Numerical computation of generalized Wasserstein distances with applications to traffic model analysis

TL;DR

This paper introduces four numerical methods to approximate generalized Wasserstein distances and demonstrates their application in traffic flow model sensitivity analysis, providing a quantitative tool for comparing mass distributions with varying total mass.

Contribution

The paper presents four novel numerical methods for approximating generalized Wasserstein distances and explores their application in traffic model sensitivity analysis.

Findings

Four numerical methods for Wasserstein distances approximation.

Application of these methods to traffic flow model sensitivity analysis.

Quantitative comparison of solutions with different boundary conditions.

Abstract

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.