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 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.