Modeling Advection on Directed Graphs using Mat'ern Gaussian Processes for Traffic Flow
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Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 6 of its 20 references that are in the map. First posted on arXiv 14 Dec 2021.
Builds on
6 of 20 references.
References · 6
- 2018GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Accelerationcited by 603
- 2021GRAND: Graph Neural Diffusioncited by 258
- 2020Mat'ern Gaussian Processes on Graphscited by 65
- 2018Machine Learning of Space-Fractional Differential Equationscited by 12
- 2015PDE Approaches to Graph Analysiscited by 3
- 2019Numerical Gaussian process Kalman filteringcited by 1
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Citing papers per year: 2026: 2.
2 papers.