Related papers: Dimensional reduction of dynamical systems on grap…
We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining function values. The method for approximating the unknown…
This paper considers the problem of detecting topology variations in dynamical networks. We consider a network whose behavior can be represented via a linear dynamical system. The problem of interest is then that of finding conditions under…
For dynamical systems that switch between different modes of operation, parameter variation can cause periodic solutions to lose or acquire new switching events. When this causes the eigenvalues (stability multipliers) associated with the…
The large size of multiscale, distribution and transmission, power grids hinder fast system-wide estimation and real-time control and optimization of operations. This paper studies graph reduction methods of power grids that are favorable…
A powerful approach for understanding neural population dynamics is to extract low-dimensional trajectories from population recordings using dimensionality reduction methods. Current approaches for dimensionality reduction on neural data…
Many engineering, social, and biological complex systems consist of dynamical elements connected via a large-scale network. Monitoring the network's dynamics is essential for a variety of maintenance and scientific purposes. Whilst we…
By incorporating physical consistency as inductive bias, deep neural networks display increased generalization capabilities and data efficiency in learning nonlinear dynamic models. However, the complexity of these models generally…
Deep graph generative modeling has proven capable of learning the distribution of complex, multi-scale structures characterizing real-world graphs. However, one of the main limitations of existing methods is their large output space, which…
Structural and topological information play a key role in modeling flow and transport through fractured rock in the subsurface. Discrete fracture network (DFN) computational suites such as dfnWorks are designed to simulate flow and…
Network representation learning, as an approach to learn low dimensional representations of vertices, has attracted considerable research attention recently. It has been proven extremely useful in many machine learning tasks over large…
Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal…
Graph neural networks (GNNs) have emerged as a powerful tool for effectively mining and learning from graph-structured data, with applications spanning numerous domains. However, most research focuses on static graphs, neglecting the…
A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…
A network provides powerful means of representing complex relationships between entities by abstracting entities as vertices, and relationships as edges connecting vertices in a graph. Beyond the presence or absence of relationships, a…
This paper proposes a dynamic sensor scheduling method for sensor networks. In sensor network applications, we often need multiple equally-informative node subsets that are activated sequentially to make a sensor network robust against…
Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as…
Graph neural network (GNN) is a popular tool to learn the lower-dimensional representation of a graph. It facilitates the applicability of machine learning tasks on graphs by incorporating domain-specific features. There are various options…
Graphon-based control has recently been proposed and developed to solve control problems for dynamical systems on networks which are very large or growing without bound (see Gao and Caines, CDC 2017, CDC 2018). In this paper, spectral…
Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks,…
Learning low-dimensional topological representation of a network in dynamic environments is attracting much attention due to the time-evolving nature of many real-world networks. The main and common objective of Dynamic Network Embedding…