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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.

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