I've been wondering this since machine learning first became blew up in the 2010s and I guess this is as good a place ask to ask as any: is there some sort of law/theory/conjecture/whatever that states that neural networks are algebraically incapable of modeling physical phenomena in general, or at least within the boundary conditions implied by the training data? For example, if the physical calculation includes imaginary numbers or some other exotic function.
I'm thinking specifically of linear motors [1] which are capable of sub-micron positioning as long as the rotor and stators can be manufactured with enough precision. Is there some fundamental problem preventing us from using an interferometric laser encoder to train a neural network to control each linear motor coming off the assembly line, thus eliminating the much of the precision manufacturing?