Approximate Wasserstein attraction flows for dynamic mass transport over networks

Journal Article (2022)







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This paper presents a Wasserstein attraction approach for solving dynamic mass transport problems over networks. In the transport problem over networks, we start with a distribution over the set of nodes that needs to be "transported" to a target distribution accounting for the network topology. We exploit the specic structure of the problem, characterized by the computation of implicit gradient steps, and formulate an approach based on discretized ows. As a result, our proposed algorithm relies on the iterative computation of constrained Wasserstein barycenters. We show how the proposed method approximates solutions to the network transport problem, taking into account the topology of the network, the capacity of the communication channels, and the capacity of the individual nodes. Finally, we show the performance of this approach applied to large-scale water transportation networks.


automation, control theory, optimisation.

Author keywords

Optimal transport, Wasserstein distance, constrained Wasserstein barycenter, discrete flow, network

Scientific reference

F. Arqué, C. Uribe and C. Ocampo-Martínez. Approximate Wasserstein attraction flows for dynamic mass transport over networks. Automatica, 143: 110432, 2022.