h1

%0 Thesis
%A Merger, Claudia
%T Interactions on structured networks
%I RWTH Aachen University
%V Dissertation
%C Aachen
%M RWTH-2024-00402
%P 1 Online-Ressource : Illustrationen
%D 2024
%Z Veröffentlicht auf dem Publikationsserver der RWTH Aachen University
%Z Dissertation, RWTH Aachen University, 2024
%X Structured systems appear ubiquitously in nature. Indubitably, the structure of a system determines its characteristic behavior. However, predicting the behavior of a system given its structure, or vice versa, is not straightforward. We here demonstrate that the mapping from structure to behavior can be tackled using a systematic fluctuation expansion, and develop a new method to infer structure given observations of the system. Often, structure can be represented as a network of nodes, where the nodes represent the agents, the elementary degrees of freedom of the system, and the connections define their interactions. One common feature of structured systems are hubs: nodes with significantly more connections than average, which are expected to be key to the observed overall system behavior. To understand the influence of hubs, we investigate to which extent the hubs of a scale-free network can drive a system of binary agents into an ordered or disordered state. We find that a typical mean-field approach to these systems introduces a nonphysical process: the signal sent by a node to its neighbors may travel back and influence the same node, leading to a self-feedback loop. The phenomenon is most prominent in the presence of hubs; their accumulated self-feedback grows with the number of connections. We show that a second-order fluctuation correction eliminates this spurious self-feedback. These insights are then translated to a model of disease spreading: We investigate the SIR model, where each agent can be in one of three states (susceptible, infected, or recovered), and transitions between these states follow a stochastic process. A typical approach in literature to predict average infection curves is to assume that all agents are statistically independent, introducing self-feedback artificially into the system, which yields inflated infection curves. We use a dynamical Plefka expansion to calculate a fluctuation correction, which eliminates the self-feedback effect, leading to more accurate predictions on the spread of disease. We then approach the reverse direction: inferring pairwise and higher-order interactions from data, these interactions constitute the structure of the underlying system. In principle, inference problems require an optimization over the space of all possible interactions, whose number increases exponentially with the system size. Nevertheless, machine learning models can infer structures efficiently from data. Typically, however, the inferred structure is hidden in the parameters of the trained mdoel. We here show how to extract the learned structure, formulated in terms of interactions up to the fourth order. This process uncovers how the model hierarchically constructs interactions via nonlinear transformations of pairwise relations. This yields a fully understandable AI-powered tool for inference. Thus, we close the loop, demonstrating how collective behavior can emerge from structure and vice versa.
%F PUB:(DE-HGF)11
%9 Dissertation / PhD Thesis
%R 10.18154/RWTH-2024-00402
%U https://publications.rwth-aachen.de/record/976873