Is your feature request related to a problem? Please describe.

We should be able to create global graphs in icosahedral mesh arrangements.

These need to create nodes and edges on the fly from coordinates (or base grid). Ideally, these should be capable of building a multi-scale mesh that generates levels with connections to local representations in the different scales.

This issue is almost identical to #5 but for a different geometry.

Describe the solution you'd like

This should probably use networkx and trimesh to build the graphs, to have a well-tested base to build off of and generate a HeteroData Pytorch geometric object that can be used in anemoi-training and implements similar interfaces to #1 and #2.

It could be built in conjunction with #5 to re-use components.

Describe alternatives you've considered

Building the graph directly in Pytorch geometric. This would mean that we can easily re-use the objects in the rest of anemoi-graphs. However, the graph editing capability of networkx and the specific implementation of the multiscales in trimesh are already well-defined and used across many projects.

Additional context

This would be similar to the multiscale implemented in AIFS v0.1 and GraphCast.

Organisation

ECMWF