Modeling Advection on Directed Graphs using Mat\'ern Gaussian Processes for Traffic Flow

TL;DR

This paper introduces DGAMGP, a novel Gaussian Process model that captures traffic flow dynamics on directed graphs by reformulating graph advection as a finite difference scheme within a probabilistic framework.

Contribution

It reformulates the graph advection operator as a finite difference scheme and integrates it into a Matérn Gaussian Process for modeling traffic flow on directed graphs.

Findings

Effective modeling of traffic flow and uncertainty.

Reformulation of graph advection as finite difference scheme.

Enhanced traffic prediction accuracy.

Abstract

The transport of traffic flow can be modeled by the advection equation. Finite difference and finite volumes methods have been used to numerically solve this hyperbolic equation on a mesh. Advection has also been modeled discretely on directed graphs using the graph advection operator [4, 18]. In this paper, we first show that we can reformulate this graph advection operator as a finite difference scheme. We then propose the Directed Graph Advection Mat\'ern Gaussian Process (DGAMGP) model that incorporates the dynamics of this graph advection operator into the kernel of a trainable Mat\'ern Gaussian Process to effectively model traffic flow and its uncertainty as an advective process on a directed graph.