论文标题
公制图上的高斯晶体麦片字段
Gaussian Whittle-Matérn fields on metric graphs
论文作者
论文摘要
我们在街道或河网等紧凑型公制图上定义了一类新的高斯流程。所提出的模型，晶体 - 马特纳场，是通过紧凑型公制图上的分数随机微分方程来定义的，并且是具有Matérn协方差在欧几里得域上函数在非欧亚人公制图设置上的高斯场的自然扩展。得出了过程的存在及其某些主要特性，例如样本路径的规律性。模型类特别包含可区分的过程。据我们所知，这是在一般紧凑型公制图上的第一次构造高斯过程。此外，我们证明了这些过程的内在特性：它们在添加或删除二级的顶点时不会改变。最后，我们获得了过程的karhunen-loève扩展，提供数值实验，并将它们与各向同性协方差函数进行比较。
We define a new class of Gaussian processes on compact metric graphs such as street or river networks. The proposed models, the Whittle--Matérn fields, are defined via a fractional stochastic differential equation on the compact metric graph and are a natural extension of Gaussian fields with Matérn covariance functions on Euclidean domains to the non-Euclidean metric graph setting. Existence of the processes, as well as some of their main properties, such as sample path regularity are derived. The model class in particular contains differentiable processes. To the best of our knowledge, this is the first construction of a differentiable Gaussian process on general compact metric graphs. Further, we prove an intrinsic property of these processes: that they do not change upon addition or removal of vertices with degree two. Finally, we obtain Karhunen--Loève expansions of the processes, provide numerical experiments, and compare them to Gaussian processes with isotropic covariance functions.
