We present a novel scheme to accurately predict atomic forces as vector quantities, rather than sets of scalar components, by Gaussian process (GP) regression. This is based on matrix-valued kernel functions, on which we impose the requirements that the predicted force rotates with the target configuration and is independent of any rotations applied to the configuration database entries. We show that such covariant GP kernels can be obtained by integration over the elements of the rotation group SO(d) for the relevant dimensionality d. Remarkably, in specific cases the integration can be carried out analytically and yields a conservative force field that can be recast into a pair interaction form. Finally, we show that restricting the integration to a summation over the elements of a finite point group relevant to the target system is sufficient to recover an accurate GP. The accuracy of our kernels in predicting quantum-mechanical forces in real materials is investigated by tests on pure and defective Ni, Fe, and Si crystalline systems.

Accurate interatomic force fields via machine learning with covariant kernels

De Vita, Alessandro
Supervision
2017-01-01

Abstract

We present a novel scheme to accurately predict atomic forces as vector quantities, rather than sets of scalar components, by Gaussian process (GP) regression. This is based on matrix-valued kernel functions, on which we impose the requirements that the predicted force rotates with the target configuration and is independent of any rotations applied to the configuration database entries. We show that such covariant GP kernels can be obtained by integration over the elements of the rotation group SO(d) for the relevant dimensionality d. Remarkably, in specific cases the integration can be carried out analytically and yields a conservative force field that can be recast into a pair interaction form. Finally, we show that restricting the integration to a summation over the elements of a finite point group relevant to the target system is sufficient to recover an accurate GP. The accuracy of our kernels in predicting quantum-mechanical forces in real materials is investigated by tests on pure and defective Ni, Fe, and Si crystalline systems.
6-ago-2017
Pubblicato
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.214302
File in questo prodotto:
File Dimensione Formato  
PhysRevB.95.214302.pdf

Accesso chiuso

Descrizione: articolo principale
Tipologia: Documento in Versione Editoriale
Licenza: Copyright Editore
Dimensione 1.1 MB
Formato Adobe PDF
1.1 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
CK_13_final_SM.pdf

Accesso chiuso

Descrizione: supporting information
Tipologia: Altro materiale allegato
Licenza: Copyright Editore
Dimensione 206.27 kB
Formato Adobe PDF
206.27 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2918466
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 141
  • ???jsp.display-item.citation.isi??? 138
social impact