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The limitations of centralized optimization methods for power systems operation have led to the distributed computing paradigm, particularly in power distribution systems. The existing techniques reported in recent literature for solving…
In the present paper a detailed mathematical model is derived for district heating networks. After semidiscretization of the convective heat equation and introducing coupling conditions at the nodes of the network one gets a…
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 goal of this paper is to investigate distributed temporal difference (TD) learning for a networked multi-agent Markov decision process. The proposed approach is based on distributed optimization algorithms, which can be interpreted as…
The present paper is an attempt to demonstrate how the energy minimization principle may be considered as a governing rule for the physical equilibrium that determines the flow fields in tubes and networks. We previously investigated this…
In analysis and control of large-scale nonlinear dynamical systems, a distributed approach is often an attractive option due to its computational tractability and usually low communication requirements. Success of the distributed control…
Energy decomposition analysis (EDA) based on absolutely localized molecular orbitals provides detailed insights into intermolecular bonding by decomposing the total molecular binding energy into physically meaningful components. Here, we…
The $\mathcal{H}_2$-optimal Model Order Reduction (MOR) is one of the most significant frameworks for reduction methodologies for linear dynamical systems. In this context, the Iterative Rational Krylov Algorithm (\IRKA) is a well…
In this paper a unifying energy-based approach is provided to the modeling and stability analysis of power systems coupled with market dynamics. We consider a standard model of the power network with a third-order model for the synchronous…
In this paper, Hamiltonian and energy preserving reduced-order models are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form with the state-dependent Poisson matrix. The high fidelity…
The article proposes a computer program for calculating economic crises according to the generalized mathematical model of S.V. Dubovsky. This model is represented by a system of ordinary nonlinear differential equations with fractional…
Optimal operation of distribution grid resources relies on accurate estimation of its state and topology. Practical estimation of such quantities is complicated by the limited presence of real-time meters. This paper discusses a theoretical…
We study spatial networks that are designed to distribute or collect a commodity, such as gas pipelines or train tracks. We focus on the cost of a network, as represented by the total length of all its edges, and its efficiency in terms of…
Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such…
In this paper, we present a distributed algorithm for solving convex, constraint-coupled, optimization problems over peer-to-peer networks. We consider a network of processors that aim to cooperatively minimize the sum of local cost…
Natural gas consumption by users of pipeline networks is subject to increasing uncertainty that originates from the intermittent nature of electric power loads serviced by gas-fired generators. To enable computationally efficient…
The computation of electrical flows is a crucial primitive for many recently proposed optimization algorithms on weighted networks. While typically implemented as a centralized subroutine, the ability to perform this task in a fully…
This chapter describes techniques for the numerical resolution of optimal transport problems. We will consider several discretizations of these problems, and we will put a strong focus on the mathematical analysis of the algorithms to solve…
Power distribution in remote communities often depends on off-grid microgrids. In order to address the reliability challenges for these microgrids, we develop a mathematical model for topology design, capacity planning, and operation of…
Interpolation-based methods are well-established and effective approaches for the efficient generation of accurate reduced-order surrogate models. Common challenges for such methods are the automatic selection of good or even optimal…