Modeling Advection on Directed Graphs using Matérn Gaussian Processes for Traffic Flow

12/14/2021

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by   Danielle C. Maddix, et al.

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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.