{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/efficient-nonparametric-n-body-force-fields","title":"Efficient nonparametric $n$-body force fields from machine learning","arxiv_id":"1801.04823","date":"2018-01-15","proceeding":null,"authors":["Aldo Glielmo","Claudio Zeni","Alessandro De Vita"],"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 $\\text{meV/} \\AA$ 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.","url_abs":"http://arxiv.org/abs/1801.04823v2","url_pdf":"http://arxiv.org/pdf/1801.04823v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"efficient-nonparametric-n-body-force-fields","repo_url":"https://github.com/kcl-tscm/M-FF","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"efficient-nonparametric-n-body-force-fields","repo_url":"https://github.com/kcl-tscm/mff","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}