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.
翻译:交通流量的传输可以通过平流方程式进行模型化。 已经使用微量差异和有限量方法在网状中用数字方式解决这个双曲方程式。 也使用图形平流操作员( [, 18] 在定向图形平流操作员( 4, 18] ) 在定向图形图上进行了不独立的模拟。 在本文中, 我们首先显示, 我们可以重新配置这个图形平流操作员, 作为一种有限的差异方案。 然后我们提出“ 定向图形对流 Mat\' ern Gaussian 进程( DGAMGP) ” 模型, 将这个图形对流操作员的动态纳入可训练的 Mat\ ern Gaussian 进程的核心, 以便有效地模拟流量及其不确定性, 将其作为定向图上的模拟过程。