{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T19:12:13Z","timestamp":1780341133705,"version":"3.54.1"},"reference-count":78,"publisher":"Springer Science and Business Media LLC","issue":"18","license":[{"start":{"date-parts":[[2019,9,18]],"date-time":"2019-09-18T00:00:00Z","timestamp":1568764800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,9,18]],"date-time":"2019-09-18T00:00:00Z","timestamp":1568764800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2020,9]]},"DOI":"10.1007\/s00521-019-04480-7","type":"journal-article","created":{"date-parts":[[2019,9,18]],"date-time":"2019-09-18T18:06:51Z","timestamp":1568830011000},"page":"14359-14373","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["A machine-learning-enhanced hierarchical multiscale method for bridging from molecular dynamics to continua"],"prefix":"10.1007","volume":"32","author":[{"given":"Shaoping","family":"Xiao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Renjie","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhen","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Siamak","family":"Attarian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kaj-Mikael","family":"Bj\u00f6rk","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amaury","family":"Lendasse","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,9,18]]},"reference":[{"issue":"6","key":"4480_CR1","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1063\/1.168756","volume":"12","author":"FF Abraham","year":"1998","unstructured":"Abraham FF, Broughton JQ, Bernstein N, Kaxiras E (1998) Spanning the length scales in dynamic simulation. Comput Phys 12(6):538\u2013546","journal-title":"Comput Phys"},{"key":"4480_CR2","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.cma.2017.06.033","volume":"325","author":"A Ademiloye","year":"2017","unstructured":"Ademiloye A, Zhang L, Liew K (2017) Atomistic-continuum model for probing the biomechanical properties of human erythrocyte membrane under extreme conditions. Comput Methods Appl Mech Eng 325:22\u201336","journal-title":"Comput Methods Appl Mech Eng"},{"key":"4480_CR3","doi-asserted-by":"crossref","first-page":"1011","DOI":"10.1109\/ACCESS.2015.2450498","volume":"3","author":"A Akusok","year":"2015","unstructured":"Akusok A, Bjork KM, Miche Y, Lendasse A (2015) High-performance extreme learning machines: a complete toolbox for big data applications. IEEE Access 3:1011\u20131025","journal-title":"IEEE Access"},{"issue":"3\u20136","key":"4480_CR4","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/S0167-6636(02)00270-3","volume":"35","author":"M Arroyo","year":"2003","unstructured":"Arroyo M, Belytschko T (2003) A finite deformation membrane based on inter-atomic potentials for the transverse mechanics of nanotubes. Mech Mater 35(3\u20136):193\u2013215","journal-title":"Mech Mater"},{"key":"4480_CR5","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.commatsci.2015.11.047","volume":"114","author":"N Artrith","year":"2016","unstructured":"Artrith N, Urban A (2016) An implementation of artificial neural-network potentials for atomistic materials simulations: performance for TiO 2. Comput Mater Sci 114:135\u2013150","journal-title":"Comput Mater Sci"},{"issue":"5","key":"4480_CR6","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1615\/IntJMultCompEng.v5.i5.30","volume":"5","author":"S Badia","year":"2007","unstructured":"Badia S, Bochev P, Lehoucq R, Parks ML, Fish J, Nuggehally MA, Gunzburger M (2007) A Force-Based Blending Model forAtomistic-to-Continuum Coupling. Int J Multiscale Comput Eng 5(5):387\u2013406","journal-title":"Int J Multiscale Comput Eng"},{"key":"4480_CR7","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.commatsci.2014.10.032","volume":"98","author":"E B\u00e9lisle","year":"2015","unstructured":"B\u00e9lisle E, Huang Z, Le Digabel S, Gheribi AE (2015) Evaluation of machine learning interpolation techniques for prediction of physical properties. Comput Mater Sci 98:170\u2013177","journal-title":"Comput Mater Sci"},{"issue":"3","key":"4480_CR8","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/s00466-015-1177-7","volume":"56","author":"MJ Bogdanor","year":"2015","unstructured":"Bogdanor MJ, Oskay C, Clay SB (2015) Multiscale modeling of failure in composites under model parameter uncertainty. Comput Mech 56(3):389\u2013404","journal-title":"Comput Mech"},{"issue":"4","key":"4480_CR9","doi-asserted-by":"crossref","first-page":"043603","DOI":"10.1103\/PhysRevMaterials.1.043603","volume":"1","author":"C Chen","year":"2017","unstructured":"Chen C, Deng Z, Tran R, Tang H, Chu IH, Ong SP (2017) Accurate force field for molybdenum by machine learning large materials data. Phys Rev Mater 1(4):043603","journal-title":"Phys Rev Mater"},{"issue":"2","key":"4480_CR10","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1109\/72.80341","volume":"2","author":"S Chen","year":"1991","unstructured":"Chen S, Cowan C, Grant P (1991) Orthogonal least squares learning algorithm for radial basis function networks. IEEE Trans Neural Netw 2(2):302\u2013309","journal-title":"IEEE Trans Neural Netw"},{"issue":"2","key":"4480_CR11","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1109\/72.991427","volume":"13","author":"Chih-Wei Hsu","year":"2002","unstructured":"Hsu Chih-Wei, Lin Chih-Jen (2002) A comparison of methods for multiclass support vector machines. IEEE Trans Neural Netw 13(2):415\u2013425","journal-title":"IEEE Trans Neural Netw"},{"issue":"3","key":"4480_CR12","first-page":"273","volume":"20","author":"C Cortes","year":"1995","unstructured":"Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273\u2013297","journal-title":"Mach Learn"},{"issue":"3","key":"4480_CR13","doi-asserted-by":"crossref","first-page":"R33","DOI":"10.1088\/0965-0393\/11\/3\/201","volume":"11","author":"WA Curtin","year":"2003","unstructured":"Curtin WA, Miller RE (2003) Atomistic\/continuum coupling in computational materials science. Modell Simul Mater Sci Eng 11(3):R33\u2013R68","journal-title":"Modell Simul Mater Sci Eng"},{"key":"4480_CR14","doi-asserted-by":"crossref","unstructured":"Ericksen J (1984) The Cauchy and Born hypotheses for crystals. In: Phase Transformations and Material Instabilities in Solids. Elsevier, pp 61\u201377","DOI":"10.1016\/B978-0-12-309770-5.50008-4"},{"issue":"5","key":"4480_CR15","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1007\/s11051-006-9090-9","volume":"8","author":"J Fish","year":"2006","unstructured":"Fish J (2006) Bridging the scales in nano engineering and science. J Nanopart Res 8(5):577\u2013594","journal-title":"J Nanopart Res"},{"key":"4480_CR16","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.euromechsol.2017.11.007","volume":"69","author":"F Fritzen","year":"2018","unstructured":"Fritzen F, Kunc O (2018) Two-stage data-driven homogenization for nonlinear solids using a reduced order model. Eur J Mech A Solids 69:201\u2013220","journal-title":"Eur J Mech A Solids"},{"key":"4480_CR17","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.ijfatigue.2017.11.005","volume":"108","author":"MA Ghaffari","year":"2018","unstructured":"Ghaffari MA, Zhang Y, Xiao S (2018) Multiscale modeling and simulation of rolling contact fatigue. Int J Fatigue 108:9\u201317","journal-title":"Int J Fatigue"},{"issue":"21","key":"4480_CR18","doi-asserted-by":"crossref","first-page":"214302","DOI":"10.1103\/PhysRevB.95.214302","volume":"95","author":"A Glielmo","year":"2017","unstructured":"Glielmo A, Sollich P, De Vita A (2017) Accurate interatomic force fields via machine learning with covariant kernels. Phys Rev B 95(21):214302","journal-title":"Phys Rev B"},{"key":"4480_CR19","volume-title":"Deep learning","author":"I Goodfellow","year":"2016","unstructured":"Goodfellow I, Bengio Y, Courville A (2016) Deep learning. MIT Press, Cambridge"},{"key":"4480_CR20","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.commatsci.2017.04.019","volume":"135","author":"K Grabowski","year":"2017","unstructured":"Grabowski K, Zbyrad P, Uhl T, Staszewski WJ, Packo P (2017) Multiscale electro-mechanical modeling of carbon nanotube composites. Comput Mater Sci 135:169\u2013180","journal-title":"Comput Mater Sci"},{"issue":"4\u20135","key":"4480_CR21","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1002\/nme.3112","volume":"86","author":"R Gracie","year":"2011","unstructured":"Gracie R, Belytschko T (2011) An adaptive concurrent multiscale method for the dynamic simulation of dislocations. Int J Numer Meth Eng 86(4\u20135):575\u2013597","journal-title":"Int J Numer Meth Eng"},{"key":"4480_CR22","unstructured":"Huang G-B, Zhu Q-Y, Siew C-K (2004) Extreme learning machine: a new learning scheme of feedforward neural networks. In: IEEE international joint conference on neural networks (IEEE Cat. No.04CH37541), vol\u00a02. IEEE, pp 985\u2013990"},{"key":"4480_CR23","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.actamat.2015.02.045","volume":"91","author":"A Gupta","year":"2015","unstructured":"Gupta A, Cecen A, Goyal S, Singh AK, Kalidindi SR (2015) Structure-property linkages using a data science approach: application to a non-metallic inclusion\/steel composite system. Acta Mater 91:239\u2013254","journal-title":"Acta Mater"},{"issue":"12","key":"4480_CR24","doi-asserted-by":"crossref","first-page":"2326","DOI":"10.1021\/acs.jpclett.5b00831","volume":"6","author":"K Hansen","year":"2015","unstructured":"Hansen K, Biegler F, Ramakrishnan R, Pronobis W, von Lilienfeld OA, M\u00fcller KR, Tkatchenko A (2015) Machine learning predictions of molecular properties: accurate many-body potentials and nonlocality in chemical space. J Phys Chem Lett 6(12):2326\u20132331","journal-title":"J Phys Chem Lett"},{"issue":"5","key":"4480_CR25","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/0893-6080(89)90020-8","volume":"2","author":"K Hornik","year":"1989","unstructured":"Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359\u2013366","journal-title":"Neural Netw"},{"key":"4480_CR26","doi-asserted-by":"crossref","unstructured":"Hu R, Roshdibenam V, Johnson HJ, Eirola E, Akusok A, Miche Y, Bj\u00f6rk KM, Lendasse A (2018) Elm-som: A continuous self-organizing map for visualization. In: International joint conference on neural networks (IJCNN). IEEE, pp 1\u20138","DOI":"10.1109\/IJCNN.2018.8489268"},{"key":"4480_CR27","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.neunet.2014.10.001","volume":"61","author":"G Huang","year":"2015","unstructured":"Huang G, Huang GB, Song S, You K (2015) Trends in extreme learning machines: a review. Neural Netw 61:32\u201348","journal-title":"Neural Netw"},{"issue":"3","key":"4480_CR28","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1007\/s12559-014-9255-2","volume":"6","author":"GB Huang","year":"2014","unstructured":"Huang GB (2014) An insight into extreme learning machines: random neurons random features and kernels. Cogn Comput 6(3):376\u2013390","journal-title":"Cogn Comput"},{"key":"4480_CR29","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s12559-015-9333-0","volume":"7","author":"GB Huang","year":"2015","unstructured":"Huang GB (2015) What are extreme learning machines? Filling the gap between Frank Rosenblatt\u2019s dream and John von Neumann\u2019s puzzle. Cogn Comput 7:263\u2013278","journal-title":"Cogn Comput"},{"issue":"1\u20133","key":"4480_CR30","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.neucom.2005.12.126","volume":"70","author":"GB Huang","year":"2006","unstructured":"Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70(1\u20133):489\u2013501","journal-title":"Neurocomputing"},{"issue":"1","key":"4480_CR31","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s11831-016-9197-9","volume":"25","author":"R Iba\u00f1ez","year":"2018","unstructured":"Iba\u00f1ez R, Abisset-Chavanne E, Aguado JV, Gonzalez D, Cueto E, Chinesta F (2018) A manifold learning approach to data-driven computational elasticity and inelasticity. Arch Comput Methods Eng 25(1):47\u201357","journal-title":"Arch Comput Methods Eng"},{"issue":"5","key":"4480_CR32","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1007\/s00466-017-1440-1","volume":"60","author":"R Iba\u00f1ez","year":"2017","unstructured":"Iba\u00f1ez R, Borzacchiello D, Aguado JV, Abisset-Chavanne E, Cueto E, Ladeveze P, Chinesta F (2017) Data-driven non-linear elasticity: constitutive manifold construction and problem discretization. Comput Mech 60(5):813\u2013826","journal-title":"Comput Mech"},{"issue":"6","key":"4480_CR33","doi-asserted-by":"crossref","first-page":"1320","DOI":"10.1109\/72.471375","volume":"6","author":"B Igelnik","year":"1995","unstructured":"Igelnik B, Pao YH (1995) Stochastic choice of basis functions in adaptive function approximation and the functional-link net. IEEE Trans Neural Networks 6(6):1320\u20131329","journal-title":"IEEE Trans Neural Networks"},{"issue":"4","key":"4480_CR34","doi-asserted-by":"crossref","first-page":"e52","DOI":"10.1002\/rcs.1493","volume":"9","author":"A Jahya","year":"2013","unstructured":"Jahya A, Herink M, Misra S (2013) A framework for predicting three-dimensional prostate deformation in real time. Int J Med Robot Comput Assist Surg 9(4):e52\u2013e60","journal-title":"Int J Med Robot Comput Assist Surg"},{"issue":"08","key":"4480_CR35","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1557\/jmr.2016.80","volume":"31","author":"A Jain","year":"2016","unstructured":"Jain A, Hautier G, Ong SP, Persson K (2016) New opportunities for materials informatics: resources and data mining techniques for uncovering hidden relationships. J Mater Res 31(08):977\u2013994","journal-title":"J Mater Res"},{"issue":"2","key":"4480_CR36","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1177\/1056789516688747","volume":"26","author":"S Jiang","year":"2017","unstructured":"Jiang S, Tao J, Sewell TD, Chen Z (2017) Hierarchical multiscale simulations of crystalline $$\\beta$$-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine ($$\\beta$$-HMX): Generalized interpolation material point method simulations of brittle fracture using an elastodamage model derived from molecular dynamics. Int J Damage Mech 26(2):293\u2013313","journal-title":"Int J Damage Mech"},{"issue":"4","key":"4480_CR37","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1007\/s11837-011-0057-7","volume":"63","author":"SR Kalidindi","year":"2011","unstructured":"Kalidindi SR, Niezgoda SR, Salem AA (2011) Microstructure informatics using higher-order statistics and efficient data-mining protocols. JOM 63(4):34\u201341","journal-title":"JOM"},{"issue":"17","key":"4480_CR38","doi-asserted-by":"crossref","first-page":"11085","DOI":"10.1103\/PhysRevB.58.11085","volume":"58","author":"CL Kelchner","year":"1998","unstructured":"Kelchner CL, Plimpton SJ, Hamilton JC (1998) Dislocation nucleation and defect structure during surface indentation. Phys Rev B 58(17):11085\u201311088","journal-title":"Phys Rev B"},{"issue":"12","key":"4480_CR39","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1002\/nme.4953","volume":"104","author":"BA Le","year":"2015","unstructured":"Le BA, Yvonnet J, He QC (2015) Computational homogenization of nonlinear elastic materials using neural networks. Int J Numer Meth Eng 104(12):1061\u20131084","journal-title":"Int J Numer Meth Eng"},{"key":"#cr-split#-4480_CR40.1","doi-asserted-by":"crossref","unstructured":"Lendasse A, Wertz V, Verleysen M (2003) Model selection with cross-validations and bootstraps-application to time series prediction with RBFN models. In: Xu L, Kaynak O, Alpaydin E, Oja E","DOI":"10.1007\/3-540-44989-2_68"},{"key":"#cr-split#-4480_CR40.2","unstructured":"(ed) Artificial neural networks and neural information processing-ICANN\/ICONIP 2003. Lecture notes in computer science, vol 2714. Springer, Berlin, pp 573-580"},{"issue":"17\u201320","key":"4480_CR41","doi-asserted-by":"crossref","first-page":"1529","DOI":"10.1016\/j.cma.2003.12.008","volume":"193","author":"W Liu","year":"2004","unstructured":"Liu W, Karpov E, Zhang S, Park H (2004) An introduction to computational nanomechanics and materials. Comput Methods Appl Mech Eng 193(17\u201320):1529\u20131578","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"8\u20139","key":"4480_CR42","first-page":"1039","volume":"83","author":"WK Liu","year":"2010","unstructured":"Liu WK, Qian D, Gonella S, Li S, Chen W, Chirputkar S (2010) Multiscale methods for mechanical science of complex materials: Bridging from quantum to stochastic multiresolution continuum. Int J Numer Meth Eng 83(8\u20139):1039\u20131080","journal-title":"Int J Numer Meth Eng"},{"key":"4480_CR43","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.cma.2016.04.004","volume":"306","author":"Z Liu","year":"2016","unstructured":"Liu Z, Bessa M, Liu WK (2016) Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials. Comput Methods Appl Mech Eng 306:319\u2013341","journal-title":"Comput Methods Appl Mech Eng"},{"key":"4480_CR44","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/j.cma.2017.11.005","volume":"330","author":"Z Liu","year":"2018","unstructured":"Liu Z, Fleming M, Liu WK (2018) Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials. Comput Methods Appl Mech Eng 330:547\u2013577","journal-title":"Comput Methods Appl Mech Eng"},{"key":"4480_CR45","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1016\/j.eswa.2016.11.037","volume":"71","author":"D Lorente","year":"2017","unstructured":"Lorente D, Mart\u00ednez-Mart\u00ednez F, Rup\u00e9rez M, Lago M, Mart\u00ednez-Sober M, Escandell-Montero P, Mart\u00ednez-Mart\u00ednez J, Mart\u00ednez-Sanchis S, Serrano-L\u00f3pez A, Monserrat C, Mart\u00edn-Guerrero J (2017) A framework for modelling the biomechanical behaviour of the human liver during breathing in real time using machine learning. Expert Syst Appl 71:342\u2013357","journal-title":"Expert Syst Appl"},{"key":"4480_CR46","unstructured":"Marcus G (2018) Deep learning: a critical appraisal. arXiv preprint \narXiv:1801.00631"},{"key":"4480_CR47","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.jcp.2016.10.070","volume":"330","author":"K Matou\u0161","year":"2017","unstructured":"Matou\u0161 K, Geers MG, Kouznetsova VG, Gillman A (2017) A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials. J Comput Phys 330:192\u2013220","journal-title":"J Comput Phys"},{"key":"4480_CR48","volume-title":"Integrated design of multiscale, multifunctional materials and products","author":"DL McDowell","year":"2010","unstructured":"McDowell DL, Panchal J, Choi HJ, Seepersad C, Allen J, Mistree F (2010) Integrated design of multiscale, multifunctional materials and products, 1st edn. Butterworth-Heinemann, Oxford","edition":"1"},{"key":"4480_CR49","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.jmps.2017.03.004","volume":"103","author":"Q Meng","year":"2017","unstructured":"Meng Q, Li B, Li T, Feng XQ (2017) A multiscale crack-bridging model of cellulose nanopaper. J Mech Phys Solids 103:22\u201339","journal-title":"J Mech Phys Solids"},{"issue":"4\u20136","key":"4480_CR50","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.cplett.2004.04.054","volume":"390","author":"SL Mielke","year":"2004","unstructured":"Mielke SL, Troya D, Zhang S, Li JL, Xiao S, Car R, Ruoff RS, Schatz GC, Belytschko T (2004) The role of vacancy defects and holes in the fracture of carbon nanotubes. Chem Phys Lett 390(4\u20136):413\u2013420","journal-title":"Chem Phys Lett"},{"issue":"5","key":"4480_CR51","doi-asserted-by":"crossref","first-page":"053001","DOI":"10.1088\/0965-0393\/17\/5\/053001","volume":"17","author":"RE Miller","year":"2009","unstructured":"Miller RE, Tadmor EB (2009) A unified framework and performance benchmark of fourteen multiscale atomistic\/continuum coupling methods. Modell Simul Mater Sci Eng 17(5):053001","journal-title":"Modell Simul Mater Sci Eng"},{"issue":"5","key":"4480_CR52","doi-asserted-by":"crossref","first-page":"3393","DOI":"10.1103\/PhysRevB.59.3393","volume":"59","author":"Y Mishin","year":"1999","unstructured":"Mishin Y, Farkas D, Mehl MJ, Papaconstantopoulos DA (1999) Interatomic potentials for monoatomic metals from experimental data and ab initio calculations. Phys Rev B 59(5):3393\u20133407","journal-title":"Phys Rev B"},{"issue":"1","key":"4480_CR53","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1006\/jcph.1995.1039","volume":"117","author":"S Plimpton","year":"1995","unstructured":"Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117(1):1\u201319","journal-title":"J Comput Phys"},{"key":"4480_CR54","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/j.cma.2017.03.021","volume":"320","author":"MM Rahman","year":"2017","unstructured":"Rahman MM, Feng Y, Yankeelov TE, Oden JT (2017) A fully coupled space-time multiscale modeling framework for predicting tumor growth. Comput Methods Appl Mech Eng 320:261\u2013286","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"3","key":"4480_CR55","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/S0954-1810(98)00021-1","volume":"13","author":"Y Reich","year":"1999","unstructured":"Reich Y, Barai S (1999) Evaluating machine learning models for engineering problems. Artif Intell Eng 13(3):257\u2013272","journal-title":"Artif Intell Eng"},{"issue":"6","key":"4480_CR56","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1037\/h0042519","volume":"65","author":"F Rosenblatt","year":"1958","unstructured":"Rosenblatt F (1958) The perceptron: a probabilistic model for information storage and organization in the brain. Psychol Rev 65(6):386\u2013408","journal-title":"Psychol Rev"},{"issue":"3","key":"4480_CR57","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1023\/B:STCO.0000035301.49549.88","volume":"14","author":"AJ Smola","year":"2004","unstructured":"Smola AJ, Sch\u00f6lkopf B (2004) A tutorial on support vector regression. Stat Comput 14(3):199\u2013222","journal-title":"Stat Comput"},{"issue":"6","key":"4480_CR58","doi-asserted-by":"crossref","first-page":"868","DOI":"10.1002\/nme.1652","volume":"67","author":"JH Song","year":"2006","unstructured":"Song JH, Areias PMA, Belytschko T (2006) A method for dynamic crack and shear band propagation with phantom nodes. Int J Numer Meth Eng 67(6):868\u2013893","journal-title":"Int J Numer Meth Eng"},{"key":"4480_CR59","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1016\/j.carbon.2015.07.051","volume":"94","author":"N Subramanian","year":"2015","unstructured":"Subramanian N, Rai A, Chattopadhyay A (2015) Atomistically informed stochastic multiscale model to predict the behavior of carbon nanotube-enhanced nanocomposites. Carbon 94:661\u2013672","journal-title":"Carbon"},{"issue":"1\u20132","key":"4480_CR60","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1016\/S0020-7683(99)00095-5","volume":"37","author":"E Tadmor","year":"2000","unstructured":"Tadmor E, Phillips R, Ortiz M (2000) Hierarchical modeling in the mechanics of materials. Int J Solids Struct 37(1\u20132):379\u2013389","journal-title":"Int J Solids Struct"},{"issue":"7","key":"4480_CR61","doi-asserted-by":"crossref","first-page":"071001","DOI":"10.1088\/1361-651X\/aa834f","volume":"25","author":"EB Tadmor","year":"2017","unstructured":"Tadmor EB, Miller RE (2017) Benchmarking, validation and reproducibility of concurrent multiscale methods are still needed. Modell Simul Mater Sci Eng 25(7):071001","journal-title":"Modell Simul Mater Sci Eng"},{"issue":"6","key":"4480_CR62","doi-asserted-by":"crossref","first-page":"1529","DOI":"10.1080\/01418619608243000","volume":"73","author":"EB Tadmor","year":"1996","unstructured":"Tadmor EB, Ortiz M, Phillips R (1996) Quasicontinuum analysis of defects in solids. Philos Mag A 73(6):1529\u20131563","journal-title":"Philos Mag A"},{"key":"4480_CR63","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.advengsoft.2014.09.016","volume":"80","author":"H Talebi","year":"2015","unstructured":"Talebi H, Silani M, Rabczuk T (2015) Concurrent multiscale modeling of three dimensional crack and dislocation propagation. Adv Eng Softw 80:82\u201392","journal-title":"Adv Eng Softw"},{"issue":"5","key":"4480_CR64","doi-asserted-by":"crossref","first-page":"1806","DOI":"10.1016\/j.jmps.2007.11.012","volume":"56","author":"M Tschopp","year":"2008","unstructured":"Tschopp M, McDowell D (2008) Influence of single crystal orientation on homogeneous dislocation nucleation under uniaxial loading. J Mech Phys Solids 56(5):1806\u20131830","journal-title":"J Mech Phys Solids"},{"issue":"3","key":"4480_CR65","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4018\/jdwm.2007070101","volume":"3","author":"G Tsoumakas","year":"2007","unstructured":"Tsoumakas G, Katakis I (2007) Multi-label classification: an overview. Int J Data Wareh Min 3(3):1\u201313","journal-title":"Int J Data Wareh Min"},{"issue":"1","key":"4480_CR66","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/S0021-9991(03)00273-0","volume":"190","author":"GJ Wagner","year":"2003","unstructured":"Wagner GJ, Liu WK (2003) Coupling of atomistic and continuum simulations using a bridging scale decomposition. J Comput Phys 190(1):249\u2013274","journal-title":"J Comput Phys"},{"key":"4480_CR67","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1002\/nme.1565","volume":"66","author":"S Xiao","year":"2006","unstructured":"Xiao S (2006) A non-oscillatory method for spallation studies. Int J Numer Meth Eng 66:364\u2013380","journal-title":"Int J Numer Meth Eng"},{"issue":"1","key":"4480_CR68","first-page":"142","volume":"3","author":"S Xiao","year":"2006","unstructured":"Xiao S, Andersen DR, Han R, Hou W (2006) Studies of carbon nanotube-based oscillators using molecular dynamics. J Comput Theor Nanosci 3(1):142\u2013147","journal-title":"J Comput Theor Nanosci"},{"key":"4480_CR69","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1007\/s11671-008-9167-8","volume":"3","author":"S Xiao","year":"2008","unstructured":"Xiao S, Andersen DR, Yang W (2008) Design and analysis of nanotube-based memory cells. Nanoscale Res Lett 3:416\u2013420","journal-title":"Nanoscale Res Lett"},{"issue":"17\u201320","key":"4480_CR70","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.1016\/j.cma.2003.12.053","volume":"193","author":"S Xiao","year":"2004","unstructured":"Xiao S, Belytschko T (2004) A bridging domain method for coupling continua with molecular dynamics. Comput Methods Appl Mech Eng 193(17\u201320):1645\u20131669","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"11","key":"4480_CR71","doi-asserted-by":"crossref","first-page":"115406","DOI":"10.1103\/PhysRevB.73.115406","volume":"73","author":"S Xiao","year":"2006","unstructured":"Xiao S, Hou W (2006) Fracture of vacancy-defected carbon nanotubes and their embedded nanocomposites. Phys Rev B 73(11):115406","journal-title":"Phys Rev B"},{"issue":"12","key":"4480_CR72","doi-asserted-by":"crossref","first-page":"125414","DOI":"10.1103\/PhysRevB.75.125414","volume":"75","author":"S Xiao","year":"2007","unstructured":"Xiao S, Hou W (2007) Studies of nanotube-based resonant oscillators through multiscale modeling and simulation. Phys Rev B 75(12):125414","journal-title":"Phys Rev B"},{"issue":"4","key":"4480_CR73","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1166\/jctn.2008.2495","volume":"5","author":"S Xiao","year":"2008","unstructured":"Xiao S, Wang S, Ni J, Briggs R, Rysz M (2008) Reliability analysis of carbon nanotubes using molecular dynamics with the aid of grid computing. J Comput Theor Nanosci 5(4):528\u2013534","journal-title":"J Comput Theor Nanosci"},{"issue":"3","key":"4480_CR74","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1016\/j.commatsci.2005.09.007","volume":"37","author":"S Xiao","year":"2006","unstructured":"Xiao S, Yang W (2006) Temperature-related Cauchy-Born rule for multiscale modeling of crystalline solids. Comput Mater Sci 37(3):374\u2013379","journal-title":"Comput Mater Sci"},{"issue":"10","key":"4480_CR75","doi-asserted-by":"crossref","first-page":"2099","DOI":"10.1002\/nme.1841","volume":"69","author":"S Xiao","year":"2007","unstructured":"Xiao S, Yang W (2007) A temperature-related homogenization technique and its implementation in the meshfree particle method for nanoscale simulations. Int J Numer Meth Eng 69(10):2099\u20132125","journal-title":"Int J Numer Meth Eng"},{"issue":"4","key":"4480_CR76","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.commatsci.2007.04.023","volume":"41","author":"W Yang","year":"2008","unstructured":"Yang W, Xiao S (2008) Extension of the temperature-related Cauchy\u2013Born rule: material stability analysis and thermo-mechanical coupling. Comput Mater Sci 41(4):431\u2013439","journal-title":"Comput Mater Sci"},{"issue":"2037","key":"4480_CR77","doi-asserted-by":"crossref","first-page":"2347","DOI":"10.1098\/rspa.2003.1127","volume":"459","author":"M Zhou","year":"2003","unstructured":"Zhou M (2003) A new look at the atomic level virial stress: on continuum-molecular system equivalence. Proc R Soc A: Math Phys Eng Sci 459(2037):2347\u20132392","journal-title":"Proc R Soc A: Math Phys Eng Sci"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-019-04480-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-019-04480-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-019-04480-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,5]],"date-time":"2020-10-05T15:24:30Z","timestamp":1601911470000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-019-04480-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,18]]},"references-count":78,"journal-issue":{"issue":"18","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["4480"],"URL":"https:\/\/doi.org\/10.1007\/s00521-019-04480-7","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,9,18]]},"assertion":[{"value":"1 January 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 August 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 September 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}