https://github.com/DanielRobertNicoud/imv-gps

Code for the paper "Intrinsic Gaussian Vector Fields on Manifolds" by Robert-Nicoud, Krause, and Borovitskiy
https://github.com/DanielRobertNicoud/imv-gps

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Code for the paper "Intrinsic Gaussian Vector Fields on Manifolds" by Robert-Nicoud, Krause, and Borovitskiy

• Host: GitHub
• URL: https://github.com/DanielRobertNicoud/imv-gps
• Owner: DanielRobertNicoud
• License: mit
• Created: 2024-02-20T19:46:55.000Z (9 months ago)
• Default Branch: main
• Last Pushed: 2024-03-07T20:20:15.000Z (8 months ago)
• Last Synced: 2024-08-03T15:06:31.424Z (3 months ago)
• Language: Jupyter Notebook
• Size: 449 KB
• Stars: 5
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Intrinsic manifold vector GPs

Code for the paper "Intrinsic Gaussian Vector Fields on Manifolds" by Robert-Nicoud, Krause, and Borovitskiy.

**Note of the author:**

* The code extends `scikit-learn`'s GP implementation. It is a bit of a hack and it is a bit messy, but it works.s A cleaner version will soon be available in the [https://github.com/GPflow/GeometricKernels/tree/main](GeometricKernels) package.

* The ERA5 dataset is too large to be uploaded. It can be freely downloaded at

  https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-pressure-levels-monthly-means?tab=form

  and then uploaded in the `era5` folder. One should select the options:

  * Product type -> Reanalysis

  * Variable -> U-component of wind + V-component of wind

  * Pressure level -> 500 hPa

  * Year -> 2010

  * Month -> all available

  * Time -> 00:00

  * Format -> NetCDF

* The numbered scripts should be ran in order, as some generate data that is consuimed by the ones following.

## Scripts present

1. `aux_functions.py`: Auxiliary functions used to treat ponts and vectors on the sphere.

2. `sphere_vector_kernel.py`: Implementation of vector kernels on the sphere extending `sklearn.gaussian_process.kernels.Kernel`.

3. `sphere_vector_gp.py`: Implementation of manifold vector GPs extending `sklearn.gaussian_process.GaussianProcessRegressor`.

4. `blender_file_generation.py`: Utility for saving outputs ready to be treated by blender.

5. `001_gp_prior_samples`.ipynb: Generate samples from GP priors with various kernels.

6. `002_blender_eigenvf.ipynb`: Some heat equation eigen-vector fields on the sphere.

7. `003_era5_experiments.ipynb`: Run GP experiments on the ERA5 data.

8. `004_flat_plots.ipynb`: Shows some of the results in paper-grade quality on projected maps.

9. `005_synthetic_experiments.ipynb`: Experiments on synthetically generated data.

10. `006_var_div.ipynb`: Computation of variance of the divergence of various GPs.