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Moment-closure approximations are an important tool in the analysis of the dynamics on both static and adaptive networks. Here, we provide a broad survey over different approximation schemes by applying each of them to the adaptive voter…
It is a critical issue to compute the shortest paths between nodes in networks. Exact algorithms for shortest paths are usually inapplicable for large scale networks due to the high computational complexity. In this paper, we propose a…
This study addresses the challenge of predicting network dynamics, such as forecasting disease spread in social networks or estimating species populations in predator-prey networks. Accurate predictions in large networks are difficult due…
Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural…
Network systems consist of subsystems and their interconnections, and provide a powerful framework for analysis, modeling and control of complex systems. However, subsystems may have high-dimensional dynamics, and the amount and nature of…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…
Dynamical networks are versatile models that can describe a variety of behaviours such as synchronisation and feedback. However, applying these models in real world contexts is difficult as prior information pertaining to the connectivity…
Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…
The study of neural computation aims to understand the function of a neural system as an information processing machine. Neural systems are undoubtedly complex, necessitating principled and automated tools to abstract away details to…
Learning the structure of a network from time series data, in particular cyclostationary data, is of significant interest in many disciplines such as power grids, biology and finance. In this article, an algorithm is presented for…
Network embeddings learn to represent nodes as low-dimensional vectors to preserve the proximity between nodes and communities of the network for network analysis. The temporal edges (e.g., relationships, contacts, and emails) in dynamic…
We consider the problem of approximating flow functions of continuous-time dynamical systems with inputs. It is well-known that continuous-time recurrent neural networks are universal approximators of this type of system. In this paper, we…
Network dynamics offers critical insights into the behavior and evolution of complex systems. Here, we focus on the topological dynamics of networks to explore a unique process for reducing the average distance: topological compression. The…
Delay-coupled networks are investigated with nonidentical delay times and the effects of such heterogeneity on the emergent dynamics of complex systems are characterized. A simple decomposition method is presented that decouples the…
Interface problems depict many fundamental physical phenomena and widely apply in the engineering. However, it is challenging to develop efficient fully decoupled numerical methods for solving degenerate interface problems in which the…
The characterization of various properties of real-world systems requires the knowledge of the underlying network of connections among the system's components. Unfortunately, in many situations the complete topology of this network is…
A foremost challenge in modern network science is the inverse problem of reconstruction (inference) of coupling equations and network topology from the measurements of the network dynamics. Of particular interest are the methods that can…