Consider using Wyckoff positions instead of atomic sites

[sgbaird]

Almost always fewer than the total number of sites, e.g. mp-19841, mp-500, mp-19770. Would cut down the dimensionality by a significant amount, though it also introduces the possibility of representations that aren't able to be reconstructed (disregarding whether the structure would be realistic or not). See e.g. pyxtal: checking compatibility. There's also the question of how to numerically encode the Wyckoff position types. Might be worth digging more into Wren's representation https://github.com/CompRhys/aviary.

[sgbaird]

Asymmetric unit cell == primitive unit cell, meaning the minimum # of Wyckoff sites that let you reproduce the full unit cell IIUC.

[sgbaird]

#97

[sgbaird]

Related methods from CDVAE (emphasis added):

There are infinitely many different ways of choosing the lattice for the same material. We compute the Niggli reduced lattice (Grosse-Kunstleve et al., 2004) with pymatgen (Ong et al., 2013), which is a unique lattice for any given material. Since the lattice matrix L is not rotation invariant, we instead predict the 6 lattice parameters, i.e. the lengths of the 3 lattice vectors and the angles between them. We normalize the lengths of lattice vectors with [N^(1/3)], where N is the number of atoms, to ensure that the lengths for materials of different sizes are at the same scale.

See get_reduced_structure()

[kjappelbaum]

disregarding whether the structure would be realistic or not

I think this would be an interesting thing to analyze at some point - does symmetrization lead to more "realistic" structures. My intuition is that, on average, this is the case