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EnglishWe 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.
| Titolo: | Efficient nonparametric n -body force fields from machine learning |
| Autori: | |
| Data di pubblicazione: | 2018 |
| Stato di pubblicazione: | Pubblicato |
| Rivista: | |
| 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. |
| Handle: | http://hdl.handle.net/11368/2928405 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1103/PhysRevB.97.184307 |
| URL: | http://harvest.aps.org/v2/bagit/articles/10.1103/PhysRevB.97.184307/apsxml |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| Efficient_nonparametric_n_body.pdf | articolo principale | Bozza finale post-referaggio (post-print) | Digital Rights Management non definito | Open Access Visualizza/Apri |
http://hdl.handle.net/11368/2928405
