Learning interpretable collective variables for spreading processes on networks

Lücke, Marvin; Winkelmann, Stefanie; Heitzig, Jobst; Molkenthin, Nora; Koltai, Péter

doi:10.1103/PhysRevE.109.L022301

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Learning interpretable collective variables for spreading processes on networks

Authors

Lücke, Marvin
Potsdam Institute for Climate Impact Research;

Winkelmann, Stefanie
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Heitzig, Jobst
Potsdam Institute for Climate Impact Research;

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Molkenthin, Nora
Potsdam Institute for Climate Impact Research;

Koltai, Péter
External Organizations;

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https://doi.org/10.5281/zenodo.14161126
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Citation

Lücke, M., Winkelmann, S., Heitzig, J., Molkenthin, N., Koltai, P. (2024): Learning interpretable collective variables for spreading processes on networks. - Physical Review E, 109, 2, L022301.
https://doi.org/10.1103/PhysRevE.109.L022301

Cite as: https://publications.pik-potsdam.de/pubman/item/item_30463

Abstract

Collective variables (CVs) are low-dimensional projections of high-dimensional system states. They are used to gain insights into complex emergent dynamical behaviors of processes on networks. The relation between CVs and network measures is not well understood and its derivation typically requires detailed knowledge of both the dynamical system and the network topology. In this Letter, we present a data-driven method for algorithmically learning and understanding CVs for binary-state spreading processes on networks of arbitrary topology. We demonstrate our method using four example networks: the stochastic block model, a ring-shaped graph, a random regular graph, and a scale-free network generated by the Albert-Barabási model. Our results deliver evidence for the existence of low-dimensional CVs even in cases that are not yet understood theoretically.