Modeling Advection on Directed Graphs using Matérn Gaussian Processes for Traffic Flow
This work addresses traffic flow prediction for urban planning or transportation systems, but it appears incremental as it builds on existing graph advection operators and Gaussian process methods.
The paper tackles modeling traffic flow as an advection process on directed graphs by reformulating a graph advection operator as a finite difference scheme and proposing a Directed Graph Advection Matérn Gaussian Process (DGAMGP) model that incorporates these dynamics into a trainable kernel to effectively capture flow and uncertainty.
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 Matérn Gaussian Process (DGAMGP) model that incorporates the dynamics of this graph advection operator into the kernel of a trainable Matérn Gaussian Process to effectively model traffic flow and its uncertainty as an advective process on a directed graph.