标题： 在有向图上使用Matérn高斯过程进行交通流的对流建模 显示英文标题

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

摘要： 交通流的传输可以通过对流方程进行建模。有限差分和有限体积方法已被用于在网格上数值求解这个双曲方程。对流也已在有向图上使用图对流算子[4, 18]进行了离散建模。在本文中，我们首先表明可以将这个图对流算子重新表述为有限差分格式。然后，我们提出了有向图对流马特恩高斯过程（DGAMGP）模型，该模型将图对流算子的动力学纳入可训练马特恩高斯过程的核中，以有效地将交通流及其不确定性建模为有向图上的对流过程。 显示英文摘要

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 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.