Non-linear least squares and machine learning

My research group does work in nonlinear dynamics and parameter fitting. We don't exactly approach the problem as one of machine learning though it arguably is a form of it. Part of our work involves mapping vectors into a higher dimensional space, predicting forward in time in the higher dimensional space, and then converting those predictions back into the lower dimensional space (a classically ill-posed problem). This last step seems to be an example of some form of non-linear regression, specifically NLLS (for us). The wikipedia page doesn't seem to be very helpful, so I was curious if anyone here had a good reference or tutorial on the matter of non-linear least squares.