> use that along with other rules that you know to re-infer what the 3D structure is
Great answer, thank you :-) Saved me a bunch of typing to explain it less well than you just did.
It's worth adding, for this crowd, that another way of thinking about the "other rules" you allude to is as a system of constraints; you can then set this up as an optimization problem (find the set of atomic positions minimizing reconstruction error under the set of symmetry constraints implied by the space group – so that means that solving crystal structures and machine learning are functionally isomorphic problems.
Great answer, thank you :-) Saved me a bunch of typing to explain it less well than you just did.
It's worth adding, for this crowd, that another way of thinking about the "other rules" you allude to is as a system of constraints; you can then set this up as an optimization problem (find the set of atomic positions minimizing reconstruction error under the set of symmetry constraints implied by the space group – so that means that solving crystal structures and machine learning are functionally isomorphic problems.