# Learn to mimic function adaptively

Assume I have a function $$F: R^n \to R$$ that is slow to evaluate, which I, therefore, would like to approximate with something faster by using machine learning. I have seen some work proceeding by generating a dataset by considering a grid in $$R^n$$ evaluating $$F$$ on the grid and training a neural network to that dataset. What I wonder is, does there exist some method that is adaptive, in the sense that it will itself figure out where the function needs to be evaluated and then does it. I feel one throws a lot of information away by using a static dataset when it could be dynamically updated during training instead.