Work

Atomic Cluster Expansion: Completeness, Efficiency and Stability

Year: 2019

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1911.03550

Authors: Dusson, Genevieve, Bachmayr, Markus, Csanyi, Gabor, Drautz, Ralf, Etter, Simon, van der Oord, Cas, Ortner, Christoph

Institutions: Centre National de la Recherche Scientifique, Université Bourgogne Franche-Comté, Laboratoire de Mathématiques de Besançon

Language: English

Topic: Machine Learning in Materials Science

Subfield: Materials Chemistry

Field: Materials Science

Domain: Physical Sciences

Open Access status: green

Funders: Leverhulme Trust, Agence Nationale de la Recherche

Awards: G195474297, G6273714036, ISITE « BFC

OpenAlex ID: W4288026468

Cites:

Cited by: 6

Related to: 10