We provide an implementation to compute the flat metric in any dimension. The
flat metric, also called dual bounded Lipschitz distance, generalizes the
well-known Wasserstein distance W1 to the case that the distributions are of
unequal total mass. This is of particular interest for unbalanced optimal
transport tasks and for the analysis of data distributions where the sample
size is important or normalization is not possible. The core of the method is
based on a neural network to determine on optimal test function realizing the
distance between two given measures. Special focus was put on achieving
comparability of pairwise computed distances from independently trained
networks. We tested the quality of the output in several experiments where
ground truth was available as well as with simulated data.

我们提供了一个在任意维度计算平坦度量的实现。平坦度量，也称为双有界利普希茨距离，将众所周知的 Wasserstein 距离 W1 推广到分布总质量不相等的情况。这对于不平衡的最优传输任务以及样本大小重要或不可归一化的数据分布的分析非常重要。该方法的核心是基于神经网络来确定一个实现两个给定度量之间距离的最优测试函数。我们特别关注实现了从独立训练的网络中计算出的成对距离的可比较性。我们通过多个实验以及使用模拟数据来测试输出的质量。