I have a function $f:\mathbf{x} \mapsto \mathbf{y}$ where $\mathbf{x} \in \mathbb{R}^n$ and $\mathbf{y} \in \mathbb{R}^m$.
I can evaluate this function numerically, but it is relatively expensive (a few minutes of computation for a single point). I'd like to know how to best sample the bounded $n$-dimensional domain so that the function can be approximated or interpolated from a finite number of points $f(\mathbf{x}_i)$. In other words, which values of $\mathbf{x}$ will give me the most information about the form of the function?