Approximate Wasserstein Attraction Flows for Dynamic Mass Transport over Networks

TL;DR

This paper introduces an approximate Wasserstein attraction flow method for efficiently solving dynamic mass transport problems over networks, considering network topology and capacities, demonstrated on large-scale water networks.

Contribution

It proposes a novel discretized flow approach based on constrained Wasserstein barycenters for network transport problems, incorporating topology and capacity constraints.

Findings

Effective in large-scale water transportation networks

Provides approximate solutions considering network constraints

Demonstrates scalability and performance

Abstract

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 specific structure of the problem, characterized by the computation of implicit gradient steps, and formulate an approach based on discretized flows. As a result, our proposed algorithm relies on the iterative computation of constrained Wasserstein barycenters. We show how the proposed method finds approximate 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.