arXiv subjects

Ariane Fazeny

Publications and source records attributed to Ariane Fazeny.

4 recordsLinked to original sources

arXiv2026

p-Wasserstein distances on networks and 3D to 1D convergence

We study transport distances on metric graphs representing gas networks. Starting from the dynamic formulation of the Wasserstein distance, we review extensions to networks, with and without the possibility of storing mass on the vertices. Next, we examine the asymptotic behavior of the static Wasserstein distance on a three-dimensional network domain that converges to a metric graph. We show convergence of the distance with a proof that is based on the characterization of optimal transport plans as $c$-cyclically monotone sets. We conclude by illustrating our finding with several numerical examples.

math.AP↗

arXiv2024

Optimal transport on gas networks

This paper models gas networks as metric graphs, with isothermal Euler equations at the edges, Kirchhoff's law at interior vertices and time-(in)dependent boundary conditions at boundary vertices. For this setup, a generalized $p$-Wasserstein metric in a dynamic formulation is introduced and utilized to derive $p$-Wasserstein gradient flows, specifically focusing on the non-standard case $p = 3$.

math.AP↗

arXiv2023

Hypergraph $p$-Laplacians and Scale Spaces

This paper introduces gradient, adjoint, and $p$-Laplacian definitions for oriented hypergraphs as well as differential and averaging operators for unoriented hypergraphs. These definitions are used to define gradient flows in the form of diffusion equations with applications in modelling group dynamics and information flow in social networks as well as performing local and non-local image processing.

cs.SI↗

arXiv2023

$p$-Laplacian Operators on Hypergraphs

This thesis generalizes the differential operators on standard oriented graphs and oriented hypergraphs introduced in 10.1137/15M1022793 and arXiv:2007.00325. The extended concepts of gradients, adjoints and $p$-Laplacians for vertices and (hyper)arcs include novel parametrization possibilities, while simultaneously fulfilling expected properties of the continuum setting, which are not granted by current definitions.

math.CO↗