  Developing data-driven machine-learning interatomic potentials for materials
containing many elements becomes increasingly challenging due to the vast
configuration space that must be sampled by the training data. We study the
learning rates and achievable accuracy of machine-learning interatomic
potentials for many-element alloys with different combinations of descriptors
for the local atomic environments. We show that for a five-element alloy
system, potentials using simple low-dimensional descriptors can reach
meV/atom-accuracy with modestly sized training datasets, significantly
outperforming the high-dimensional SOAP descriptor in data efficiency,
accuracy, and speed. In particular, we develop a computationally fast
machine-learned and tabulated Gaussian approximation potential (tabGAP) for
Mo-Nb-Ta-V-W alloys with a combination of two-body, three-body, and a new
simple scalar many-body density descriptor based on the embedded atom method.
