  Alloys composed of several elements in roughly equimolar composition, often
referred to as high-entropy alloys, have long been of interest for their
thermodynamics and peculiar mechanical properties, and more recently for their
potential application in catalysis. They are a considerable challenge to
traditional atomistic modeling, and also to data-driven potentials that for the
most part have memory footprint, computational effort and data requirements
which scale poorly with the number of elements included. We apply a recently
proposed scheme to compress chemical information in a lower-dimensional space,
which reduces dramatically the cost of the model with negligible loss of
accuracy, to build a potential that can describe 25 d-block transition metals.
The model shows semi-quantitative accuracy for prototypical alloys, and is
remarkably stable when extrapolating to structures outside its training set. We
use this framework to study element segregation in a computational experiment
that simulates an equimolar alloy of all 25 elements, mimicking the seminal
experiments by Cantor et al., and use our observations on the short-range order
relations between the elements to define a data-driven set of Hume-Rothery
rules that can serve as guidance for alloy design. We conclude with a study of
three prototypical alloys, CoCrFeMnNi, CoCrFeMoNi and IrPdPtRhRu, determining
their stability and the short-range order behavior of their constituents.
