{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T16:40:36Z","timestamp":1774370436468,"version":"3.50.1"},"reference-count":171,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2023,7,14]],"date-time":"2023-07-14T00:00:00Z","timestamp":1689292800000},"content-version":"vor","delay-in-days":10,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2018R1A5A7025409"],"award-info":[{"award-number":["2018R1A5A7025409"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100014188","name":"Ministry of Science and ICT","doi-asserted-by":"publisher","award":["2022\u20130-00969"],"award-info":[{"award-number":["2022\u20130-00969"]}],"id":[{"id":"10.13039\/501100014188","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100014188","name":"Ministry of Science and ICT","doi-asserted-by":"publisher","award":["2022\u20130-00986"],"award-info":[{"award-number":["2022\u20130-00986"]}],"id":[{"id":"10.13039\/501100014188","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,7,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Topology optimization (TO) is a method of deriving an optimal design that satisfies a given load and boundary conditions within a design domain. This method enables effective design without initial design, but has been limited in use due to high computational costs. At the same time, machine learning (ML) methodology including deep learning has made great progress in the 21st century, and accordingly, many studies have been conducted to enable effective and rapid optimization by applying ML to TO. Therefore, this study reviews and analyzes previous research on ML-based TO (MLTO). Two different perspectives of MLTO are used to review studies: (i) TO and (ii) ML perspectives. The TO perspective addresses \u201cwhy\u201d to use ML for TO, while the ML perspective addresses \u201chow\u201d to apply ML to TO. In addition, the limitations of current MLTO research and future research directions are examined.<\/jats:p>","DOI":"10.1093\/jcde\/qwad072","type":"journal-article","created":{"date-parts":[[2023,7,14]],"date-time":"2023-07-14T01:05:58Z","timestamp":1689296758000},"page":"1736-1766","source":"Crossref","is-referenced-by-count":69,"title":["Topology optimization via machine learning and deep learning: a review"],"prefix":"10.1093","volume":"10","author":[{"given":"Seungyeon","family":"Shin","sequence":"first","affiliation":[{"name":"Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology , 34051, Daejeon, Republic of Korea"}]},{"given":"Dongju","family":"Shin","sequence":"additional","affiliation":[{"name":"Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology , 34051, Daejeon, Republic of Korea"},{"name":"Narnia Labs , 34051, Daejeon, Republic of Korea"}]},{"given":"Namwoo","family":"Kang","sequence":"additional","affiliation":[{"name":"Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology , 34051, Daejeon, Republic of Korea"},{"name":"Narnia Labs , 34051, Daejeon, Republic of Korea"}]}],"member":"286","published-online":{"date-parts":[[2023,7,13]]},"reference":[{"key":"2023102618005602600_bib1","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1007\/s00158-014-1157-0","article-title":"Topology optimization using PETSc: An easy-to-use, fully parallel, open source topology optimization framework","volume":"51","author":"Aage","year":"2015","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"2023102618005602600_bib2","doi-asserted-by":"crossref","first-page":"106283","DOI":"10.1016\/j.compstruc.2020.106283","article-title":"Topology optimization of 2D structures with nonlinearities using deep learning","volume":"237","author":"Abueidda","year":"2020","journal-title":"Computers & Structures"},{"key":"2023102618005602600_bib3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/ICEngTechnol.2017.8308186","article-title":"Understanding of a convolutional neural network","volume-title":"Proceedings of the 2017 International Conference on Engineering and Technology (ICET)","author":"Albawi","year":"2017"},{"issue":"12","key":"2023102618005602600_bib4","doi-asserted-by":"crossref","first-page":"1125","DOI":"10.1016\/S1631-073X(02)02412-3","article-title":"A level-set method for shape optimization","volume":"334","author":"Allaire","year":"2002","journal-title":"Comptes Rendus Mathematique"},{"key":"2023102618005602600_bib5","article-title":"Shape related constraints aware generation of mechanical designs through deep convolutional GAN","author":"Almasri","year":"2020"},{"key":"2023102618005602600_bib7","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s00158-010-0586-7","article-title":"On reducing computational effort in topology optimization: How far can we go?","volume":"44","author":"Amir","year":"2011","journal-title":"Structural and Multidisciplinary Optimization"},{"issue":"12","key":"2023102618005602600_bib6","doi-asserted-by":"crossref","first-page":"1474","DOI":"10.1002\/nme.2536","article-title":"Approximate reanalysis in topology optimization","volume":"78","author":"Amir","year":"2009","journal-title":"International Journal for Numerical Methods in Engineering"},{"key":"2023102618005602600_bib8","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s00158-009-0463-4","article-title":"Efficient use of iterative solvers in nested topology optimization","volume":"42","author":"Amir","year":"2010","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"2023102618005602600_bib9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00158-010-0594-7","article-title":"Efficient topology optimization in MATLAB using 88 lines of code","volume":"43","author":"Andreassen","year":"2011","journal-title":"Structural and Multidisciplinary Optimization"},{"issue":"1","key":"2023102618005602600_bib10","doi-asserted-by":"crossref","first-page":"345","DOI":"10.32604\/cmc.2019.06641","article-title":"Artificial neural network methods for the solution of second order boundary value problems","volume":"59","author":"Anitescu","year":"2019","journal-title":"Computers, Materials & Continua"},{"issue":"3","key":"2023102618005602600_bib11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TMAG.2019.2956849","article-title":"Transfer learning through deep learning: Application to topology optimization of electric motor","volume":"56","author":"Asanuma","year":"2020","journal-title":"IEEE Transactions on Magnetics"},{"key":"2023102618005602600_bib12","first-page":"3578","article-title":"Topology optimization by predicting sensitivities based on local state features","volume-title":"Proceedings of the 5th European Conference on Computational Mechanics (ECCM V)","author":"Aulig","year":"2014"},{"key":"2023102618005602600_bib13","article-title":"3D topology optimization using convolutional neural networks","volume-title":"arXiv preprint arXiv:1808.07440","author":"Banga","year":"2018"},{"key":"2023102618005602600_bib14","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1512\/iumj.1957.6.56038","article-title":"A Markovian decision process","volume":"6","author":"Bellman","year":"1957","journal-title":"Indiana University Mathematics Journal"},{"key":"2023102618005602600_bib15","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/BF01650949","article-title":"Optimal shape design as a material distribution problem","volume":"1","author":"Bends\u00f8e","year":"1989","journal-title":"Structural Optimization"},{"issue":"2","key":"2023102618005602600_bib16","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/0045-7825(88)90086-2","article-title":"Generating optimal topologies in structural design using a homogenization method","volume":"71","author":"Bends\u00f8e","year":"1988","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"2023102618005602600_bib17","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1007\/s004190050248","article-title":"Material interpolation schemes in topology optimization","volume":"69","author":"Bends\u00f8e","year":"1999","journal-title":"Archive of Applied Mechanics"},{"key":"2023102618005602600_bib18","volume-title":"Topology optimization: Theory, methods, and applications","author":"Bendsoe","year":"2003"},{"key":"2023102618005602600_bib19","article-title":"Scalable deep-learning-accelerated topology optimization for additively manufactured materials","volume-title":"arXiv preprint arXiv:2011.14177","author":"Bi","year":"2020"},{"issue":"1","key":"2023102618005602600_bib20","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1364\/OSAC.413394","article-title":"Successive training of a generative adversarial network for the design of an optical cloak","volume":"4","author":"Blanchard-Dionne","year":"2021","journal-title":"Osa Continuum"},{"issue":"46-47","key":"2023102618005602600_bib21","doi-asserted-by":"crossref","first-page":"6201","DOI":"10.1016\/S0045-7825(01)00216-X","article-title":"Large-scale topology optimization in 3D using parallel computing","volume":"190","author":"Borrvall","year":"2001","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"9","key":"2023102618005602600_bib22","doi-asserted-by":"crossref","first-page":"2143","DOI":"10.1002\/nme.116","article-title":"Filters in topology optimization","volume":"50","author":"Bourdin","year":"2001","journal-title":"International Journal for Numerical Methods in Engineering"},{"key":"2023102618005602600_bib23","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Machine Learning"},{"key":"2023102618005602600_bib24","doi-asserted-by":"crossref","first-page":"110672","DOI":"10.1016\/j.matdes.2022.110672","article-title":"Deep reinforcement learning for engineering design through topology optimization of elementally discretized design domains","volume":"218","author":"Brown","year":"2022","journal-title":"Materials & Design"},{"issue":"26-27","key":"2023102618005602600_bib25","doi-asserted-by":"crossref","first-page":"3443","DOI":"10.1016\/S0045-7825(00)00278-4","article-title":"Topology optimization of non-linear elastic structures and compliant mechanisms","volume":"190","author":"Bruns","year":"2001","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"2023102618005602600_bib26","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1145\/3205455.3205528","article-title":"Learning-based topology variation in evolutionary level set topology optimization","volume-title":"Proceedings of the Genetic and Evolutionary Computation Conference","author":"Bujny","year":"2018"},{"issue":"2","key":"2023102618005602600_bib27","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1023\/A:1009715923555","article-title":"A tutorial on support vector machines for pattern recognition","volume":"2","author":"Burges","year":"1998","journal-title":"Data Mining and Knowledge Discovery"},{"key":"2023102618005602600_bib28","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.cad.2018.12.008","article-title":"One-shot generation of near-optimal topology through theory-driven machine learning","volume":"109","author":"Cang","year":"2019","journal-title":"Computer-Aided Design"},{"key":"2023102618005602600_bib29","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1007\/s00158-020-02748-4","article-title":"TOuNN: Topology optimization using neural networks","volume":"63","author":"Chandrasekhar","year":"2021","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"2023102618005602600_bib30","doi-asserted-by":"crossref","first-page":"103017","DOI":"10.1016\/j.cad.2021.103017","article-title":"Multi-material topology optimization using neural networks","volume":"136","author":"Chandrasekhar","year":"2021","journal-title":"Computer-Aided Design"},{"key":"2023102618005602600_bib31","article-title":"Length scale control in topology optimization using Fourier enhanced neural networks","volume-title":"arXiv preprint arXiv:2109.01861","author":"Chandrasekhar","year":"2021"},{"key":"2023102618005602600_bib32","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1016\/j.cma.2018.10.010","article-title":"Functionally graded lattice structure topology optimization for the design of additive manufactured components with stress constraints","volume":"344","author":"Cheng","year":"2019","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"2023102618005602600_bib33","doi-asserted-by":"crossref","first-page":"112739","DOI":"10.1016\/j.cma.2019.112739","article-title":"Universal machine learning for topology optimization","volume":"375","author":"Chi","year":"2021","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"2023102618005602600_bib34","first-page":"10","article-title":"An effective structural boundary processing method based on support vector machine for discrete topology optimization","volume-title":"Proceedings of the 2016 20th International Conference on Computer Supported Cooperative Work in Design (CSCWD)","author":"Chu","year":"2016"},{"issue":"1","key":"2023102618005602600_bib35","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/TIT.1967.1053964","article-title":"Nearest neighbor pattern classification","volume":"13","author":"Cover","year":"1967","journal-title":"IEEE Transactions on Information Theory"},{"issue":"2","key":"2023102618005602600_bib37","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1007\/s00466-020-01859-5","article-title":"Topology optimization based on deep representation learning (DRL) for compliance and stress-constrained design","volume":"66","author":"Deng","year":"2020","journal-title":"Computational Mechanics"},{"issue":"1","key":"2023102618005602600_bib36","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1038\/s41467-021-27713-7","article-title":"Self-directed online machine learning for topology optimization","volume":"13","author":"Deng","year":"2022","journal-title":"Nature Communications"},{"issue":"6","key":"2023102618005602600_bib38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TMAG.2019.2899934","article-title":"Multi-objective topology optimization of rotating machines using deep learning","volume":"55","author":"Doi","year":"2019","journal-title":"IEEE Transactions on Magnetics"},{"key":"2023102618005602600_bib39","doi-asserted-by":"crossref","first-page":"112911","DOI":"10.1016\/j.cma.2020.112911","article-title":"Towards solving large-scale topology optimization problems with buckling constraints at the cost of linear analyses","volume":"363","author":"Ferrari","year":"2020","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"12","key":"2023102618005602600_bib40","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1167\/16.12.326","article-title":"A neural algorithm of artistic style","volume":"16","author":"Gatys","year":"2015","journal-title":"Journal of Vision"},{"issue":"1","key":"2023102618005602600_bib41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-019-51111-1","article-title":"Deep neural network and Monte Carlo tree search applied to fluid-structure topology optimization","volume":"9","author":"Gaymann","year":"2019","journal-title":"Scientific Reports"},{"key":"2023102618005602600_bib42","article-title":"A GAN based solver of black-box inverse problems","volume-title":"Proceedings of the NeurIPS 2019 Workshop on Solving Inverse Problems with Deep Networks","author":"Gillhofer","year":"2019"},{"key":"2023102618005602600_bib43","volume-title":"Deep learning","author":"Goodfellow","year":"2016"},{"issue":"11","key":"2023102618005602600_bib44","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1145\/3422622","article-title":"Generative adversarial networks","volume":"63","author":"Goodfellow","year":"2020","journal-title":"Communications of the ACM"},{"key":"2023102618005602600_bib45","first-page":"V11AT11A005","article-title":"Generative adversarial networks with synthetic training data for enforcing manufacturing constraints on topology optimization","volume-title":"Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference","author":"Greminger","year":"2020"},{"issue":"2","key":"2023102618005602600_bib46","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1002\/nme.1064","article-title":"Achieving minimum length scale in topology optimization using nodal design variables and projection functions","volume":"61","author":"Guest","year":"2004","journal-title":"International Journal for Numerical Methods in Engineering"},{"key":"2023102618005602600_bib48","doi-asserted-by":"crossref","DOI":"10.2514\/6.2018-0804","article-title":"An indirect design representation for topology optimization using variational autoencoder and style transfer","volume-title":"Proceedings of the 2018 AIAA\/ASCE\/AHS\/ASC Structures, Structural Dynamics, and Materials Conference","author":"Guo","year":"2018"},{"issue":"8","key":"2023102618005602600_bib49","doi-asserted-by":"crossref","first-page":"081009","DOI":"10.1115\/1.4027609","article-title":"Doing topology optimization explicitly and geometrically\u2014A new moving morphable components based framework","volume":"81","author":"Guo","year":"2014","journal-title":"Journal of Applied Mechanics"},{"key":"2023102618005602600_bib47","article-title":"A deep collocation method for the bending analysis of Kirchhoff plate","volume-title":"arXiv preprint arXiv:2102.02617","author":"Guo","year":"2021"},{"key":"2023102618005602600_bib50","first-page":"176","article-title":"Fit2Form: 3D generative model for robot gripper form design","volume-title":"Proceedings of the Conference on Robot Learning","author":"Ha","year":"2021"},{"issue":"19","key":"2023102618005602600_bib51","doi-asserted-by":"crossref","first-page":"9041","DOI":"10.3390\/app11199041","article-title":"An artificial intelligence\u2013Assisted design method for topology optimization without pre-optimized training data","volume":"11","author":"Halle","year":"2021","journal-title":"Applied Sciences"},{"key":"2023102618005602600_bib52","doi-asserted-by":"crossref","first-page":"59","DOI":"10.3389\/fbuil.2020.00059","article-title":"Reinforcement learning and graph embedding for binary truss topology optimization under stress and displacement constraints","volume":"6","author":"Hayashi","year":"2020","journal-title":"Frontiers in Built Environment"},{"key":"2023102618005602600_bib53","article-title":"Neural reparameterization improves structural optimization","volume-title":"arXiv preprint arXiv:1909.04240","author":"Hoyer","year":"2019"},{"issue":"14","key":"2023102618005602600_bib54","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1016\/j.finel.2007.06.006","article-title":"Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method","volume":"43","author":"Huang","year":"2007","journal-title":"Finite Elements in Analysis and Design"},{"key":"2023102618005602600_bib55","doi-asserted-by":"crossref","first-page":"103225","DOI":"10.1016\/j.cad.2022.103225","article-title":"Generative design by reinforcement learning: Enhancing the diversity of topology optimization designs","volume":"146","author":"Jang","year":"2022","journal-title":"Computer-Aided Design"},{"issue":"9","key":"2023102618005602600_bib56","doi-asserted-by":"crossref","first-page":"217","DOI":"10.3390\/act10090217","article-title":"Topology optimization of large-scale 3D morphing wing structures","volume":"10","author":"Jensen","year":"2021","journal-title":"Actuators"},{"key":"2023102618005602600_bib57","first-page":"402","article-title":"Dataless training of generative models for the inverse design of metasurfaces","volume":"401","author":"Jiang","year":"2019","journal-title":"arXiv preprint arXiv:1906.07843"},{"issue":"8","key":"2023102618005602600_bib58","doi-asserted-by":"crossref","first-page":"5366","DOI":"10.1021\/acs.nanolett.9b01857","article-title":"Global optimization of dielectric metasurfaces using a physics-driven neural network","volume":"19","author":"Jiang","year":"2019","journal-title":"Nano Letters"},{"issue":"8","key":"2023102618005602600_bib59","doi-asserted-by":"crossref","first-page":"8872","DOI":"10.1021\/acsnano.9b02371","article-title":"Free-form diffractive metagrating design based on generative adversarial networks","volume":"13","author":"Jiang","year":"2019","journal-title":"ACS Nano"},{"key":"2023102618005602600_bib60","doi-asserted-by":"crossref","first-page":"102841","DOI":"10.1016\/j.advengsoft.2020.102841","article-title":"Machine learning based parameter tuning strategy for MMC based topology optimization","volume":"149","author":"Jiang","year":"2020","journal-title":"Advances in Engineering Software"},{"key":"2023102618005602600_bib61","first-page":"338","volume-title":"Principal component analysis for special types of data","author":"Jolliffe","year":"2002"},{"key":"2023102618005602600_bib63","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1016\/j.promfg.2020.02.251","article-title":"DzAI\u2115: Deep learning based generative design","volume":"44","author":"Kallioras","year":"2020","journal-title":"Procedia Manufacturing"},{"key":"2023102618005602600_bib64","doi-asserted-by":"crossref","first-page":"7125","DOI":"10.1007\/s00521-020-05480-8","article-title":"DL-SCALE: A novel deep learning-based model order upscaling scheme for solving topology optimization problems","volume":"33","author":"Kallioras","year":"2021","journal-title":"Neural Computing and Applications"},{"issue":"24","key":"2023102618005602600_bib65","doi-asserted-by":"crossref","first-page":"12044","DOI":"10.3390\/app112412044","article-title":"MLGen: Generative design framework based on machine learning and topology optimization","volume":"11","author":"Kallioras","year":"2021","journal-title":"Applied Sciences"},{"issue":"3","key":"2023102618005602600_bib62","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1007\/s00158-020-02545-z","article-title":"Accelerated topology optimization by means of deep learning","volume":"62","author":"Kallioras","year":"2020","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"2023102618005602600_bib66","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/978-3-030-54334-1_1","article-title":"Generative design optimization and characterization of triple periodic lattice structures in AlSi10Mg","volume-title":"Industrializing Additive Manufacturing: Proceedings of AMPA2020","author":"Karlsson","year":"2021"},{"key":"2023102618005602600_bib67","doi-asserted-by":"crossref","first-page":"102947","DOI":"10.1016\/j.cad.2020.102947","article-title":"Image-based multiresolution topology optimization using deep disjunctive normal shape model","volume":"130","author":"Keshavarzzadeh","year":"2021","journal-title":"Computer-Aided Design"},{"key":"2023102618005602600_bib68","doi-asserted-by":"crossref","first-page":"112992","DOI":"10.1016\/j.cma.2020.112992","article-title":"Stress-based topology optimization under uncertainty via simulation-based Gaussian process","volume":"365","author":"Keshavarzzadeh","year":"2020","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"5","key":"2023102618005602600_bib70","doi-asserted-by":"crossref","first-page":"1602","DOI":"10.1093\/jcde\/qwac078","article-title":"Computational homogenization of additively manufactured lightweight structures with multiscale topology optimization","volume":"9","author":"Kim","year":"2022","journal-title":"Journal of Computational Design and Engineering"},{"key":"2023102618005602600_bib69","doi-asserted-by":"crossref","first-page":"114158","DOI":"10.1016\/j.cma.2021.114158","article-title":"Machine learning-combined topology optimization for functionary graded composite structure design","volume":"387","author":"Kim","year":"2021","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"2023102618005602600_bib71","article-title":"Auto-encoding variational bayes","volume-title":"arXiv preprint arXiv:1312.6114","author":"Kingma","year":"2013"},{"key":"2023102618005602600_bib72","first-page":"121","article-title":"Stochastic gradient VB and the variational auto-encoder","volume-title":"Proceedings of the Second International Conference on Learning Representations, ICLR","author":"Kingma","year":"2014"},{"key":"2023102618005602600_bib73","doi-asserted-by":"crossref","first-page":"109098","DOI":"10.1016\/j.matdes.2020.109098","article-title":"Deep learning for topology optimization of 2D metamaterials","volume":"196","author":"Kollmann","year":"2020","journal-title":"Materials & Design"},{"issue":"1","key":"2023102618005602600_bib74","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1515\/nanoph-2020-0376","article-title":"Machine learning\u2013assisted global optimization of photonic devices","volume":"10","author":"Kudyshev","year":"2021","journal-title":"Nanophotonics"},{"key":"2023102618005602600_bib75","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1007\/s00158-019-02422-4","article-title":"A density-and-strain-based K-clustering approach to microstructural topology optimization","volume":"61","author":"Kumar","year":"2020","journal-title":"Structural and Multidisciplinary Optimization"},{"issue":"7553","key":"2023102618005602600_bib76","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"2023102618005602600_bib77","doi-asserted-by":"crossref","first-page":"105887","DOI":"10.1016\/j.knosys.2020.105887","article-title":"CNN-based image recognition for topology optimization","volume":"198","author":"Lee","year":"2020","journal-title":"Knowledge-Based Systems"},{"issue":"1","key":"2023102618005602600_bib78","doi-asserted-by":"crossref","first-page":"011004","DOI":"10.1115\/1.4041319","article-title":"Machine learning-driven real-time topology optimization under moving morphable component-based framework","volume":"86","author":"Lei","year":"2019","journal-title":"Journal of Applied Mechanics"},{"key":"2023102618005602600_bib79","doi-asserted-by":"crossref","first-page":"100054","DOI":"10.1016\/j.finmec.2021.100054","article-title":"Encoding and exploring latent design space of optimal material structures via a VAE-LSTM model","volume":"5","author":"Lew","year":"2021","journal-title":"Forces in Mechanics"},{"key":"2023102618005602600_bib83","doi-asserted-by":"crossref","first-page":"111385","DOI":"10.1016\/j.compstruct.2019.111385","article-title":"Dimension reduction and surrogate based topology optimization of periodic structures","volume":"229","author":"Li","year":"2019","journal-title":"Composite Structures"},{"issue":"1","key":"2023102618005602600_bib82","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1093\/jcde\/qwab071","article-title":"Topology optimization of irregular flow domain by parametric level set method in unstructured mesh","volume":"9","author":"Li","year":"2022","journal-title":"Journal of Computational Design and Engineering"},{"key":"2023102618005602600_bib80","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.cad.2019.05.038","article-title":"Non-iterative structural topology optimization using deep learning","volume":"115","author":"Li","year":"2019","journal-title":"Computer-Aided Design"},{"key":"2023102618005602600_bib84","doi-asserted-by":"crossref","first-page":"113254","DOI":"10.1016\/j.compstruct.2020.113254","article-title":"Generative adversarial network guided topology optimization of periodic structures via subset simulation","volume":"260","author":"Li","year":"2021","journal-title":"Composite Structures"},{"key":"2023102618005602600_bib81","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/s00466-019-01716-0","article-title":"Clustering discretization methods for generation of material performance databases in machine learning and design optimization","volume":"64","author":"Li","year":"2019","journal-title":"Computational Mechanics"},{"issue":"6","key":"2023102618005602600_bib85","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1016\/S0045-7949(00)00018-3","article-title":"Optimal topology selection of continuum structures with displacement constraints","volume":"77","author":"Liang","year":"2000","journal-title":"Computers & Structures"},{"key":"2023102618005602600_bib86","doi-asserted-by":"crossref","first-page":"2481","DOI":"10.1007\/s00158-018-2121-1","article-title":"On reducing computational effort in topology optimization: We can go at least this far!","volume":"58","author":"Limkilde","year":"2018","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"2023102618005602600_bib87","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.icheatmasstransfer.2018.07.001","article-title":"Investigation into the topology optimization for conductive heat transfer based on deep learning approach","volume":"97","author":"Lin","year":"2018","journal-title":"International Communications in Heat and Mass Transfer"},{"key":"2023102618005602600_bib90","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.1007\/s00158-014-1107-x","article-title":"An efficient 3D topology optimization code written in Matlab","volume":"50","author":"Liu","year":"2014","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"2023102618005602600_bib91","first-page":"V02BT03A004","article-title":"Towards nonlinear multimaterial topology optimization using unsupervised machine learning and metamodel-based optimization","volume-title":"Proceedings of the International Design Engineering Technical Conferences and Computers and Information in Engineering Conference","author":"Liu","year":"2015"},{"key":"2023102618005602600_bib92","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.neucom.2016.12.038","article-title":"A survey of deep neural network architectures and their applications","volume":"234","author":"Liu","year":"2017","journal-title":"Neurocomputing"},{"issue":"1","key":"2023102618005602600_bib88","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1093\/jcde\/qwab073","article-title":"Multidisciplinary design optimization in design for additive manufacturing","volume":"9","author":"Liu","year":"2022","journal-title":"Journal of Computational Design and Engineering"},{"issue":"3","key":"2023102618005602600_bib89","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1093\/jcde\/qwab028","article-title":"Stress-constrained topology optimization for material extrusion polymer additive manufacturing","volume":"8","author":"Liu","year":"2021","journal-title":"Journal of Computational Design and Engineering"},{"issue":"11","key":"2023102618005602600_bib93","doi-asserted-by":"crossref","first-page":"114502","DOI":"10.1115\/1.4044228","article-title":"Machine learning to aid tuning of numerical parameters in topology optimization","volume":"141","author":"Lynch","year":"2019","journal-title":"Journal of Mechanical Design"},{"key":"2023102618005602600_bib97","doi-asserted-by":"crossref","DOI":"10.1609\/aaai.v32i1.11890","article-title":"Semi-supervised biomedical translation with cycle Wasserstein regression GANs","volume-title":"Proceedings of the AAAI Conference on Artificial Intelligence","author":"McDermott","year":"2018"},{"key":"2023102618005602600_bib94","first-page":"281","article-title":"Classification and analysis of multivariate observations","volume-title":"Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability","author":"MacQueen","year":"1967"},{"key":"2023102618005602600_bib95","doi-asserted-by":"crossref","DOI":"10.31224\/osf.io\/9gvqs","article-title":"A systematic study of deep generative models for rapid topology optimization","author":"Malviya","year":"2020"},{"key":"2023102618005602600_bib96","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.advengsoft.2017.01.009","article-title":"Efficient topology optimization using GPU computing with multilevel granularity","volume":"106","author":"Mart\u00ednez-Frutos","year":"2017","journal-title":"Advances in Engineering Software"},{"key":"2023102618005602600_bib98","article-title":"Conditional generative adversarial nets","volume-title":"arXiv preprint arXiv:1411.1784","author":"Mirza","year":"2014"},{"key":"2023102618005602600_bib99","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1007\/BF01744697","article-title":"Some aspects of the genesis of structures","volume":"5","author":"Mlejnek","year":"1992","journal-title":"Structural Optimization"},{"key":"2023102618005602600_bib100","first-page":"1928","article-title":"Asynchronous methods for deep reinforcement learning","volume-title":"Proceedings of the International Conference on Machine Learning","author":"Mnih","year":"2016"},{"key":"2023102618005602600_bib101","article-title":"Playing Atari with deep reinforcement learning","volume-title":"arXiv preprint arXiv:1312.5602","author":"Mnih","year":"2013"},{"issue":"7540","key":"2023102618005602600_bib102","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1038\/nature14236","article-title":"Human-level control through deep reinforcement learning","volume":"518","author":"Mnih","year":"2015","journal-title":"Nature"},{"key":"2023102618005602600_bib103","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1023\/A:1009744630224","article-title":"Automatic construction of decision trees from data: A multi-disciplinary survey","volume":"2","author":"Murthy","year":"1998","journal-title":"Data Mining and Knowledge Discovery"},{"issue":"1","key":"2023102618005602600_bib104","doi-asserted-by":"crossref","first-page":"011402","DOI":"10.1115\/1.4044332","article-title":"An artificial neural network approach for generating high-resolution designs from low-resolution input in topology optimization","volume":"142","author":"Napier","year":"2020","journal-title":"Journal of Mechanical Design"},{"issue":"3","key":"2023102618005602600_bib105","doi-asserted-by":"crossref","first-page":"031715","DOI":"10.1115\/1.4049533","article-title":"TopologyGAN: Topology optimization using generative adversarial networks based on physical fields over the initial domain","volume":"143","author":"Nie","year":"2021","journal-title":"Journal of Mechanical Design"},{"issue":"11","key":"2023102618005602600_bib106","doi-asserted-by":"crossref","first-page":"111405","DOI":"10.1115\/1.4044229","article-title":"Deep generative design: Integration of topology optimization and generative models","volume":"141","author":"Oh","year":"2019","journal-title":"Journal of Mechanical Design"},{"key":"2023102618005602600_bib107","first-page":"V02AT03A008","article-title":"Design automation by integrating generative adversarial networks and topology optimization","volume-title":"Proceedings of the International Design Engineering Technical Conferences and Computers and Information in Engineering Conference","author":"Oh","year":"2018"},{"issue":"5","key":"2023102618005602600_bib108","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1093\/jcde\/qwab047","article-title":"Design process of patient-specific osteosynthesis plates using topology optimization","volume":"8","author":"Park","year":"2021","journal-title":"Journal of Computational Design and Engineering"},{"issue":"4","key":"2023102618005602600_bib109","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1007\/s00158-011-0711-2","article-title":"Classification approach for reliability-based topology optimization using probabilistic neural networks","volume":"45","author":"Patel","year":"2012","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"2023102618005602600_bib110","doi-asserted-by":"crossref","first-page":"1687","DOI":"10.1007\/s00158-020-02770-6","article-title":"Accelerating gradient-based topology optimization design with dual-model artificial neural networks","volume":"63","author":"Qian","year":"2021","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"2023102618005602600_bib111","doi-asserted-by":"crossref","first-page":"110179","DOI":"10.1016\/j.matdes.2021.110179","article-title":"A deep learning approach for efficient topology optimization based on the element removal strategy","volume":"212","author":"Qiu","year":"2021","journal-title":"Materials & Design"},{"key":"2023102618005602600_bib112","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1007\/s00158-020-02755-5","article-title":"Clustering-based concurrent topology optimization with macrostructure, components, and materials","volume":"63","author":"Qiu","year":"2021","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"2023102618005602600_bib113","article-title":"Physics-consistent deep learning for structural topology optimization","volume-title":"arXiv preprint arXiv:2012.05359","author":"Rade","year":"2020"},{"key":"2023102618005602600_bib114","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","article-title":"Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","volume":"378","author":"Raissi","year":"2019","journal-title":"Journal of Computational Physics"},{"key":"2023102618005602600_bib115","article-title":"A novel topology design approach using an integrated deep learning network architecture","volume-title":"arXiv preprint arXiv:1808.02334","author":"Rawat","year":"2018"},{"key":"2023102618005602600_bib116","doi-asserted-by":"crossref","DOI":"10.4271\/2019-01-0829","article-title":"Application of adversarial networks for 3D structural topology optimization","author":"Rawat","year":"2019"},{"key":"2023102618005602600_bib117","article-title":"A novel topology optimization approach using conditional deep learning","author":"Rawat","year":"2019"},{"issue":"3","key":"2023102618005602600_bib118","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1038\/nbt0308-303","article-title":"What is principal component analysis?","volume":"26","author":"Ringn\u00e9r","year":"2008","journal-title":"Nature Biotechnology"},{"issue":"3-4","key":"2023102618005602600_bib119","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1007\/BF01742754","article-title":"Generalized shape optimization without homogenization","volume":"4","author":"Rozvany","year":"1992","journal-title":"Structural optimization"},{"key":"2023102618005602600_bib120","doi-asserted-by":"crossref","first-page":"112790","DOI":"10.1016\/j.cma.2019.112790","article-title":"An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications","volume":"362","author":"Samaniego","year":"2020","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"6","key":"2023102618005602600_bib121","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TMAG.2019.2901906","article-title":"Topology optimization accelerated by deep learning","volume":"55","author":"Sasaki","year":"2019","journal-title":"IEEE Transactions on Magnetics"},{"issue":"1","key":"2023102618005602600_bib122","doi-asserted-by":"crossref","first-page":"87","DOI":"10.3233\/JAE-171164","article-title":"Topology optimization of IPM motor with aid of deep learning","volume":"59","author":"Sasaki","year":"2019","journal-title":"International Journal of Applied Electromagnetics and Mechanics"},{"key":"2023102618005602600_bib123","first-page":"1889","article-title":"Trust region policy optimization","volume-title":"Proceedings of the International Conference on Machine Learning","author":"Schulman","year":"2015"},{"key":"2023102618005602600_bib124","article-title":"Proximal policy optimization algorithms","volume-title":"arXiv preprint arXiv:1707.06347","author":"Schulman","year":"2017"},{"issue":"2","key":"2023102618005602600_bib125","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1006\/jcph.2000.6581","article-title":"Structural boundary design via level set and immersed interface methods","volume":"163","author":"Sethian","year":"2000","journal-title":"Journal of Computational Physics"},{"key":"2023102618005602600_bib126","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-031-01560-1","volume-title":"Active learning","author":"Settles","year":"2012"},{"key":"2023102618005602600_bib127","first-page":"V02AT03A062","article-title":"Topology design with conditional generative adversarial networks","volume-title":"Proceedings of the International Design Engineering Technical Conferences and Computers and Information in Engineering Conference","author":"Sharpe","year":"2019"},{"key":"2023102618005602600_bib128","article-title":"A new CGAN technique for constrained topology design optimization","author":"Shen","year":"2019"},{"key":"2023102618005602600_bib129","article-title":"Machine learning-based topology optimization: A review","volume-title":"Proceedings of the 2021 World Congress on Advances in Structural Engineering and Mechanics (ASEM21)","author":"Shin","year":"2021"},{"issue":"4","key":"2023102618005602600_bib130","first-page":"493","article-title":"On the design of compliant mechanisms using topology optimization","volume":"25","author":"Sigmund","year":"1997","journal-title":"Journal of Structural Mechanics"},{"issue":"2","key":"2023102618005602600_bib131","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1007\/s001580050176","article-title":"A 99 line topology optimization code written in Matlab","volume":"21","author":"Sigmund","year":"2001","journal-title":"Structural and Multidisciplinary Optimization"},{"issue":"49-50","key":"2023102618005602600_bib132","doi-asserted-by":"crossref","first-page":"6605","DOI":"10.1016\/S0045-7825(01)00252-3","article-title":"Design of multiphysics actuators using topology optimization\u2013Part II: Two-material structures","volume":"190","author":"Sigmund","year":"2001","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"4-5","key":"2023102618005602600_bib133","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s00158-006-0087-x","article-title":"Morphology-based black and white filters for topology optimization","volume":"33","author":"Sigmund","year":"2007","journal-title":"Structural and Multidisciplinary Optimization"},{"issue":"6","key":"2023102618005602600_bib134","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1016\/S0022-5096(96)00114-7","article-title":"Design of materials with extreme thermal expansion using a three-phase topology optimization method","volume":"45","author":"Sigmund","year":"1997","journal-title":"Journal of the Mechanics and Physics of Solids"},{"key":"2023102618005602600_bib135","doi-asserted-by":"crossref","first-page":"102957","DOI":"10.1016\/j.advengsoft.2020.102957","article-title":"GANs and DCGANs for generation of topology optimization validation curve through clustering analysis","volume":"152","author":"Sim","year":"2021","journal-title":"Advances in Engineering Software"},{"issue":"4","key":"2023102618005602600_bib136","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1515\/rnam-2019-0018","article-title":"Neural networks for topology optimization","volume":"34","author":"Sosnovik","year":"2019","journal-title":"Russian Journal of Numerical Analysis and Mathematical Modelling"},{"key":"2023102618005602600_bib137","first-page":"130","article-title":"A generative design optimization approach for additive manufacturing","volume-title":"Proceedings of the Sim-AM 2019: II International Conference on Simulation for Additive Manufacturing","author":"Str\u00f6mberg","year":"2019"},{"issue":"7","key":"2023102618005602600_bib138","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1080\/0305215X.2019.1646258","article-title":"Efficient detailed design optimization of topology optimization concepts by using support vector machines and metamodels","volume":"52","author":"Str\u00f6mberg","year":"2020","journal-title":"Engineering Optimization"},{"issue":"2","key":"2023102618005602600_bib139","doi-asserted-by":"crossref","first-page":"10","DOI":"10.3390\/designs4020010","article-title":"Generative design by using exploration approaches of reinforcement learning in density-based structural topology optimization","volume":"4","author":"Sun","year":"2020","journal-title":"Designs"},{"key":"2023102618005602600_bib140","volume-title":"Reinforcement learning: An introduction","author":"Sutton","year":"2018"},{"key":"2023102618005602600_bib141","article-title":"Convolutional neural network-based topology optimization (CNN-TO) by estimating sensitivity of compliance from material distribution","author":"Takahashi","year":"2019"},{"issue":"2","key":"2023102618005602600_bib142","first-page":"61","article-title":"A data-driven investigation and estimation of optimal topologies under variable loading configurations","volume":"4","author":"Ulu","year":"2016","journal-title":"Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization"},{"issue":"2","key":"2023102618005602600_bib143","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/s10994-019-05855-6","article-title":"A survey on semi-supervised learning","volume":"109","author":"Van\u00a0Engelen","year":"2020","journal-title":"Machine Learning"},{"key":"2023102618005602600_bib144","doi-asserted-by":"crossref","DOI":"10.1609\/aaai.v30i1.10295","article-title":"Deep reinforcement learning with double q-learning","volume-title":"Proceedings of the AAAI Conference on Artificial Intelligence","author":"Van\u00a0Hasselt","year":"2016"},{"key":"2023102618005602600_bib146","doi-asserted-by":"crossref","first-page":"113377","DOI":"10.1016\/j.cma.2020.113377","article-title":"Deep generative modeling for mechanistic-based learning and design of metamaterial systems","volume":"372","author":"Wang","year":"2020","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"1-2","key":"2023102618005602600_bib147","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/S0045-7825(02)00559-5","article-title":"A level set method for structural topology optimization","volume":"192","author":"Wang","year":"2003","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"12","key":"2023102618005602600_bib145","doi-asserted-by":"crossref","first-page":"2108","DOI":"10.1080\/0305215X.2020.1846031","article-title":"Deep super-resolution neural network for structural topology optimization","volume":"53","author":"Wang","year":"2021","journal-title":"Engineering Optimization"},{"key":"2023102618005602600_bib148","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/BF00992698","article-title":"Q-learning","volume":"8","author":"Watkins","year":"1992","journal-title":"Machine Learning"},{"key":"2023102618005602600_bib149","article-title":"Progressive-growing of generative adversarial networks for metasurface optimization","author":"Wen","year":"2019"},{"issue":"8","key":"2023102618005602600_bib150","doi-asserted-by":"crossref","first-page":"2098","DOI":"10.1021\/acsphotonics.0c00539","article-title":"Robust freeform metasurface design based on progressively growing generative networks","volume":"7","author":"Wen","year":"2020","journal-title":"ACS Photonics"},{"key":"2023102618005602600_bib151","doi-asserted-by":"crossref","first-page":"1118","DOI":"10.1016\/j.cma.2018.09.007","article-title":"Multiscale topology optimization using neural network surrogate models","volume":"346","author":"White","year":"2019","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"4","key":"2023102618005602600_bib152","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1093\/jcde\/qwaa001","article-title":"A local solution approach for level-set based structural topology optimization in isogeometric analysis","volume":"7","author":"Wu","year":"2020","journal-title":"Journal of Computational Design and Engineering"},{"issue":"2","key":"2023102618005602600_bib153","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1093\/jcde\/qwac004","article-title":"A topology optimization approach to structure design with self-supporting constraints in additive manufacturing","volume":"9","author":"Wu","year":"2022","journal-title":"Journal of Computational Design and Engineering"},{"issue":"3","key":"2023102618005602600_bib154","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TMAG.2017.2757001","article-title":"A new topology optimization methodology based on constraint maximum-weight connected graph theorem","volume":"54","author":"Xia","year":"2017","journal-title":"IEEE Transactions on Magnetics"},{"issue":"5","key":"2023102618005602600_bib155","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1016\/0045-7949(93)90035-C","article-title":"A simple evolutionary procedure for structural optimization","volume":"49","author":"Xie","year":"1993","journal-title":"Computers & Structures"},{"key":"2023102618005602600_bib156","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1007\/978-1-4471-0985-3_2","article-title":"Basic evolutionary structural optimization","volume-title":"Evolutionary structural optimization","author":"Xie","year":"1997"},{"issue":"1","key":"2023102618005602600_bib157","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1007\/s11465-020-0614-2","article-title":"Efficient, high-resolution topology optimization method based on convolutional neural networks","volume":"16","author":"Xue","year":"2021","journal-title":"Frontiers of Mechanical Engineering"},{"issue":"3","key":"2023102618005602600_bib158","doi-asserted-by":"crossref","first-page":"1525","DOI":"10.1007\/s11831-021-09626-2","article-title":"Topology optimization methods for 3D structural problems: A comparative study","volume":"29","author":"Yago","year":"2022","journal-title":"Archives of Computational Methods in Engineering"},{"issue":"3","key":"2023102618005602600_bib159","doi-asserted-by":"crossref","first-page":"1401","DOI":"10.1007\/s00158-021-02926-y","article-title":"Data-driven topology design using a deep generative model","volume":"64","author":"Yamasaki","year":"2021","journal-title":"Structural and Multidisciplinary Optimization"},{"issue":"11","key":"2023102618005602600_bib160","doi-asserted-by":"crossref","first-page":"1483","DOI":"10.2514\/2.626","article-title":"Bidirectional evolutionary method for stiffness optimization","volume":"37","author":"Yang","year":"1999","journal-title":"AIAA Journal"},{"issue":"4","key":"2023102618005602600_bib161","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/s00158-003-0300-0","article-title":"Integrated optimal topology design and shape optimization using neural networks","volume":"25","author":"Yildiz","year":"2003","journal-title":"Structural and Multidisciplinary Optimization"},{"issue":"3","key":"2023102618005602600_bib162","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1007\/s00158-018-2101-5","article-title":"Deep learning for determining a near-optimal topological design without any iteration","volume":"59","author":"Yu","year":"2019","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"2023102618005602600_bib163","first-page":"10368","article-title":"NTopo: Mesh-free topology optimization using implicit neural representations","volume":"34","author":"Zehnder","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2023102618005602600_bib166","doi-asserted-by":"crossref","first-page":"114083","DOI":"10.1016\/j.cma.2021.114083","article-title":"TONR: An exploration for a novel way combining neural network with topology optimization","volume":"386","author":"Zhang","year":"2021","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"5","key":"2023102618005602600_bib164","doi-asserted-by":"crossref","first-page":"1367","DOI":"10.1093\/jcde\/qwab051","article-title":"A novel lattice structure topology optimization method with extreme anisotropic lattice properties","volume":"8","author":"Zhang","year":"2021","journal-title":"Journal of Computational Design and Engineering"},{"key":"2023102618005602600_bib165","article-title":"A deep convolutional neural network for topology optimization with strong generalization ability","author":"Zhang","year":"2019"},{"key":"2023102618005602600_bib167","article-title":"Energy-based generative adversarial network","author":"Zhao","year":"2016"},{"key":"2023102618005602600_bib168","doi-asserted-by":"crossref","first-page":"113894","DOI":"10.1016\/j.cma.2021.113894","article-title":"Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy","volume":"383","author":"Zheng","year":"2021","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"6","key":"2023102618005602600_bib169","doi-asserted-by":"crossref","first-page":"2073","DOI":"10.1007\/s00158-016-1628-6","article-title":"Topology optimization of composite structures with data-driven resin filling time manufacturing constraint","volume":"55","author":"Zhou","year":"2017","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"2023102618005602600_bib171","doi-asserted-by":"crossref","first-page":"104225","DOI":"10.1016\/j.euromechsol.2021.104225","article-title":"Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning","volume":"87","author":"Zhuang","year":"2021","journal-title":"European Journal of Mechanics-A\/Solids"},{"issue":"4","key":"2023102618005602600_bib170","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1093\/jcde\/qwab032","article-title":"Temperature-constrained topology optimization of nonlinear heat conduction problems","volume":"8","author":"Zhuang","year":"2021","journal-title":"Journal of Computational Design and Engineering"}],"container-title":["Journal of Computational Design and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jcde\/advance-article-pdf\/doi\/10.1093\/jcde\/qwad072\/50880408\/qwad072.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jcde\/article-pdf\/10\/4\/1736\/52600359\/qwad072.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jcde\/article-pdf\/10\/4\/1736\/52600359\/qwad072.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T18:09:17Z","timestamp":1698343757000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jcde\/article\/10\/4\/1736\/7223974"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,4]]},"references-count":171,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,7,4]]}},"URL":"https:\/\/doi.org\/10.1093\/jcde\/qwad072","relation":{},"ISSN":["2288-5048"],"issn-type":[{"value":"2288-5048","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,8]]},"published":{"date-parts":[[2023,7,4]]}}}