相关论文: Optimal transport on gas networks

We propose a model of optimal parallel transport between vector fields on a connection graph, which consists of a weighted graph along with a map from its edges to an orthogonal group. Inspired by the well-known equivalence of 1-Wasserstein…

In this paper, we are concerned with the quantification of uncertainties that arise from intra-day oscillations in the demand for natural gas transported through large-scale networks. The short-term transient dynamics of the gas flow is…

We revisit the classic problem of determining optimal routes in a graph for transporting two given distributions defined on its nodes, originally studied by Wardrop and Beckmann in the 1950s. The global congestion profile at any given time…

Many physical systems -- such as optical waveguide lattices and dense neuronal or vascular networks -- can be modeled by metric graphs, where slender "wires" (edges) support wave or diffusion equations subject to Kirchhoff conditions at the…

This paper studies the discretization of gas transport in pipeline networks by an inexact Petrov-Galerkin method. A full convergence analysis is presented for single pipes under the assumption of a linear friction law and the possible…

Within animals, oxygen exchange occurs within networks containing potentially billions of microvessels that are distributed throughout the animal's body. Innovative imaging methods now allow for mapping of the architecture and blood flows…

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…

In this manuscript we review new ideas and first results on application of the Graphical Models approach, originated from Statistical Physics, Information Theory, Computer Science and Machine Learning, to optimization problems of network…

Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…

Networks are essential models in many applications such as information technology, chemistry, power systems, transportation, neuroscience, and social sciences. In light of such broad applicability, a general theory of dynamical systems on…

We study a dynamic optimal transport problem on a network. Despite the cost for transport along the edges, an additional cost, scaled with a parameter $\kappa$, has to be paid for interchanging mass between edges and vertices. We show…

Hyperbolic systems on networks often can be written as systems of first order equations on an interval, coupled by transmission conditions at the endpoints, also called port-Hamiltonians. However, general results for the latter have been…

We introduce new coupling conditions for isentropic flow on networks based on an artificial density at the junction. The new coupling conditions can be derived from a kinetic model by imposing a condition on energy dissipation. Existence…

We formulate a nonlinear optimal control problem for intra-day operation of a natural gas pipeline network that includes storage reservoirs. The dynamics of compressible gas flow through pipes, compressors, reservoirs, and wells are…

In this article, we are interested in semilinear, possibly degenerate elliptic equations posed on a general network, with nonlinear Kirchhoff-type conditions for its interior vertices and Dirichlet boundary conditions for the boundary ones.…

In this paper, we prove that the time supremum of the Wasserstein distance between the time-marginals of a uniformly elliptic multidimensional diffusion with coefficients bounded together with their derivatives up to the order $2$ in the…

In this paper, we describe a possible generalization of the Wasserstein 2-metric, originally defined on the space of scalar probability densities, to the space of Hermitian matrices with trace one, and to the space of matrix-valued…

We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…

We define a metric---the network Gromov-Wasserstein distance---on weighted, directed networks that is sensitive to the presence of outliers. In addition to proving its theoretical properties, we supply network invariants based on optimal…

We derive conditions for monotonicity properties that characterize general flows of a commodity over a network, where the flow is described by potential and flow dynamics on the edges, as well as potential continuity and Kirchhoff-Neumann…