  The relationship between material properties and independent variables such
as temperature, external field or time, is usually represented by a curve or
surface in a multi-dimensional space. Determining such a curve or surface
requires a series of experiments or calculations which are often time and cost
consuming. A general strategy uses an appropriate utility function to sample
the space to recommend the next optimal experiment or calculation within an
active learning loop. However, knowing what the optimal sampling strategy to
use to minimize the number of experiments is an outstanding problem. We compare
a number of strategies based on directed exploration on several materials
problems of varying complexity using a Kriging based model. These include one
dimensional curves such as the fatigue life curve for 304L stainless steel and
the Liquidus line of the Fe-C phase diagram, surfaces such as the Hartmann 3
function in 3D space and the fitted intermolecular potential for Ar-SH, and a
four dimensional data set of experimental measurements for BaTiO3 based
ceramics. We also consider the effects of experimental noise on the Hartmann 3
function. We find that directed exploration guided by maximum variance provides
better performance overall, converging faster across several data sets.
However, for certain problems, the trade-off methods incorporating exploitation
can perform at least as well, if not better than maximum variance. Thus, we
discuss how the choice of the utility function depends on the distribution of
the data, the model performance and uncertainties, additive noise as well as
the budget.
