Ah, should have read the docs, thanks! It occurred to me after I posted that this is similar in a way to molecular dynamics simulations, which are essentially

Ah, should have read the docs, thanks! It occurred to me after I posted that this is similar in a way to molecular dynamics simulations, which are essentially constrained sets of points (constraints like atoms have to be within a certain distance range or angle/torsion). In those you use techniques like gradient descent (similar to Newton's method it seems) and forcefields and so on. I guess it's all numerical optimization in the end.