The world is currently seeing frequent local outbreaks of epidemics, such as COVID-19 and Monkeypox. Preventing further propagation of the outbreak requires prompt implementation of control measures, and a critical step is to quickly infer patient zero. This backtracking task is challenging for two reasons. First, due to the sudden emergence of local epidemics, information recording the spreading process is limited. Second, the spreading process has strong randomness. To address these challenges, we tailor a gnn-based model to establish the inverse statistical association between the current and initial state implicitly. This model uses contact topology and the current state of the local population to determine the possibility that each individual could be patient zero. We benchmark our model on data from important epidemiological models on five real temporal networks, showing performance significantly superior to previous methods. We also demonstrate that our method is robust to missing information about contact structure or current state. Further, we find the individuals assigned higher inferred possibility by model are closer to patient zero in terms of core number and the activity sequence recording the times at which the individual had contact with other nodes.

We consider the problem of reconstructing coupled networks (e.g., biological neural networks) connecting large numbers of variables (e.g.,nerve cells), of which state evolution is governed by dissipative dynamics consisting of strong self-drive (dominants the evolution) and weak coupling-drive. The core difficulty is sparseness of coupling effect that emerges (the coupling force is significant) only momentarily and otherwise remains quiescent in time series (e.g., neuronal activity sequence). Here we learn the idea from attention mechanism to guide the classifier to make inference focusing on the critical regions of time series data where coupling effect may manifest. Specifically, attention coefficients are assigned autonomously by artificial neural networks trained to maximise the Attentive Transfer Entropy (ATEn), which is a novel generalization of the iconic transfer entropy metric. Our results show that, without any prior knowledge of dynamics, ATEn explicitly identifies areas where the strength of coupling-drive is distinctly greater than zero. This innovation substantially improves reconstruction performance for both synthetic and real directed coupling networks using data generated by neuronal models widely used in neuroscience.