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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.13673 |
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| _version_ | 1866908834592718848 |
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| author | Spiliotis, Konstantinos Sönnerborn, Ole Hatzikirou, Haralampos Kavallaris, Nikos I. |
| author_facet | Spiliotis, Konstantinos Sönnerborn, Ole Hatzikirou, Haralampos Kavallaris, Nikos I. |
| contents | In this work, we present a computational framework for exploring and analyzing the macroscopic dynamics of complex agent-based network models by integrating Topological Data Analysis with the Equation-Free Method. To demonstrate the effectiveness of our method, we apply it to Erdős--Rényi-type random networks. Central to our approach is a Topological Data Analysis-based filtration process driven by the density of activated network nodes (agents), from which we extract a coarse-grained macroscopic topological observable. This observable is defined via persistent Betti numbers, thus requiring significantly reduced data dimensionality while retaining essential topological features. Subsequently, within the Equation-Free Method framework, we show firstly that a \textit{lifting procedure} can be achieved using topological properties and secondly, a data-driven evolution law that governs the dynamics of this macroscopic variable. Finally, we perform a numerical bifurcation and stability analysis to investigate the global behavior and qualitative transitions of the emergent macroscopic dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13673 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Data-driven macroscopic dynamics of complex networks using Topological Data Analysis and the Equation-Free Method Spiliotis, Konstantinos Sönnerborn, Ole Hatzikirou, Haralampos Kavallaris, Nikos I. Dynamical Systems 37B25 and 37G35 and 55U05 In this work, we present a computational framework for exploring and analyzing the macroscopic dynamics of complex agent-based network models by integrating Topological Data Analysis with the Equation-Free Method. To demonstrate the effectiveness of our method, we apply it to Erdős--Rényi-type random networks. Central to our approach is a Topological Data Analysis-based filtration process driven by the density of activated network nodes (agents), from which we extract a coarse-grained macroscopic topological observable. This observable is defined via persistent Betti numbers, thus requiring significantly reduced data dimensionality while retaining essential topological features. Subsequently, within the Equation-Free Method framework, we show firstly that a \textit{lifting procedure} can be achieved using topological properties and secondly, a data-driven evolution law that governs the dynamics of this macroscopic variable. Finally, we perform a numerical bifurcation and stability analysis to investigate the global behavior and qualitative transitions of the emergent macroscopic dynamics. |
| title | Data-driven macroscopic dynamics of complex networks using Topological Data Analysis and the Equation-Free Method |
| topic | Dynamical Systems 37B25 and 37G35 and 55U05 |
| url | https://arxiv.org/abs/2602.13673 |