p-Wasserstein distances on networks and 3D to 1D convergence
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909996500910080 |
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| author | Burger, Martin Fazeny, Ariane Mordant, Gilles Pietschmann, Jan-Frederik |
| author_facet | Burger, Martin Fazeny, Ariane Mordant, Gilles Pietschmann, Jan-Frederik |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14457 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | p-Wasserstein distances on networks and 3D to 1D convergence Burger, Martin Fazeny, Ariane Mordant, Gilles Pietschmann, Jan-Frederik Analysis of PDEs Optimization and Control 76N15, 49Q22, 35R02 (Primary) 35Q31, 60B10 (Secondary) 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. |
| title | p-Wasserstein distances on networks and 3D to 1D convergence |
| topic | Analysis of PDEs Optimization and Control 76N15, 49Q22, 35R02 (Primary) 35Q31, 60B10 (Secondary) |
| url | https://arxiv.org/abs/2601.14457 |