Discrete Gaussian Vector Fields On Meshes
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911079194427392 |
|---|---|
| author | Gillan, Michael Siegert, Stefan Youngman, Ben |
| author_facet | Gillan, Michael Siegert, Stefan Youngman, Ben |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20024 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discrete Gaussian Vector Fields On Meshes Gillan, Michael Siegert, Stefan Youngman, Ben Methodology Statistics Theory Machine Learning 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. |
| title | Discrete Gaussian Vector Fields On Meshes |
| topic | Methodology Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2507.20024 |