Atomic cluster expansion: Completeness, efficiency and stability

The Atomic Cluster Expansion (Drautz (2019) [21]) provides a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye modelling properties of atomistic systems. Our presentation extends the derivation by proposing precomputation algorithm that yields immediate guarantees complete is obtained. We provide fast recursive efficient evaluation illustrate its performance in numerical tests. Finally, we discuss generalisations open challenges, from stability perspective, around optimisation parameter estimation, paving way towards comprehensive analysis convergence high-fidelity reference model.