Atomic Cluster Expansion: Completeness, Efficiency and Stability

Understand

The Atomic Cluster Expansion (Drautz, Phys.

• Rev.
• B 99, 2019) provides a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling properties of atomistic systems.
• Our presentation extends the derivation by proposing a precomputation algorithm that yields immediate guarantees that a complete basis is obtained.