基于Matérn高斯过程的有向图上交通流平流建模
Modeling Advection on Directed Graphs using Matérn Gaussian Processes for Traffic Flow
摘要：
交通流的输运可以用平流方程来模拟。本文采用有限差分和有限体积法在网格上数值求解这一双曲型方程。平流也已离散建模有向图使用图平流运算符[4，18]。在本文中，我们首先表明，我们可以重新制定这个图平流算子作为一个有限差分格式。然后，我们提出了有向图平流Matérn高斯过程（DGAMGP）模型，该模型将该图平流算子的动力学引入到可训练Matérn高斯过程的内核中，以有效地将交通流及其不确定性建模为有向图上的平流过程。
英文摘要：
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.
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