600 RWTH Publication No: 956751        2021       
TITLE Atomic Cluster Expansion: Completeness, Efficiency and Stability
AUTHORS Genevieve Dusson, Markus Bachmayr, Gabor Csanyi, Ralf Drautz, Simon Etter, Cas van der Oord, Christoph Ortner
ABSTRACT 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. We provide a fast recursive algorithm for efficient evaluation and illustrate its performance in numerical tests. Finally, we discuss generalisations and open challenges, particularly from a numerical stability perspective, around basis optimisation and parameter estimation, paving the way towards a comprehensive analysis of the convergence to a high-fidelity reference model.
DOI 10.1016/j.jcp.2022.110946
PUBLICATION Journal of Computational Physics, Volume 454, 1 April 2022, 110946