Generalized Wasserstein distances allow to quantitatively compare two continuous or atomic mass distributions with equal or different total mass. In this paper, we propose four numerical methods for the approximation of three different generalized Wasserstein distances introduced in the last years, giving some insights about their physical meaning. After that, we explore their usage in the context of the sensitivity analysis of differential models for traffic flow. The quantification of models sensitivity is obtained by computing the generalized Wasserstein distances between two (numerical) solutions corresponding to different inputs, including different boundary conditions.

翻译：广义Wasserstein距离可用于定量比较两个总质量相等或不同的连续或离散质量分布。本文针对近年来提出的三种不同广义Wasserstein距离，提出了四种数值逼近方法，并阐释了其物理意义。随后，我们探讨了这些方法在交通流微分模型敏感性分析中的应用。通过计算对应于不同输入条件（包括不同边界条件）的两种（数值）解之间的广义Wasserstein距离，实现了对模型敏感性的量化分析。