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.

本文提出了一种 Wasserstein 吸引方法，用于解决网络上的动态质量传输问题。在网络传输问题中，我们从需要“传输”到考虑网络拓扑的目标分布的节点集上的分布开始. 我们利用问题的特定结构，以计算隐式梯度步骤为特征，并制定了一种基于离散流的方法。因此，我们提出的算法依赖于受约束的 Wasserstein 重心的迭代计算。我们展示了所提出的方法如何找到网络传输问题的近似解决方案，同时考虑到网络的拓扑结构、通信通道的容量和各个节点的容量。最后，我们展示了这种方法应用于大型水运网络的性能。