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In this work, we analyze Parametrized Advection-Dominated distributed Optimal Control Problems with random inputs in a Reduced Order Model (ROM) context. All the simulations are initially based on a finite element method (FEM)…

Clustering is an important topic in algorithms, and has a number of applications in machine learning, computer vision, statistics, and several other research disciplines. Traditional objectives of graph clustering are to find clusters with…

Many differential equations with physical backgrounds are described as gradient systems, which are evolution equations driven by the gradient of some functionals, and such problems have energy conservation or dissipation properties. For…

The model reduction problem for semistable infinite-dimensional control systems is studied in this paper. In relation to these systems, we study an object we call the semistability Gramian, which serves as a generalization of the ordinary…

This work examines the problem of graph learning over a diffusion network when data can be collected from a limited portion of the network (partial observability). The main question is to establish technical guarantees of consistent…

We propose a new yet natural algorithm for learning the graph structure of general discrete graphical models (a.k.a. Markov random fields) from samples. Our algorithm finds the neighborhood of a node by sequentially adding nodes that…

Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…

Partial orders and directed acyclic graphs are commonly recurring data structures that arise naturally in numerous domains and applications and are used to represent ordered relations between entities in the domains. Examples are task…

Graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most graph clustering algorithms is to find a vertex set of low…

Local graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most (local) graph clustering algorithms is to find a…

Network embedding techniques inspired by word2vec represent an effective unsupervised relational learning model. Commonly, by means of a Skip-Gram procedure, these techniques learn low dimensional vector representations of the nodes in a…

This paper introduces the concept of abstracted model reduction: a framework to improve the tractability of structure-preserving methods for the complexity reduction of interconnected system models. To effectively reduce high-order,…

In projection-based model order reduction, a reduced-order approximation of the original full-order system is obtained by projecting it onto a reduced subspace that contains its dominant characteristics. The problem of frequency-weighted…

Model order reduction (MOR) methods that are designed to preserve structural features of a given full order model (FOM) often suffer from a lower accuracy when compared to their non-structure-preserving counterparts. In this paper, we…

This work concerns control-oriented and structure-preserving learning of low-dimensional approximations of high-dimensional physical systems, with a focus on mechanical systems. We investigate the integration of neural autoencoders in model…

This paper introduces a chordal decomposition approach for scalable analysis of linear networked systems, including stability, $\mathcal{H}_2$ and $\mathcal{H}_{\infty}$ performance. Our main strategy is to exploit any sparsity within these…

For many important network types (e.g., sensor networks in complex harsh environments and social networks) physical coordinate systems (e.g., Cartesian), and physical distances (e.g., Euclidean), are either difficult to discern or…

In this paper, we revisit a well-known distributed projected subgradient algorithm which aims to minimize a sum of cost functions with a common set constraint. In contrast to most of existing results, weight matrices of the time-varying…

This paper studies the problem of reconstructing a two-dimensional scalar field using a swarm of networked robots with local communication capabilities. We consider the communication network of the robots to form either a chain or a grid…

We derive a modular fluid-flow network congestion control model based on a law of fundamental nature in networks: the conservation of information. Network elements such as queues, users, and transmission channels and network performance…