Atomic Cluster Expansion: Completeness, Efficiency and Stability

2019/11/08 by Geneviève Dusson, Genevieve Dusson, Markus Bachmayr +14 · 27 citations
Computer Science · Materials Science · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Electron and X-Ray Spectroscopy Techniques #FOS: Mathematics #Machine Learning in Materials Science #Numerical Analysis (math.NA) #X-ray Diffraction in Crystallography #cs.NA #math.NA

paper · pdf · doi:10.48550/arxiv.1911.03550

Title has changed in v3

openalex publication_date 2020/04/23 · openalex created_date 2020/04/24 · arxiv created 2021/05/12 · arxiv updated 2021/05/13 · openalex updated_date 2026/07/28

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.

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