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In this work, we formulate an efficient method to calculate descriptors that can separately represent two- and three-body atomic distribution functions, and we examine the effects of including only two- or three-body descriptors, as well as including both, in the regression model. Our study indicates that non-linear mixing of two- and three-body descriptors is essential for an efficient training and a high accuracy of the final machine-learned model. The efficiency can be further improved by weighting the two-body descriptors more strongly. We furthermore examine a sparsification of the three-body descriptors. The three-body descriptors usually provide redundant representations of the atomistic structure, and the number of descriptors can be significantly reduced without loss of accuracy by applying an automatic sparsification using a principal component analysis. Visualization of the reduced descriptors using three-body distribution functions in real-space indicates that the sparsification automatically removes the components that are less significant for describing the distribution function.<\/jats:p>","DOI":"10.1063\/5.0009491","type":"journal-article","created":{"date-parts":[[2020,6,15]],"date-time":"2020-06-15T11:32:31Z","timestamp":1592220751000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":257,"title":["Descriptors representing two- and three-body atomic distributions and their effects on the accuracy of machine-learned inter-atomic potentials"],"prefix":"10.1063","volume":"152","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0822-1161","authenticated-orcid":false,"given":"Ryosuke","family":"Jinnouchi","sequence":"first","affiliation":[{"name":"Computational Materials Physics, Faculty of Physics, University of Vienna 1 , Sensengasse 8\/16, 1090 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6383-9175","authenticated-orcid":false,"given":"Ferenc","family":"Karsai","sequence":"additional","affiliation":[{"name":"VASP Software GmbH 2 , Sensengasse 8, 1090 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8337-1066","authenticated-orcid":false,"given":"Carla","family":"Verdi","sequence":"additional","affiliation":[{"name":"Computational Materials Physics, Faculty of Physics, University of Vienna 1 , Sensengasse 8\/16, 1090 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2658-6260","authenticated-orcid":false,"given":"Ryoji","family":"Asahi","sequence":"additional","affiliation":[{"name":"Toyota Central Research and Developments Laboratories, Inc. 3 , Aichi 480-1192, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9102-4259","authenticated-orcid":false,"given":"Georg","family":"Kresse","sequence":"additional","affiliation":[{"name":"Computational Materials Physics, Faculty of Physics, University of Vienna 1 , Sensengasse 8\/16, 1090 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2020,6,15]]},"reference":[{"key":"2023080302025583100_c1","doi-asserted-by":"publisher","first-page":"146401","DOI":"10.1103\/physrevlett.98.146401","article-title":"Generalized neural-network representation of high-dimensional potential-energy surfaces","volume":"98","year":"2007","journal-title":"Phys. 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