CUED Publications database

Atomic Cluster Expansion: Completeness, Efficiency and Stability

Bachmayr, M and Csanyi, G and Drautz, R and Dusson, G and Etter, S and Oord, CVD and Ortner, C Atomic Cluster Expansion: Completeness, Efficiency and Stability. (Unpublished)

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Abstract

The {\em 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 in a way that yields immediate guarantees that a complete basis is indeed 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.

Item Type: Article
Uncontrolled Keywords: math.NA math.NA cs.NA
Subjects: UNSPECIFIED
Divisions: Div C > Applied Mechanics
Depositing User: Cron Job
Date Deposited: 15 Nov 2019 20:03
Last Modified: 02 Mar 2021 06:54
DOI: