Symmetrization layer

[CheukHinHoJerry]

I am doing that for single species case, after confirming it works fine I will then do that for multi-specices case.

A minor issue is that currently RepLieGroups is using P4ML so there is a circular dependency issue. However in RepLieGroups/src we do not need P4ML and we should remove that from deps.

[cortner]

I agree. RepLieGroups only needs to be assured that the basis transforms as expected.

However, I'm not convinced that P4ML should depend on RepLieGroups. For now can we please work in a separate "drafting repo"? I will create that now.

[CheukHinHoJerry]

Just done a first draft on this and I will wait for the 2023MitacsDV repo to set up before I push the code.

[cortner]

That repo is already ready. Just create a folder inside, eg call it jhh_ace1 with a Project and example script.

[cortner]

We should think about how we can do the synmetrisation layer for real SH. Probably not hard, probably can be reduced to specifying the CG for rSH which should be a trivial linear transformation.

[cortner]

@CheukHinHoJerry -- I talked to @zhanglw0521 about creating another package called EquivariantLux.jl in which we make available utility functions to build equivariant models from RepLie and P4ML. We can also develop some example models in that package. It could be a sort of intermediate layer between RepLie, P4ML and ACE.

[zhanglw0521]

Sorry, I should have mentioned this earlier - so now we have an elementary version in this regard, which might be served as a starting point.

Edit: Maybe Jerry doesn't yet have access to this package, though?

[CheukHinHoJerry]

Ah yes - thanks for noticing this.

[CheukHinHoJerry]

I believe this is already implemented - I will close this now.

Ref ACEsuit/RepLieGroups.jl#7 (comment)