  The Atomic Cluster Expansion (ACE) (Drautz, Phys. Rev. B 99, 2019) has been
widely applied in high energy physics, quantum mechanics and atomistic modeling
to construct many-body interaction models respecting physical symmetries.
Computational efficiency is achieved by allowing non-physical self-interaction
terms in the model. We propose and analyze an efficient method to evaluate and
parameterize an orthogonal, or, non-self-interacting cluster expansion model.
We present numerical experiments demonstrating improved conditioning and more
robust approximation properties than the original expansion in regression tasks
both in simplified toy problems and in applications in the machine learning of
interatomic potentials.
