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Modeling Advection on Directed Graphs using Mat\'{e}rn Gaussian Processes for Traffic Flow
Nadim Saad · Danielle Maddix · Bernie Wang

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.

Author Information

Nadim Saad (Stanford University)
Danielle Maddix (Amazon Web Services)
Bernie Wang (AWS AI Labs)

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