I've got a real-world problem that I'm trying to solve with as few computations as possible. In this 2D problem, everything is parameterized on a unit square, $f(x,y); x, y \in [0, 1]$. Anecdotal evidence suggests that there is a smooth, potentially non-convex boundary in this range that splits the region into two domains $A$ and $B$ where $f_A \ll f_B$.
Given that it is very expensive to compute a single value of $f$ and that I've sampled $n$ points already, how can I choose the next point that will give me the most new information?
My rudimentary understanding of Gaussian Processes suggests that I can use them to sample from a posterior. From there I think I can find the region of most variance ... but I'm not at all sure if this is even possible.