Collective variables for spreading processes on complex networks

• Applicants: Professor Dr. Péter Koltai; Dr. Stefanie Winkelmann
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 546032594

The collective dynamics arising from the interaction of many interconnected components often lead to high-impact emergent phenomena that cannot be understood by examining individual entities in isolation. However, modeling the evolution of many interacting units poses significant challenges in terms of model synthesis, simulation, and analysis. While modeling all individual components aims to capture effects that are elusive to less detailed models, one is simultaneously interested in reduced-order models that retain the central phenomena of the full model and still allow for comprehension, computational feasibility, and estimation from sparse observations. This project aims to enhance understanding of emergent collective phenomena through the reduced modeling of random spreading processes on networks, where each network node's state evolves based on its neighbors. Current model reduction paradigms often rely on analytical treatments assuming uncorrelated quantities. We propose a novel approach that combines probabilistic mathematical analysis with the computational discovery of so-called collective variables. The latter are coarse observables of the detailed system state that contain the information relevant for describing emergent behavior and enable predictions without requiring additional knowledge about the full system state. For different types of spreading processes and a range of random network topologies, we will derive theoretical foundations for the existence of collective variables, along with developing data-driven numerical techniques to detect them and infer their dynamics in more complex scenarios, that are inaccessible to current analytical methods.

• DFG Programme: Research Grants
• International Connection: Australia
• Cooperation Partner: Professor Dr. Gary Froyland