{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T10:55:05Z","timestamp":1783421705466,"version":"3.54.6"},"reference-count":44,"publisher":"IOP Publishing","issue":"2","license":[{"start":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T00:00:00Z","timestamp":1743638400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T00:00:00Z","timestamp":1743638400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"crossref","award":["N000014-16-12280"],"award-info":[{"award-number":["N000014-16-12280"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000078","name":"Division of Materials Research","doi-asserted-by":"crossref","award":["DMR-2219489"],"award-info":[{"award-number":["DMR-2219489"]}],"id":[{"id":"10.13039\/100000078","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100016755","name":"International Institute for Nanotechnology, Northwestern University","doi-asserted-by":"crossref","award":["Ryan Fellowship"],"award-info":[{"award-number":["Ryan Fellowship"]}],"id":[{"id":"10.13039\/100016755","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2025,6,30]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Graph neural networks (GNNs) have excelled in predictive modeling for both crystals and molecules, owing to the expressiveness of graph representations. High-entropy alloys (HEAs), however, lack chemical long-range order, limiting the applicability of current graph representations. To overcome this challenge, we propose a representation of HEAs as a collection of local environment graphs. Based on this representation, we introduce the LESets machine learning model, an accurate, interpretable GNN for HEA property prediction. We demonstrate the accuracy of LESets in modeling the mechanical properties of quaternary HEAs. Through analyses and interpretation, we further extract insights into the modeling and design of HEAs. In a broader sense, LESets extends the potential applicability of GNNs to disordered materials with combinatorial complexity formed by diverse constituents and their flexible configurations.<\/jats:p>","DOI":"10.1088\/2632-2153\/adc0e1","type":"journal-article","created":{"date-parts":[[2025,3,14]],"date-time":"2025-03-14T22:53:10Z","timestamp":1741992790000},"page":"025005","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Graph representation of local environments for learning high-entropy alloy properties"],"prefix":"10.1088","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3183-1654","authenticated-orcid":true,"given":"Hengrui \u6052\u777f","family":"Zhang \u5f20","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruishu","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9772-765X","authenticated-orcid":true,"given":"Jie","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0508-2175","authenticated-orcid":true,"given":"James M","family":"Rondinelli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4653-7124","authenticated-orcid":false,"given":"Wei","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2025,4,3]]},"reference":[{"key":"mlstadc0e1bib1","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1038\/s43246-022-00315-6","article-title":"Graph neural networks for materials science and chemistry","volume":"3","author":"Reiser","year":"2022","journal-title":"Commun. Mater."},{"key":"mlstadc0e1bib2","first-page":"pp 1263","article-title":"Neural message passing for quantum chemistry","volume":"vol 70","author":"Gilmer","year":"2017"},{"key":"mlstadc0e1bib3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.120.145301","article-title":"Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties","volume":"120","author":"Xie","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"mlstadc0e1bib4","doi-asserted-by":"publisher","first-page":"1031","DOI":"10.1038\/s42256-023-00716-3","article-title":"CHGNet as a pretrained universal neural network potential for charge-informed atomistic modelling","volume":"5","author":"Deng","year":"2023","journal-title":"Nat. Mach. Intell."},{"key":"mlstadc0e1bib5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.109.144426","article-title":"Spin-dependent graph neural network potential for magnetic materials","volume":"109","author":"Yu","year":"2024","journal-title":"Phys. Rev. B"},{"key":"mlstadc0e1bib6","first-page":"pp 9323","article-title":"E(n) equivariant graph neural networks","volume":"vol 139","author":"Satorras","year":"2021"},{"key":"mlstadc0e1bib7","doi-asserted-by":"publisher","DOI":"10.1016\/j.pmatsci.2022.101018","article-title":"Machine learning for high-entropy alloys: progress, challenges and opportunities","volume":"131","author":"Liu","year":"2023","journal-title":"Prog. Mater. Sci."},{"key":"mlstadc0e1bib8","doi-asserted-by":"publisher","first-page":"1280","DOI":"10.1557\/s43577-023-00591-8","article-title":"Understanding and leveraging short-range order in compositionally complex alloys","volume":"48","author":"Taheri","year":"2023","journal-title":"MRS Bull."},{"key":"mlstadc0e1bib9","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1126\/science.abo4940","article-title":"Machine learning-enabled high-entropy alloy discovery","volume":"378","author":"Rao","year":"2022","journal-title":"Science"},{"key":"mlstadc0e1bib10","doi-asserted-by":"publisher","first-page":"978","DOI":"10.1126\/science.abp8070","article-title":"Exceptional fracture toughness of CrCoNi-based medium- and high-entropy alloys at 20 kelvin","volume":"378","author":"Liu","year":"2022","journal-title":"Science"},{"key":"mlstadc0e1bib11","doi-asserted-by":"publisher","first-page":"834","DOI":"10.1016\/j.joule.2018.12.015","article-title":"High-entropy alloys as a discovery platform for electrocatalysis","volume":"3","author":"Batchelor","year":"2019","journal-title":"Joule"},{"key":"mlstadc0e1bib12","doi-asserted-by":"publisher","first-page":"1318","DOI":"10.1016\/j.matt.2020.07.029","article-title":"Neural network-assisted development of high-entropy alloy catalysts: decoupling ligand and coordination effects","volume":"3","author":"Lu","year":"2020","journal-title":"Matter"},{"key":"mlstadc0e1bib13","doi-asserted-by":"publisher","first-page":"14864","DOI":"10.1021\/acscatal.2c03675","article-title":"Machine-learning-driven high-entropy alloy catalyst discovery to circumvent the scaling relation for CO2 reduction reaction","volume":"12","author":"Chen","year":"2022","journal-title":"ACS Catal."},{"key":"mlstadc0e1bib14","doi-asserted-by":"publisher","DOI":"10.1016\/j.actamat.2022.117924","article-title":"Efficient machine-learning model for fast assessment of elastic properties of high-entropy alloys","volume":"232","author":"Vazquez","year":"2022","journal-title":"Acta Mater."},{"key":"mlstadc0e1bib15","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1038\/s41524-022-00945-x","article-title":"Element-wise representations with ECNet for material property prediction and applications in high-entropy alloys","volume":"8","author":"Wang","year":"2022","journal-title":"npj Comput. Mater."},{"key":"mlstadc0e1bib16","doi-asserted-by":"publisher","DOI":"10.1103\/PRXEnergy.3.023006","article-title":"Learning molecular mixture property using chemistry-aware graph neural network","volume":"3","author":"Zhang","year":"2024","journal-title":"PRX Energy"},{"key":"mlstadc0e1bib17","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1021\/acs.jcim.3c01250","article-title":"Chemprop: a machine learning package for chemical property prediction","volume":"64","author":"Heid","year":"2024","journal-title":"J. Chem. Inf. Model."},{"key":"mlstadc0e1bib18","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1038\/s41524-021-00650-1","article-title":"Atomistic line graph neural network for improved materials property predictions","volume":"7","author":"Choudhary","year":"2021","journal-title":"npj Comput. Mater."},{"key":"mlstadc0e1bib19","doi-asserted-by":"publisher","first-page":"718","DOI":"10.1038\/s43588-022-00349-3","article-title":"A universal graph deep learning interatomic potential for the periodic table","volume":"2","author":"Chen","year":"2022","journal-title":"Nat. Comput. Sci."},{"key":"mlstadc0e1bib20","first-page":"pp 11423","article-title":"MACE: higher order equivariant message passing neural networks for fast and accurate force fields","volume":"vol 35","author":"Batatia","year":"2022"},{"key":"mlstadc0e1bib21","first-page":"pp 21260","article-title":"Efficient approximations of complete interatomic potentials for crystal property prediction","volume":"vol 202","author":"Lin","year":"2023"},{"key":"mlstadc0e1bib22","first-page":"pp 9377","article-title":"Equivariant message passing for the prediction of tensorial properties and molecular spectra","volume":"vol 139","author":"Sch\u00fctt","year":"2021"},{"key":"mlstadc0e1bib23","first-page":"pp 15066","article-title":"Periodic graph transformers for crystal material property prediction","volume":"vol 35","author":"Yan","year":"2022"},{"key":"mlstadc0e1bib24","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijmecsci.2022.107800","article-title":"Molecular dynamics simulations of tensile response for FeNiCrCoCu high-entropy alloy with voids","volume":"237","author":"Gao","year":"2023","journal-title":"Int. J. Mech. Sci."},{"key":"mlstadc0e1bib25","doi-asserted-by":"publisher","first-page":"15809","DOI":"10.1021\/acs.jpcc.3c03404","article-title":"Density functional theory-machine learning characterization of the adsorption energy of oxygen intermediates on high-entropy alloys made of earth-abundant metals","volume":"127","author":"Yuan","year":"2023","journal-title":"J. Phys. Chem. C"},{"key":"mlstadc0e1bib26","doi-asserted-by":"publisher","first-page":"2881","DOI":"10.1557\/jmr.2018.222","article-title":"Modeling the structure and thermodynamics of high-entropy alloys","volume":"33","author":"Widom","year":"2018","journal-title":"J. Mater. Res."},{"key":"mlstadc0e1bib27","doi-asserted-by":"publisher","DOI":"10.1016\/j.matdes.2024.112634","article-title":"Machine learning assisted design of high-entropy alloys with ultra-high microhardness and unexpected low density","volume":"238","author":"Zhao","year":"2024","journal-title":"Mater. Des."},{"key":"mlstadc0e1bib28","doi-asserted-by":"publisher","first-page":"3742","DOI":"10.1021\/acscatal.3c05017","article-title":"Supervised AI and deep neural networks to evaluate high-entropy alloys as reduction catalysts in aqueous environments","volume":"14","author":"Araujo","year":"2024","journal-title":"ACS Catal."},{"key":"mlstadc0e1bib29","article-title":"Deep sets","volume":"vol 30","author":"Zaheer","year":"2017"},{"key":"mlstadc0e1bib30","article-title":"Attention is all you need","volume":"vol 30","author":"Vaswani","year":"2017"},{"key":"mlstadc0e1bib31","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1038\/s41524-022-00779-7","article-title":"Composition design of high-entropy alloys with deep sets learning","volume":"8","author":"Zhang","year":"2022","journal-title":"npj Comput. Mater."},{"key":"mlstadc0e1bib32","first-page":"2825","article-title":"Scikit-learn: machine learning in Python","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"mlstadc0e1bib33","article-title":"Decoupled weight decay regularization","author":"Loshchilov","year":"2019"},{"key":"mlstadc0e1bib34","first-page":"pp 71","article-title":"Elasticity and viscoelasticity","author":"Meyers","year":"2008"},{"key":"mlstadc0e1bib35","doi-asserted-by":"publisher","first-page":"7283","DOI":"10.1038\/s41467-023-42992-y","article-title":"Exploiting redundancy in large materials datasets for efficient machine learning with less data","volume":"14","author":"Li","year":"2023","journal-title":"Nat. Commun."},{"key":"mlstadc0e1bib36","first-page":"pp 435","article-title":"Mechanical behavior of high-entropy alloys: a review","author":"Shang","year":"2021"},{"key":"mlstadc0e1bib37","doi-asserted-by":"publisher","first-page":"697","DOI":"10.1038\/s41586-023-06894-9","article-title":"Negative mixing enthalpy solid solutions deliver high strength and ductility","volume":"625","author":"An","year":"2024","journal-title":"Nature"},{"key":"mlstadc0e1bib38","doi-asserted-by":"publisher","DOI":"10.1002\/adma.201805295","article-title":"Heteroanionic materials by design: progress toward targeted properties","volume":"31","author":"Harada","year":"2019","journal-title":"Adv. Mater."},{"key":"mlstadc0e1bib39","doi-asserted-by":"publisher","first-page":"17317","DOI":"10.1021\/acs.inorgchem.3c02595","article-title":"Chemical and structural factors affecting the stability of Wadsley\u2013Roth block phases","volume":"62","author":"Saber","year":"2023","journal-title":"Inorg. Chem."},{"key":"mlstadc0e1bib40","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/j.matt.2019.06.013","article-title":"Deliberate deficiencies: expanding electronic function through non-stoichiometry","volume":"1","author":"Rondinelli","year":"2019","journal-title":"Matter"},{"key":"mlstadc0e1bib41","doi-asserted-by":"publisher","DOI":"10.1002\/adma.202402442","article-title":"Distinguishing elements at the sub-nanometer scale on the surface of a high entropy alloy","volume":"36","author":"Kim","year":"2024","journal-title":"Adv. Mater."},{"key":"mlstadc0e1bib42","doi-asserted-by":"publisher","DOI":"10.1016\/j.matdes.2022.110875","article-title":"Additive manufactured high entropy alloys: a review of the microstructure and properties","volume":"220","author":"Zhang","year":"2022","journal-title":"Mater. Des."},{"key":"mlstadc0e1bib43","author":"Biewald","year":"2020"},{"key":"mlstadc0e1bib44","first-page":"pp 4602","article-title":"Weisfeiler and Leman go neural: higher-order graph neural networks","volume":"vol 33","author":"Morris","year":"2019"}],"container-title":["Machine Learning: Science and Technology"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adc0e1","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adc0e1\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adc0e1","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adc0e1\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adc0e1\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adc0e1\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adc0e1\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adc0e1\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T20:46:37Z","timestamp":1743713197000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adc0e1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,3]]},"references-count":44,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,4,3]]},"published-print":{"date-parts":[[2025,6,30]]}},"URL":"https:\/\/doi.org\/10.1088\/2632-2153\/adc0e1","relation":{},"ISSN":["2632-2153"],"issn-type":[{"value":"2632-2153","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,3]]},"assertion":[{"value":"Graph representation of local environments for learning high-entropy alloy properties","name":"article_title","label":"Article Title"},{"value":"Machine Learning: Science and Technology","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2025 The Author(s). Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2024-12-01","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-03-14","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-04-03","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}