  We show that the magnetic properties of high-entropy alloys (HEAs) can be
captured by \textit{ab initio} calculations within the coherent potential
approximation, where the atomic details of the high-entropy mixing are
considered as an effective medium that possesses the translational symmetry of
the lattice. This is demonstrated using the face-centered cubic (FCC) phase of
$\textrm{FeCoNiMnCu}$ and the $L1_0$ phase of $\textrm{(FeCoNiMnCu)Pt}$ by
comparing the density functional theory (DFT) results with the experimental
values. Working within the first Brillouin zone and the primitive unit cell, we
show that DFT can capture the smooth profile of magnetic properties such as the
saturation magnetization, the Curie temperature and the magnetic anisotropy,
using only a sparse set of sampling points in the vast compositional space. The
smooth profiles given by DFT indeed follow the experimental trend,
demonstrating the promising potential of using machine learning to explore the
magnetic properties of HEAs, by establishing reasonably large datasets with
high-throughput calculations using density-functional theory.
