to analyse and simulate as the number of agents grows. In this project, we addressed two complementary challenges: (a) deriving reduced continuum models for large agent populations and (b) analysing optimal control problems in which only a small number of lead agents can influence the system. We developed low-dimensional continuum descriptions that accurately reproduce the collective behaviour of the underlying ABMs while substantially reducing computational complexity. These include both deterministic and stochastic partial differential equation models, with the stochastic models capturing long-term clustering phenomena. We also established rigorous connections between optimal control problems for finite-agent systems and their continuum limits, and developed an efficient numerical method for computing such controls.

Selected Pictures

Snapshot from one realization of our agent-based model and stochastic PDE on a reduced state space. The positions of the agents are shown on a two-dimensional social space and they are coloured according to their opinions.

Project Webpages

ZIB Webpage

Selected Publications

  1. N. Djurdjevac Conrad, J. Köppl and  A. Djurdjevac. Feedback Loops in Opinion Dynamics of Agent-Based Models with Multiplicative Noise. Entropy 24(10), 2022.
  2. L. Helfmann, N. Djurdjevac Conrad, P. Lorenz-Spreen and C. Schütte. Modelling opinion dynamics under the impact of influencer and media strategies. Scientific Reports 13(19375), 2023.
  3. L. Helfmann, N. Djurdjevac Conrad, P. Lorenz-Spreen and C. Schütte. Implementation of the model for the paper “Modelling opinion dynamics under the impact of influencer and media strategies”. Zenodo, 2024.
  4. N. Djurdjevac Conrad, N. Quang Vu and S. Nagel. Co-evolving networks for opinion and social dynamics in agent-based models. Chaos 34, 093116, (2024).
  5. S. Zimper, F. Cornalba, N. Djurdjevac Conrad and A. Djurdjevac. On reduced intertial PDE models for Cucker-Smale flocking dynamics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 481(2310), 2025.
  6. S. Zimper, A. Djurdjevac, C. Hartmann, C. Schütte and N. Djurdjevac Conrad. Mean-field optimal control with stochastic leaders. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. Accepted for publication, 2026.
  7. S. Zimper, N. Djurdjevac Conrad, F. Cornalba and A. Djurdjevac. Clustering in co-evolving opinion dynamics: reduced SPDE models. Under review, 2026. (arxiv)
  8. S. Zimper, F. Cornalba, N. Djurdjevac Conrad and A. Djurdjevac. Code implementation for the paper “On reduced intertial PDE models for Cucker-Smale flocking dynamics”. Zenodo, 2025.
  9. S. Zimper, A. Djurdjevac, C. Hartmann, C. Schütte and N. Djurdjevac Conrad. Code implementation for the paper “Mean-field optimal control with stochastic leaders”. Zenodo, 2026.

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