A majority of experimental disciplines face the challenge of exploring large
and high-dimensional parameter spaces in search of new scientific discoveries.
Materials science is no exception; the wide variety of synthesis, processing,
and environmental conditions that influence material properties gives rise to
particularly vast parameter spaces. Recent advances have led to an increase in
efficiency of materials discovery by increasingly automating the exploration
processes. Methods for autonomous experimentation have become more
sophisticated recently, allowing for multi-dimensional parameter spaces to be
explored efficiently and with minimal human intervention, thereby liberating
the scientists to focus on interpretations and big-picture decisions. Gaussian
process regression (GPR) techniques have emerged as the method of choice for
steering many classes of experiments. We have recently demonstrated the
positive impact of GPR-driven decision-making algorithms on autonomously
steering experiments at a synchrotron beamline. However, due to the complexity
of the experiments, GPR often cannot be used in its most basic form, but rather
has to be tuned to account for the special requirements of the experiments. Two
requirements seem to be of particular importance, namely inhomogeneous
measurement noise (input dependent or non-i.i.d.) and anisotropic kernel
functions, which are the two concepts that we tackle in this paper. Our
synthetic and experimental tests demonstrate the importance of both concepts
for experiments in materials science and the benefits that result from
including them in the autonomous decision-making process