Computational and Applied Mathematics seminar

Abstract: We propose a computational framework for analyzing the macroscopic dynamics of complex agent-based networks by integrating Topological Data Analysis (TDA) with the Equation-Free Method. The approach is demonstrated on Erdős–Rényi random networks. A TDA-based filtration, driven by the density of activated nodes, yields a coarse macroscopic observable defined via persistent Betti numbers, enabling significant dimensionality reduction while preserving essential topology. Within the Equation-Free framework, we construct a lifting procedure based on topological features and identify a data-driven evolution law for this variable. Finally, we perform numerical bifurcation and stability analyses to characterize the global behavior and qualitative transitions of the emergent dynamics. This is a joint work with Konstantinos Spiliotis, Ole Sönnerborn, and Haralampos Hatzikirou.