{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T22:46:39Z","timestamp":1776379599794,"version":"3.51.2"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,11,13]],"date-time":"2021-11-13T00:00:00Z","timestamp":1636761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,11,13]],"date-time":"2021-11-13T00:00:00Z","timestamp":1636761600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["OAC-1835690"],"award-info":[{"award-number":["OAC-1835690"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-SC0020310"],"award-info":[{"award-number":["DE-SC0020310"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2022,3]]},"DOI":"10.1007\/s00521-021-06616-0","type":"journal-article","created":{"date-parts":[[2021,11,13]],"date-time":"2021-11-13T07:02:36Z","timestamp":1636786956000},"page":"4625-4632","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Graph neural network for Hamiltonian-based material property prediction"],"prefix":"10.1007","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4639-1401","authenticated-orcid":false,"given":"Hexin","family":"Bai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Chu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jeng-Yuan","family":"Tsai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nathan","family":"Wilson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaofeng","family":"Qian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qimin","family":"Yan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haibin","family":"Ling","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,11,13]]},"reference":[{"issue":"1","key":"6616_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41524-016-0001-z","volume":"2","author":"WLA Agrawal","year":"2016","unstructured":"Agrawal WLA, Choudhary A, Wolverton C (2016) A general-purpose machine learning framework for predicting properties of inorganic materials. npj Comput Mater 2(1):1\u20137","journal-title":"npj Comput Mater"},{"key":"6616_CR2","doi-asserted-by":"publisher","first-page":"136403","DOI":"10.1103\/PhysRevLett.104.136403","volume":"104","author":"AP Bartok","year":"2010","unstructured":"Bartok AP, Payne MC, Kondor R, Csanyi G (2010) Gaussian approximation potentials: the accuracy of quantum mechanics without the electrons. Phys Rev Lett 104:136403","journal-title":"Phys Rev Lett"},{"key":"6616_CR3","doi-asserted-by":"publisher","first-page":"17930","DOI":"10.1039\/c1cp21668f","volume":"13","author":"J Behler","year":"2011","unstructured":"Behler J (2011) Neural network potential-energy surfaces in chemistry: a tool for large-scale simulations. Phys Chem Chem Phys 13:17930\u201317955","journal-title":"Phys Chem Chem Phys"},{"key":"6616_CR4","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1109\/MSP.2017.2693418","volume":"34","author":"MM Bronstein","year":"2017","unstructured":"Bronstein MM, Bruna J, LeCun Y, Szlam A, Vandergheynst P (2017) Geometric deep learning: going beyond euclidean data. IEEE Sig Process Mag 34:18\u201342","journal-title":"IEEE Sig Process Mag"},{"key":"6616_CR5","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1038\/s41524-019-0162-7","volume":"5","author":"A Chandrasekaran","year":"2019","unstructured":"Chandrasekaran A, Kamal D, Batra R, Kim C, Chen L, Ramprasad R (2019) Solving the electronic structure problem with machine learning. npj Comput Mater 5:22","journal-title":"npj Comput Mater"},{"key":"6616_CR6","doi-asserted-by":"publisher","first-page":"135503","DOI":"10.1103\/PhysRevLett.91.135503","volume":"91","author":"S Curtarolo","year":"2003","unstructured":"Curtarolo S, Morgan D, Persson K, Rodgers J, Ceder G (2003) Predicting crystal structures with data mining of quantum calculations. Phys Rev Lett 91:135503","journal-title":"Phys Rev Lett"},{"key":"6616_CR7","unstructured":"Defferrard M and Bresson X and Vandergheynst P (2016) Convolutional neural networks on graphs with fast localized spectral filtering. Adv Neural Inform Process Syste 3844 \u2013 3852"},{"key":"6616_CR8","unstructured":"Dwivedi VP and Joshi CK and Laurent T et al. (2020) Benchmarking graph neural networks 5:188 \u2013 200"},{"key":"6616_CR9","unstructured":"Fey M and Lenssen JE (2019) Fast graph representation learning with PyTorch Geometric"},{"key":"6616_CR10","doi-asserted-by":"publisher","first-page":"105503","DOI":"10.1103\/PhysRevLett.114.105503","volume":"114","author":"LM Ghiringhelli","year":"2015","unstructured":"Ghiringhelli LM, Vybiral J, Levchenko SV, Draxl C, Scheffler M (2015) Big data of materials science: critical role of the descriptor. Phys Rev Lett 114:105503","journal-title":"Phys Rev Lett"},{"key":"6616_CR11","unstructured":"Gilmer J and Schoenholz SS and Riley PF et al. (2017) Neural message passing for quantum chemistry. ICML, 1263 \u2013 1272"},{"key":"6616_CR12","unstructured":"Gu Q, Zhang L, and Feng J (2020) Neural network representation of electronic structure from ab initio molecular dynamics"},{"key":"6616_CR13","unstructured":"Hamilton WL, Ying R, and Leskovec J (2017) Inductive representation learning on large graphs"},{"key":"6616_CR14","doi-asserted-by":"crossref","unstructured":"Hansen K and Montavon G and Biegler et al. (2013) Assessment and validation of machine learning methods for predicting molecular atomization energies. J Chem Theory Comput 9:3404 \u2013 3419","DOI":"10.1021\/ct400195d"},{"key":"6616_CR15","doi-asserted-by":"publisher","first-page":"3762","DOI":"10.1021\/cm100795d","volume":"22","author":"G Hautier","year":"2010","unstructured":"Hautier G, Fischer CC, Jain A, Mueller T, Ceder G (2010) Finding nature\u2019s missing ternary oxide compounds using machine learning and density functional theory. Chem Mater 22:3762\u20133767","journal-title":"Chem Mater"},{"key":"6616_CR16","unstructured":"Henaff M and Bruna J and LeCun Y (2015) Deep convolutional networks on graph-structured data"},{"key":"6616_CR17","doi-asserted-by":"crossref","unstructured":"Anubhav J, Ping OS, Hautier Geoffroy C et al (2013) Commentary: the materials project: a materials genome approach to accelerating materials innovation. APL Mater 1:011002","DOI":"10.1063\/1.4812323"},{"key":"6616_CR18","doi-asserted-by":"publisher","first-page":"011002","DOI":"10.1063\/1.4812323","volume":"1","author":"A Jain","year":"2013","unstructured":"Jain A, Ong SP, Hautier G, Chen W et al (2013) Commentary: the materials project: a materials genome approach to accelerating materials innovation. Apl Mater 1:011002","journal-title":"Apl Mater"},{"key":"6616_CR19","unstructured":"Kipf TN and Welling M (2016) Semi-supervised classification with graph convolutional networks. ICLR"},{"key":"6616_CR20","unstructured":"Krizhevsky A and Sutskever I and Hinton GE (2012) Imagenet classification with deep convolutional neural networks. Adv Neural Inform Process Syst, 1097\u20131105"},{"key":"6616_CR21","doi-asserted-by":"publisher","first-page":"2278","DOI":"10.1109\/5.726791","volume":"86","author":"Y LeCun","year":"2008","unstructured":"LeCun Y, Bottou L, Bengio Y, Haffner P (2008) Gradient-based learning applied to document recognition. Proc IEEE 86:2278\u20132324","journal-title":"Proc IEEE"},{"issue":"11","key":"6616_CR22","doi-asserted-by":"publisher","first-page":"115104","DOI":"10.1103\/PhysRevB.93.115104","volume":"93","author":"J Lee","year":"2016","unstructured":"Lee J, Seko A, Shitara K, Nakayama K, Tanaka I (2016) Prediction model of band gap for inorganic compounds by combination of density functional theory calculations and machine learning techniques. Phys Rev B 93(11):115104","journal-title":"Phys Rev B"},{"key":"6616_CR23","doi-asserted-by":"publisher","first-page":"115104","DOI":"10.1103\/PhysRevB.93.115104","volume":"93","author":"J Lee","year":"2016","unstructured":"Lee J, Seko A, Shitara K, Nakayama K, Tanaka I (2016) Prediction model of band gap for inorganic compounds by combination of density functional theory calculations and machine learning techniques. Phys Rev B 93:115104","journal-title":"Phys Rev B"},{"key":"6616_CR24","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1002\/sam.10034","volume":"1","author":"R LeSar","year":"2009","unstructured":"LeSar R (2009) Materials informatics: an emerging technology for materials development. Stat Anal Data Min 1:372\u2013374","journal-title":"Stat Anal Data Min"},{"key":"6616_CR25","unstructured":"Li H, Wang Z, Zou N, Ye M, Duan W, and Xu Y (2021) Deep neural network representation of density functional theory hamiltonian"},{"key":"6616_CR26","doi-asserted-by":"publisher","first-page":"072217","DOI":"10.1063\/1.2755487","volume":"78","author":"CJ Long","year":"2007","unstructured":"Long CJ, Hattrick-Simpers J, Murakami M, Srivastava RC, Takeuchi I, Karen VL, Li X (2007) Rapid structural mapping of ternary metallic alloy systems using the combinatorial approach and cluster analysis. Rev Sci Instrum 78:072217","journal-title":"Rev Sci Instrum"},{"key":"6616_CR27","doi-asserted-by":"publisher","first-page":"12847","DOI":"10.1103\/PhysRevB.56.12847","volume":"56","author":"N Marzari","year":"1997","unstructured":"Marzari N, Vanderbilt D (1997) Maximally localized generalized Wannier functions for composite energy bands. Phys Rev B 56:12847\u201312865","journal-title":"Phys Rev B"},{"key":"6616_CR28","doi-asserted-by":"publisher","first-page":"7356","DOI":"10.1021\/jp401225b","volume":"117","author":"T Morawietz","year":"2013","unstructured":"Morawietz T, Behler J (2013) A density-functional theory-based neural network potential for water clusters including van der waals corrections. J Phys Chem A 117:7356\u20137366","journal-title":"J Phys Chem A"},{"key":"6616_CR29","doi-asserted-by":"publisher","first-page":"2309","DOI":"10.1016\/j.cpc.2014.05.003","volume":"185","author":"AA Mostofi","year":"2014","unstructured":"Mostofi AA, Yates JR, Pizzi G et al (2014) An updated version of wannier90: a tool for obtaining maximally-localised Wannier functions. Comput Phys Commun 185:2309\u20132310","journal-title":"Comput Phys Commun"},{"issue":"7\u20138","key":"6616_CR30","doi-asserted-by":"publisher","first-page":"1900023","DOI":"10.1002\/qute.201900023","volume":"2","author":"B Olsthoorn","year":"2019","unstructured":"Olsthoorn B, Matthias Geilhufe R, Borysov SS, Balatsky AV (2019) Band gap prediction for large organic crystal structures with machine learning. Adv Quant Technol 2(7\u20138):1900023","journal-title":"Adv Quant Technol"},{"key":"6616_CR31","unstructured":"Peter W and Hamrick JB and Bapst V and Sanchez-Gonzalez A et al. (2018) Relational inductive biases, deep learning, and graph networks"},{"issue":"1","key":"6616_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/srep02810","volume":"3","author":"G Pilania","year":"2013","unstructured":"Pilania G, Wang C, Jiang X, Rajasekaran S, Ramprasad R (2013) Accelerating materials property predictions using machine learning. Sci Rep 3(1):1\u20136","journal-title":"Sci Rep"},{"key":"6616_CR33","doi-asserted-by":"publisher","first-page":"19375","DOI":"10.1038\/srep19375","volume":"6","author":"G Pilania","year":"2016","unstructured":"Pilania G, Mannodi-Kanakkithodi A, Uberuaga BP, Ramprasad R, Gubernatis JE, Lookman T (2016) Machine learning bandgaps of double perovskites. Sci Rep 6:19375","journal-title":"Sci Rep"},{"issue":"1","key":"6616_CR34","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/srep19375","volume":"6","author":"G Pilania","year":"2016","unstructured":"Pilania G, Arun Mannodi-Kanakkithodi BP, Uberuaga Rampi Ramprasad, Gubernatis JE, Lookman T (2016) Machine learning bandgaps of double perovskites. Sci Rep 6(1):1\u201310","journal-title":"Sci Rep"},{"key":"6616_CR35","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1016\/j.commatsci.2016.12.004","volume":"129","author":"G Pilania","year":"2017","unstructured":"Pilania G, Gubernatis JE, Lookman T (2017) Multi-fidelity machine learning models for accurate bandgap predictions of solids. Comput Mater Sci 129:156\u2013163","journal-title":"Comput Mater Sci"},{"key":"6616_CR36","doi-asserted-by":"publisher","first-page":"245112","DOI":"10.1103\/PhysRevB.78.245112","volume":"78","author":"X Qian","year":"2008","unstructured":"Qian X, Li J, Qi L et al (2008) Quasiatomic orbitals for ab initio tight-binding analysis. Phys Rev B 78:245112","journal-title":"Phys Rev B"},{"key":"6616_CR37","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1016\/S1369-7021(05)71123-8","volume":"8","author":"K Rajan","year":"2005","unstructured":"Rajan K (2005) Materials informatics. Mater Today 8:38\u201345","journal-title":"Mater Today"},{"issue":"12","key":"6616_CR38","doi-asserted-by":"publisher","first-page":"4031","DOI":"10.1021\/acs.chemmater.8b00686","volume":"30","author":"AC Rajan","year":"2018","unstructured":"Rajan AC, Mishra A, Satsangi S, Vaish R, Mizuseki H, Lee K-R, Singh AK (2018) Machine-learning-assisted accurate band gap predictions of functionalized MXene. Chem Mater 30(12):4031\u20134038","journal-title":"Chem Mater"},{"key":"6616_CR39","doi-asserted-by":"publisher","first-page":"4117","DOI":"10.1073\/pnas.1818555116","volume":"116","author":"Z Shi","year":"2019","unstructured":"Shi Z, Tsymbalov E, Dao M, Suresh S, Shapeev A, Li J (2019) Deep elastic strain engineering of bandgap through machine learning. Proc Natll Acad Sci 116:4117","journal-title":"Proc Natll Acad Sci"},{"key":"6616_CR40","doi-asserted-by":"publisher","first-page":"253002","DOI":"10.1103\/PhysRevLett.108.253002","volume":"108","author":"JC Snyder","year":"2012","unstructured":"Snyder JC, Rupp M, Hansen K, Muller KR, Burke K (2012) Finding density functionals with machine learning. Phys Rev Lett 108:253002","journal-title":"Phys Rev Lett"},{"key":"6616_CR41","doi-asserted-by":"crossref","unstructured":"Wu Z, Pan S, Chen F, Long G, Zhang C, and Yu Philip S (2020) A comprehensive survey on graph neural networks. IEEE Trans Neural Netw Learn sSyst","DOI":"10.1109\/TNNLS.2020.2978386"},{"issue":"1","key":"6616_CR42","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41524-021-00601-w","volume":"7","author":"WZS Ye","year":"2021","unstructured":"Ye WZS, Wang H, He J, Huang Q, Chang S (2021) Machine learning method for tight-binding Hamiltonian parameterization from ab-initio band structure. npj Comput Mater 7(1):1\u201310","journal-title":"npj Comput Mater"},{"key":"6616_CR43","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1038\/s41524-019-0165-4","volume":"5","author":"D Yuan","year":"2019","unstructured":"Yuan D, Chuhan W, Zhang C, Liu Y, Cheng J, Lin J (2019) Bandgap prediction by deep learning in configurationally hybridized graphene and boron nitride. npj Comput Mater 5:26","journal-title":"npj Comput Mater"},{"key":"6616_CR44","unstructured":"Zhou J, Cui G, Zhang Z et al. (2018) Graph neural networks: a review of methods and applications"},{"issue":"7","key":"6616_CR45","doi-asserted-by":"publisher","first-page":"1668","DOI":"10.1021\/acs.jpclett.8b00124","volume":"9","author":"Y Zhuo","year":"2018","unstructured":"Zhuo Y, Tehrani AM, Brgoch J (2018) Predicting the band gaps of inorganic solids by machine learning. The J Phys Chem Lett 9(7):1668\u20131673","journal-title":"The J Phys Chem Lett"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-021-06616-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-021-06616-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-021-06616-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,2]],"date-time":"2022-03-02T16:17:17Z","timestamp":1646237837000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-021-06616-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,13]]},"references-count":45,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2022,3]]}},"alternative-id":["6616"],"URL":"https:\/\/doi.org\/10.1007\/s00521-021-06616-0","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,13]]},"assertion":[{"value":"2 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 October 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 November 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that there are no conflicts of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}