Title: Discrete Gaussian Vector Fields On Meshes Show Chinese title

Title: 离散高斯网格场

Abstract: Though the underlying fields associated with vector-valued environmental data are continuous, observations themselves are discrete. For example, climate models typically output grid-based representations of wind fields or ocean currents, and these are often downscaled to a discrete set of points. By treating the area of interest as a two-dimensional manifold that can be represented as a triangular mesh and embedded in Euclidean space, this work shows that discrete intrinsic Gaussian processes for vector-valued data can be developed from discrete differential operators defined with respect to a mesh. These Gaussian processes account for the geometry and curvature of the manifold whilst also providing a flexible and practical formulation that can be readily applied to any two-dimensional mesh. We show that these models can capture harmonic flows, incorporate boundary conditions, and model non-stationary data. Finally, we apply these models to downscaling stationary and non-stationary gridded wind data on the globe, and to inference of ocean currents from sparse observations in bounded domains. Show Chinese abstract

Abstract: 尽管与向量值环境数据相关的基础场是连续的，但观测本身是离散的。 例如，气候模型通常输出风场或海洋洋流的网格表示，这些通常被降尺度为一组离散点。 通过将感兴趣区域视为一个可以表示为三角形网格并嵌入欧几里得空间的二维流形，这项工作表明可以从相对于网格定义的离散微分算子中开发出适用于向量值数据的离散内在高斯过程。 这些高斯过程考虑了流形的几何形状和曲率，同时提供了一种灵活且实用的公式，可以轻易应用于任何二维网格。 我们证明这些模型可以捕捉调和流，包含边界条件，并对非平稳数据进行建模。 最后，我们将这些模型应用于全球静态和非静态网格风数据的降尺度，以及在有限域中从稀疏观测中推断海洋洋流。