We provide a definition and explicit expressions for n-body Gaussian Process (GP) kernels which can learn any interatomic interaction occurring in a physical system, up to n-body contributions, for any value of n. The series is complete, as it can be shown that the "universal approximator" squared exponential kernel can be written as a sum of n-body kernels. These recipes enable the choice of optimally efficient force models for each target system, as confirmed by extensive testing on various materials. We furthermore describe how the n-body kernels can be "mapped" on equivalent representations that provide database-size-independent predictions and are thus crucially more efficient. We explicitly carry out this mapping procedure for the first non-trivial (3-body) kernel of the series, and show that this reproduces the GP-predicted forces with meV/A accuracy while being orders of magnitude faster. These results open the way to using novel force models (here named "M-FFs") that are computationally as fast as their corresponding standard parametrised n-body force fields, while retaining the nonparametric character, the ease of training and validation, and the accuracy of the best recently proposed machine learning potentials.

Efficient nonparametric n -body force fields from machine learning

De Vita, Alessandro
2018-01-01

Abstract

We provide a definition and explicit expressions for n-body Gaussian Process (GP) kernels which can learn any interatomic interaction occurring in a physical system, up to n-body contributions, for any value of n. The series is complete, as it can be shown that the "universal approximator" squared exponential kernel can be written as a sum of n-body kernels. These recipes enable the choice of optimally efficient force models for each target system, as confirmed by extensive testing on various materials. We furthermore describe how the n-body kernels can be "mapped" on equivalent representations that provide database-size-independent predictions and are thus crucially more efficient. We explicitly carry out this mapping procedure for the first non-trivial (3-body) kernel of the series, and show that this reproduces the GP-predicted forces with meV/A accuracy while being orders of magnitude faster. These results open the way to using novel force models (here named "M-FFs") that are computationally as fast as their corresponding standard parametrised n-body force fields, while retaining the nonparametric character, the ease of training and validation, and the accuracy of the best recently proposed machine learning potentials.
2018
Pubblicato
http://harvest.aps.org/v2/bagit/articles/10.1103/PhysRevB.97.184307/apsxml
File in questo prodotto:
File Dimensione Formato  
Efficient_nonparametric_n_body.pdf

accesso aperto

Descrizione: articolo principale
Tipologia: Bozza finale post-referaggio (post-print)
Licenza: Digital Rights Management non definito
Dimensione 1.19 MB
Formato Adobe PDF
1.19 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

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/11368/2928405
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 104
  • ???jsp.display-item.citation.isi??? 104
social impact