I mean perhaps I am not entirely sure myself. I imagine that the solution space to this problem is some very complicated, lets say algebraic variety/manifold/sp

I mean perhaps I am not entirely sure myself. I imagine that the solution space to this problem is some very complicated, lets say algebraic variety/manifold/space/configuration space, but obviously it is still low enough dimension it can be sort of picked out nicely from some huge ambient space. For example specific points on this object are a folded proteins. I suppose then it is how well does this get encoded, does it know about "properties" of this surface, or is it more like a rough kind of point cloud because you have sampled enough and then it does some crude interpolation. But maybe that does not respect the sort of properties in this object. Maybe there are conservation laws, symmetry properties, etc which are actually important, and then not respecting that you have just produced garbage. So I think it is important to know what kind of problem you are dealing with. Imagine a long time scale n-body problem with lots of sensitivity. Maybe in a video game it doesn't matter if there is something non physical about what it produces, as long as it looks good enough. Maybe this interpolation is practical for its purpose. But I think we should still be careful and question what kind of problem it is applied to perhaps. Maybe it's more like a complexity vs complicated question.