My very naive view on approaches to mathematical modeling is that historically differential equations and in particular partial differential equations have been used with great success to model processes from physics to economics. With the advent of higher power computers, machine learning techniques seem to now be a popular option in modeling these types of things as well.
When do machine learning techniques fall short of what PDE/DE can produce in terms of an accurate model? If I was given a ton of data to train my model, would machine learning techniques be the clear cut winner every time or do DE/PDE sometimes prove more effective even when data is plentiful?