论文标题
使用MatérnGaussian流量进行对流图建模对流
Modeling Advection on Directed Graphs using Matérn Gaussian Processes for Traffic Flow
论文作者
论文摘要
交通流量的运输可以通过对流方程进行建模。有限的差异和有限体积方法已用于在网格上数值求解该双曲方程。也已使用图形对流操作员[4，18]对对流进行了离散对准图的建模。在本文中，我们首先表明我们可以将该图对流操作员作为有限差分计划进行重新重新制定。然后，我们提出了定向的图形对流MatérnGaussian工艺（DGAMGP）模型，该模型将该图对流操作员的动力学结合到了可训练的Matérn高斯过程的内核中，以有效地模拟了在有向图上的对流过程的不确定性。
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.
