  Understanding the physical origin of deformation mechanisms in random alloys
requires an understanding of their average behavior and, equally important, the
role of local fluctuations around the average. Material properties of random
alloys can be computed using direct simulations on random configurations but
some properties are very difficult to compute, for others it is not even fully
understood how to compute them using random sampling, in particular,
interaction energies between multiple defects. To that end, we develop an
atomistic model that does the averaging on the level of interatomic potentials.
Then, the problem of averaging via random sampling is bypassed since computing
material properties on random configurations reduces to computing material
properties on a single crystal, the average alloy.
  We develop our average model on the class of linear machine-learning
interatomic potentials. To that end, using tools from higher-order statistics,
we derive an analytic expansion of the average many-body per-atom energy in
terms of average tensor products of the feature vectors that scales linearly
with the size of an atomic neighborhood. In order to avoid forming higher-order
tensors composed of products of feature vectors, we develop an implementation
using equivariant tensor network potentials in which the feature vectors are
contracted to small-sized tensors before taking the average. We show that our
average model predicts the compact screw dislocation core structure in the
NbMoTaW medium-entropy alloy, in agreement with density functional theory, as
opposed to state-of-the-art average embedded atom method potentials that
predict artificial polarized cores. Hence, we anticipate that our model will
become useful for understanding mechanistic origins of material properties and
for developing predictive models of mechanical properties of random alloys.
