# How to choose my next sample point in a 2D boundary problem?

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.

• The problem you want to solve is not clear. Do you want (1) an estimate of $f$ and the fact that there are regions $A$ and $B$ is additional (prior) information or are you (2) seeking a classification of points whether they belong to $A$ or $B$ or (3) would you like to test the hypothesis that regions $A$ and $B$ exist? – g g Jan 11 at 22:28