{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T10:38:44Z","timestamp":1775731124761,"version":"3.50.1"},"reference-count":86,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,5,17]],"date-time":"2023-05-17T00:00:00Z","timestamp":1684281600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,5,17]],"date-time":"2023-05-17T00:00:00Z","timestamp":1684281600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100000084","name":"Directorate for Engineering","doi-asserted-by":"publisher","award":["CMMI 1561899"],"award-info":[{"award-number":["CMMI 1561899"]}],"id":[{"id":"10.13039\/100000084","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2024,4]]},"DOI":"10.1007\/s00366-023-01827-6","type":"journal-article","created":{"date-parts":[[2023,5,17]],"date-time":"2023-05-17T08:04:35Z","timestamp":1684310675000},"page":"971-987","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["FluTO: Graded multi-scale topology optimization of large contact area fluid-flow devices using neural networks"],"prefix":"10.1007","volume":"40","author":[{"given":"Rahul Kumar","family":"Padhy","sequence":"first","affiliation":[]},{"given":"Aaditya","family":"Chandrasekhar","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9688-9697","authenticated-orcid":false,"given":"Krishnan","family":"Suresh","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,5,17]]},"reference":[{"issue":"6","key":"1827_CR1","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1007\/s00158-013-0978-6","volume":"48","author":"O Sigmund","year":"2013","unstructured":"Sigmund O, Maute K (2013) Topology optimization approaches: a comparative review. Struct Multidiscip Optim 48(6):1031\u20131055","journal-title":"Struct Multidiscip Optim"},{"key":"1827_CR2","doi-asserted-by":"crossref","unstructured":"Alexandersen J, Andreasen CS (2020) A review of topology optimisation for fluid-based problems. Fluids 5(1):29","DOI":"10.3390\/fluids5010029"},{"issue":"1","key":"1827_CR3","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1002\/fld.426","volume":"41","author":"T Borrvall","year":"2003","unstructured":"Borrvall T, Petersson J (2003) Topology optimization of fluids in stokes flow. Int J Numer Methods Fluids 41(1):77\u2013107","journal-title":"Int J Numer Methods Fluids"},{"issue":"7173","key":"1827_CR4","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1038\/nature06385","volume":"450","author":"S Nagrath","year":"2007","unstructured":"Nagrath S, Lecia V, Sequist SM, Bell DW, Irimia D, Ulkus L, Smith MR, Kwak EL, Digumarthy S, Muzikansky A et al (2007) Isolation of rare circulating tumour cells in cancer patients by microchip technology. Nature 450(7173):1235\u20131239","journal-title":"Nature"},{"issue":"21","key":"1827_CR5","doi-asserted-by":"crossref","first-page":"4851","DOI":"10.1021\/ac9902190","volume":"71","author":"Z Hugh Fan","year":"1999","unstructured":"Hugh Fan Z, Mangru S, Granzow R, Heaney P, Ho W, Dong Q, Kumar R (1999) Dynamic dna hybridization on a chip using paramagnetic beads. Anal Chem 71(21):4851\u20134859","journal-title":"Anal Chem"},{"issue":"24","key":"1827_CR6","doi-asserted-by":"crossref","first-page":"5896","DOI":"10.1021\/ac0104680","volume":"73","author":"MA Hayes","year":"2001","unstructured":"Hayes MA, Polson NA, Phayre AN, Garcia AA (2001) Flow-based microimmunoassay. Anal Chem 73(24):5896\u20135902","journal-title":"Anal Chem"},{"issue":"12","key":"1827_CR7","doi-asserted-by":"crossref","first-page":"2176","DOI":"10.1039\/b005999o","volume":"125","author":"G Jiang","year":"2000","unstructured":"Jiang G, Jed Harrison D (2000) mrna isolation in a microfluidic device for eventual integration of cdna library construction. Analyst 125(12):2176\u20132179","journal-title":"Analyst"},{"issue":"24","key":"1827_CR8","doi-asserted-by":"crossref","first-page":"4713","DOI":"10.1002\/elps.200700212","volume":"28","author":"Y-J Liu","year":"2007","unstructured":"Liu Y-J, Guo S-S, Zhang Z-L, Huang W-H, Baigl D, Xie M, Chen Y, Pang D-W (2007) A micropillar-integrated smart microfluidic device for specific capture and sorting of cells. Electrophoresis 28(24):4713\u20134722","journal-title":"Electrophoresis"},{"issue":"1","key":"1827_CR9","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1039\/b107540n","volume":"2","author":"C Jin-Woo","year":"2002","unstructured":"Jin-Woo C, Oh KW, Thomas JH, Heineman WR, Halsall BH, Nevin JH, Helmicki AJ, Henderson Thurman H, Ahn CH (2002) An integrated microfluidic biochemical detection system for protein analysis with magnetic bead-based sampling capabilities. Lab Chip 2(1):27\u201330","journal-title":"Lab Chip"},{"issue":"7","key":"1827_CR10","doi-asserted-by":"crossref","first-page":"1920","DOI":"10.1021\/acs.langmuir.5b04502","volume":"32","author":"Y Zhu","year":"2016","unstructured":"Zhu Y, Antao DS, Zhengmao L, Somasundaram S, Zhang T, Wang EN (2016) Prediction and characterization of dry-out heat flux in micropillar wick structures. Langmuir 32(7):1920\u20131927","journal-title":"Langmuir"},{"key":"1827_CR11","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.ijthermalsci.2013.07.003","volume":"74","author":"D Guo","year":"2013","unstructured":"Guo D, Alan JH, McGaughey JG, Fedder GK, Lee M, Yao S-C (2013) Multiphysics modeling of a micro-scale Stirling refrigeration system. Int J Therm Sci 74:44\u201352","journal-title":"Int J Therm Sci"},{"key":"1827_CR12","doi-asserted-by":"crossref","unstructured":"Moran M, Wesolek D, Berhane B, Rebello K (2004) Microsystem cooler development. In: 2nd international energy conversion engineering conference, p 5611","DOI":"10.2514\/6.2004-5611"},{"issue":"44","key":"1827_CR13","doi-asserted-by":"crossref","first-page":"11271","DOI":"10.1039\/c2sm26655e","volume":"8","author":"D Gregory","year":"2012","unstructured":"Gregory D, Bixler BB (2012) Bioinspired rice leaf and butterfly wing surface structures combining shark skin and lotus effects. Soft Matter 8(44):11271\u201311284","journal-title":"Soft Matter"},{"issue":"17","key":"1827_CR14","doi-asserted-by":"crossref","first-page":"7685","DOI":"10.1039\/c3nr01710a","volume":"5","author":"D Gregory","year":"2013","unstructured":"Gregory D, Bixler BB (2013) Fluid drag reduction and efficient self-cleaning with rice leaf and butterfly wing bioinspired surfaces. Nanoscale 5(17):7685\u20137710","journal-title":"Nanoscale"},{"issue":"1","key":"1827_CR15","doi-asserted-by":"crossref","first-page":"30","DOI":"10.3762\/bjnano.9.5","volume":"9","author":"X Huang","year":"2018","unstructured":"Huang X, Wang J, Li T, Wang J, Min X, Weixing Yu, El Abed A, Zhang X (2018) Review on optofluidic microreactors for artificial photosynthesis. Beilstein J Nanotechnol 9(1):30\u201341","journal-title":"Beilstein J Nanotechnol"},{"issue":"33","key":"1827_CR16","doi-asserted-by":"crossref","first-page":"19270","DOI":"10.1016\/j.ijhydene.2014.05.098","volume":"39","author":"L Li","year":"2014","unstructured":"Li L, Chen R, Liao Q, Zhu X, Wang G, Wang D (2014) High surface area optofluidic microreactor for redox mediated photocatalytic water splitting. Int J Hydrogen Energy 39(33):19270\u201319276","journal-title":"Int J Hydrogen Energy"},{"issue":"6","key":"1827_CR17","doi-asserted-by":"crossref","first-page":"060502","DOI":"10.1103\/PhysRevFluids.1.060502","volume":"1","author":"GV Lauder","year":"2016","unstructured":"Lauder GV, Wainwright DK, Domel AG, Weaver JC, Wen L, Bertoldi K (2016) Structure, biomimetics, and fluid dynamics of fish skin surfaces. Phys Rev Fluids 1(6):060502","journal-title":"Phys Rev Fluids"},{"issue":"1","key":"1827_CR18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-016-0001-8","volume":"6","author":"HB Evans","year":"2016","unstructured":"Evans HB, Gorumlu S, Aksak B, Castillo L, Sheng J (2016) Holographic microscopy and microfluidics platform for measuring wall stress and 3d flow over surfaces textured by micro-pillars. Sci Rep 6(1):1\u201312","journal-title":"Sci Rep"},{"key":"1827_CR19","unstructured":"Wu T (2019) Topology optimization of multiscale structures coupling fluid, thermal and mechanical analysis. Ph.D. thesis, Purdue University Graduate School"},{"issue":"3","key":"1827_CR20","doi-asserted-by":"crossref","first-page":"1455","DOI":"10.1007\/s00158-021-02881-8","volume":"63","author":"W Jun","year":"2021","unstructured":"Jun W, Ole S, Groen JP (2021) Topology optimization of multi-scale structures: a review. Struct Multidiscip Optim 63(3):1455\u20131480","journal-title":"Struct Multidiscip Optim"},{"issue":"15","key":"1827_CR21","doi-asserted-by":"crossref","first-page":"5157","DOI":"10.1007\/s10853-008-2722-y","volume":"43","author":"S Zhou","year":"2008","unstructured":"Zhou S, Li Q (2008) Design of graded two-phase microstructures for tailored elasticity gradients. J Mater Sci 43(15):5157\u20135167","journal-title":"J Mater Sci"},{"issue":"10","key":"1827_CR22","doi-asserted-by":"crossref","first-page":"1284","DOI":"10.1002\/nme.2616","volume":"79","author":"VJ Challis","year":"2009","unstructured":"Challis VJ, Guest JK (2009) Level set topology optimization of fluids in Stokes flow. Int J Numer Methods Eng 79(10):1284\u20131308","journal-title":"Int J Numer Methods Eng"},{"issue":"3","key":"1827_CR23","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/s00158-004-0508-7","volume":"30","author":"G-H Allan","year":"2005","unstructured":"Allan G-H, Ole S, Haber RB (2005) Topology optimization of channel flow problems. Struct Multidiscip Optim 30(3):181\u2013192","journal-title":"Struct Multidiscip Optim"},{"issue":"3","key":"1827_CR24","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1002\/nme.1560","volume":"66","author":"JK Guest","year":"2006","unstructured":"Guest JK, Pr\u00e9vost JH (2006) Topology optimization of creeping fluid flows using a Darcy\u2013Stokes finite element. Int J Numer Methods Eng 66(3):461\u2013484","journal-title":"Int J Numer Methods Eng"},{"issue":"7","key":"1827_CR25","doi-asserted-by":"crossref","first-page":"1374","DOI":"10.1002\/nme.1811","volume":"69","author":"N Wiker","year":"2007","unstructured":"Wiker N, Klarbring A, Borrvall T (2007) Topology optimization of regions of Darcy and Stokes flow. Int J Numer Methods Eng 69(7):1374\u20131404","journal-title":"Int J Numer Methods Eng"},{"issue":"5","key":"1827_CR26","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.1007\/s00158-014-1182-z","volume":"54","author":"A Pereira","year":"2016","unstructured":"Pereira A, Talischi C, Paulino GH, Menezes IFM, Carvalho MS (2016) Fluid flow topology optimization in polytop: stability and computational implementation. Struct Multidiscip Optim 54(5):1345\u20131364","journal-title":"Struct Multidiscip Optim"},{"key":"1827_CR27","doi-asserted-by":"crossref","unstructured":"Su\u00e1rez MAA, Romero JS, Pereira A, Menezes IFM (2022) On the virtual element method for topology optimization of non-Newtonian fluid-flow problems. In: Engineering with computers, pp 1\u201322","DOI":"10.1007\/s00366-022-01637-2"},{"key":"1827_CR28","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s002110050253","volume":"76","author":"G Allaire","year":"1997","unstructured":"Allaire G, Bonnetier E, Francfort G, Jouve F (1997) Shape optimization by the homogenization method. Numer Math 76:27\u201368","journal-title":"Numer Math"},{"issue":"6","key":"1827_CR29","first-page":"839","volume":"12","author":"G Allaire","year":"1993","unstructured":"Allaire G, Kohn RV (1993) Optimal design for minimum weight and compliance in plane stress using extremal microstructures. Eur J Mech A Solids 12(6):839\u2013878","journal-title":"Eur J Mech A Solids"},{"issue":"8","key":"1827_CR30","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1002\/nme.5575","volume":"113","author":"JP Groen","year":"2018","unstructured":"Groen JP, Sigmund O (2018) Homogenization-based topology optimization for high-resolution manufacturable microstructures. Int J Numer Methods Eng 113(8):1148\u20131163","journal-title":"Int J Numer Methods Eng"},{"key":"1827_CR31","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s00158-007-0141-3","volume":"35","author":"PG Coelho","year":"2008","unstructured":"Coelho PG, Fernandes PR, Guedes JM, Rodrigues HC (2008) A hierarchical model for concurrent material and topology optimisation of three-dimensional structures. Struct Multidiscip Optim 35:107\u2013115","journal-title":"Struct Multidiscip Optim"},{"key":"1827_CR32","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1016\/j.cma.2014.05.022","volume":"278","author":"L Xia","year":"2014","unstructured":"Xia L, Breitkopf P (2014) Concurrent topology optimization design of material and structure within fe2 nonlinear multiscale analysis framework. Comput Methods Appl Mech Eng 278:524\u2013542","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"4\u20136","key":"1827_CR33","doi-asserted-by":"crossref","first-page":"1006","DOI":"10.1016\/j.cma.2006.08.006","volume":"196","author":"JK Guest","year":"2007","unstructured":"Guest JK, Pr\u00e9vost JH (2007) Design of maximum permeability material structures. Comput Methods Appl Mech Eng 196(4\u20136):1006\u20131017","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"22\u201323","key":"1827_CR34","doi-asserted-by":"crossref","first-page":"7028","DOI":"10.1016\/j.ijsolstr.2006.03.001","volume":"43","author":"JK Guest","year":"2006","unstructured":"Guest JK, Pr\u00e9vost JH (2006) Optimizing multifunctional materials: design of microstructures for maximized stiffness and fluid permeability. Int J Solids Struct 43(22\u201323):7028\u20137047","journal-title":"Int J Solids Struct"},{"issue":"4","key":"1827_CR35","doi-asserted-by":"crossref","first-page":"2203","DOI":"10.1007\/s00158-020-02580-w","volume":"62","author":"EM Dede","year":"2020","unstructured":"Dede EM, Zhou Y, Nomura T (2020) Inverse design of microchannel fluid flow networks using Turing pattern dehomogenization. Struct Multidiscip Optim 62(4):2203\u20132210","journal-title":"Struct Multidiscip Optim"},{"key":"1827_CR36","doi-asserted-by":"crossref","first-page":"134587","DOI":"10.1016\/j.cej.2022.134587","volume":"435","author":"Y Zhou","year":"2022","unstructured":"Zhou Y, Lohan DJ, Zhou F, Nomura T, Dede EM (2022) Inverse design of microreactor flow fields through anisotropic porous media optimization and dehomogenization. Chem Eng J 435:134587","journal-title":"Chem Eng J"},{"issue":"2","key":"1827_CR37","doi-asserted-by":"crossref","first-page":"24","DOI":"10.3390\/biomimetics5020024","volume":"5","author":"Z Jak\u0161i\u0107","year":"2020","unstructured":"Jak\u0161i\u0107 Z, Jak\u0161i\u0107 O (2020) Biomimetic nanomembranes: an overview. Biomimetics 5(2):24","journal-title":"Biomimetics"},{"issue":"4","key":"1827_CR38","doi-asserted-by":"crossref","first-page":"1983","DOI":"10.1007\/s00158-021-02959-3","volume":"64","author":"CHP Nguyen","year":"2021","unstructured":"Nguyen CHP, Choi Y (2021) Multiscale design of functionally graded cellular structures for additive manufacturing using level-set descriptions. Struct Multidiscip Optim 64(4):1983\u20131995","journal-title":"Struct Multidiscip Optim"},{"issue":"8","key":"1827_CR39","doi-asserted-by":"crossref","first-page":"1882","DOI":"10.1002\/nme.6920","volume":"123","author":"R Zhao","year":"2022","unstructured":"Zhao R, Zhao J, Wang C (2022) Stress-constrained multiscale topology optimization with connectable graded microstructures using the worst-case analysis. Int J Numer Methods Eng 123(8):1882\u20131906","journal-title":"Int J Numer Methods Eng"},{"key":"1827_CR40","doi-asserted-by":"crossref","first-page":"113894","DOI":"10.1016\/j.cma.2021.113894","volume":"383","author":"L Zheng","year":"2021","unstructured":"Zheng L, Kumar S, Kochmann DM (2021) Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy. Comput Methods Appl Mech Eng 383:113894","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1827_CR41","doi-asserted-by":"crossref","unstructured":"Wang L, Tao S, Zhu P, Chen W (2021) Data-driven topology optimization with multiclass microstructures using latent variable gaussian process. J Mech Des 143(3):1\u201335","DOI":"10.1115\/1.4048628"},{"key":"1827_CR42","doi-asserted-by":"crossref","first-page":"114949","DOI":"10.1016\/j.compstruct.2021.114949","volume":"280","author":"L Wang","year":"2022","unstructured":"Wang L, van Beek A, Da D, Chan Y-C, Zhu P, Chen W (2022) Data-driven multiscale design of cellular composites with multiclass microstructures for natural frequency maximization. Compos Struct 280:114949","journal-title":"Compos Struct"},{"issue":"5","key":"1827_CR43","doi-asserted-by":"crossref","first-page":"1887","DOI":"10.1007\/s00158-019-02297-5","volume":"60","author":"W Seth","year":"2019","unstructured":"Seth W, William A, Jun K, Tortorelli DA, White DA (2019) Simple, accurate surrogate models of the elastic response of three-dimensional open truss micro-architectures with applications to multiscale topology design. Struct Multidiscip Optim 60(5):1887\u20131920","journal-title":"Struct Multidiscip Optim"},{"key":"1827_CR44","doi-asserted-by":"crossref","first-page":"1118","DOI":"10.1016\/j.cma.2018.09.007","volume":"346","author":"DA White","year":"2019","unstructured":"White DA, Arrighi WJ, Kudo J, Watts SE (2019) Multiscale topology optimization using neural network surrogate models. Comput Methods Appl Mech Eng 346:1118\u20131135","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1827_CR45","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1016\/j.cma.2016.08.015","volume":"316","author":"Y Wang","year":"2017","unstructured":"Wang Y, Hang X, Pasini D (2017) Multiscale isogeometric topology optimization for lattice materials. Comput Methods Appl Mech Eng 316:568\u2013585","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1827_CR46","doi-asserted-by":"crossref","unstructured":"Chandrasekhar A, Sridhara S, Suresh K (2022) Gm-tounn: graded multiscale topology optimization using neural networks. arXiv preprint arXiv:2204.06682","DOI":"10.1016\/j.advengsoft.2022.103359"},{"key":"1827_CR47","doi-asserted-by":"crossref","unstructured":"Li D, Dai N, Tang Y, Dong G, Zhao YF (2019) Design and optimization of graded cellular structures with triply periodic level surface-based topological shapes. J Mech Des 141(7):1\u201313","DOI":"10.1115\/1.4042617"},{"key":"1827_CR48","doi-asserted-by":"crossref","first-page":"798","DOI":"10.1016\/j.cma.2018.01.032","volume":"340","author":"ED Sanders","year":"2018","unstructured":"Sanders ED, Aguil\u00f3 MA, Paulino GH (2018) Multi-material continuum topology optimization with arbitrary volume and mass constraints. Comput Methods Appl Mech Eng 340:798\u2013823","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"8","key":"1827_CR49","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1007\/s00158-022-03336-4","volume":"65","author":"D Geng","year":"2022","unstructured":"Geng D, Wei C, Liu Y, Zhou M (2022) Concurrent topology optimization of multi-scale cooling channels with inlets and outlets. Struct Multidiscip Optim 65(8):234","journal-title":"Struct Multidiscip Optim"},{"key":"1827_CR50","first-page":"285","volume":"28","author":"A Takezawa","year":"2019","unstructured":"Takezawa A, Zhang X, Kato M, Kitamura M (2019) Method to optimize an additively-manufactured functionally-graded lattice structure for effective liquid cooling. Addit Manuf 28:285\u2013298","journal-title":"Addit Manuf"},{"key":"1827_CR51","doi-asserted-by":"crossref","first-page":"118564","DOI":"10.1016\/j.ijheatmasstransfer.2019.118564","volume":"143","author":"A Takezawa","year":"2019","unstructured":"Takezawa A, Zhang X, Kitamura M (2019) Optimization of an additively manufactured functionally graded lattice structure with liquid cooling considering structural performances. Int J Heat Mass Transf 143:118564","journal-title":"Int J Heat Mass Transf"},{"key":"1827_CR52","doi-asserted-by":"crossref","unstructured":"Xu L, Cheng G (2018) Two-scale concurrent topology optimization with multiple micro materials based on principal stress direction. In: Advances in structural and multidisciplinary optimization: Proceedings of the 12th World congress of structural and multidisciplinary optimization (WCSMO12) 12. Springer, pp 1726\u20131737","DOI":"10.1007\/978-3-319-67988-4_130"},{"issue":"6","key":"1827_CR53","doi-asserted-by":"crossref","first-page":"2227","DOI":"10.1007\/s00158-020-02497-4","volume":"61","author":"Z Liu","year":"2020","unstructured":"Liu Z, Xia L, Xia Q, Shi T (2020) Data-driven design approach to hierarchical hybrid structures with multiple lattice configurations. Struct Multidiscip Optim 61(6):2227\u20132235","journal-title":"Struct Multidiscip Optim"},{"key":"1827_CR54","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1016\/j.cma.2018.12.018","volume":"347","author":"Y Wang","year":"2019","unstructured":"Wang Y, Kang Z (2019) Concurrent two-scale topological design of multiple unit cells and structure using combined velocity field level set and density model. Comput Methods Appl Mech Eng 347:340\u2013364","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"1","key":"1827_CR55","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00158-021-03092-x","volume":"65","author":"H Zhou","year":"2022","unstructured":"Zhou H, Zhu J, Wang C, Zhang Y, Wang J, Zhang W (2022) Hierarchical structure optimization with parameterized lattice and multiscale finite element method. Struct Multidiscip Optim 65(1):1\u201320","journal-title":"Struct Multidiscip Optim"},{"key":"1827_CR56","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.cma.2015.02.028","volume":"290","author":"A Joe","year":"2015","unstructured":"Alexandersen J, Lazarov BS (2015) Topology optimisation of manufacturable microstructural details without length scale separation using a spectral coarse basis preconditioner. Comput Methods Appl Mech Eng 290:156\u2013182","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1827_CR57","volume-title":"Multiscale topology optimization of solid and fluid structures","author":"CS Andreasen","year":"2011","unstructured":"Andreasen CS (2011) Multiscale topology optimization of solid and fluid structures. DTU Technical University of Denmark Mechanical Engineering, Delhi"},{"issue":"1","key":"1827_CR58","doi-asserted-by":"crossref","first-page":"162","DOI":"10.4208\/cicp.2009.v6.p162","volume":"6","author":"P Popov","year":"2009","unstructured":"Popov P, Efendiev Y, Qin G (2009) Multiscale modeling and simulations of flows in naturally fractured karst reservoirs. Commun Comput Phys 6(1):162","journal-title":"Commun Comput Phys"},{"key":"1827_CR59","unstructured":"Laptev V (2003) Numerical solution of coupled flow in plain and porous media. Ph.D. thesis, Technische Universit\u00e4t Kaiserslautern"},{"key":"1827_CR60","unstructured":"Aziz E-S, Chassapis C, Esche S, Dai S, Xu S, Jia R (2008) Online wind tunnel laboratory. In: 2008 annual conference and exposition, pp 13\u2013949"},{"issue":"4","key":"1827_CR61","first-page":"586","volume":"47","author":"MG Mohammed","year":"2016","unstructured":"Mohammed MG, Messerman AF, Mayhan BD, Trauth KM (2016) Theory and practice of the hydrodynamic redesign of artificial hellbender habitat. Herpetol Rev 47(4):586\u2013591","journal-title":"Herpetol Rev"},{"issue":"82","key":"1827_CR62","doi-asserted-by":"crossref","first-page":"20130109","DOI":"10.1098\/rsif.2013.0109","volume":"10","author":"V Balbi","year":"2013","unstructured":"Balbi V, Ciarletta P (2013) Morpho-elasticity of intestinal villi. J R Soc Interface 10(82):20130109","journal-title":"J R Soc Interface"},{"key":"1827_CR63","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.euromechsol.2018.02.011","volume":"71","author":"M Mohammed Ameen","year":"2018","unstructured":"Mohammed Ameen M, Peerlings RHJ, Geers MGD (2018) A quantitative assessment of the scale separation limits of classical and higher-order asymptotic homogenization. Eur J Mech A Solids 71:89\u2013100","journal-title":"Eur J Mech A Solids"},{"key":"1827_CR64","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1016\/j.commatsci.2013.09.006","volume":"83","author":"Erik Andreassen and Casper Schousboe Andreasen","year":"2014","unstructured":"Erik Andreassen and Casper Schousboe Andreasen (2014) How to determine composite material properties using numerical homogenization. Comput Mater Sci 83:488\u2013495","journal-title":"Comput Mater Sci"},{"issue":"8","key":"1827_CR65","doi-asserted-by":"crossref","first-page":"6288","DOI":"10.1002\/2014JB011027","volume":"119","author":"PS Lang","year":"2014","unstructured":"Lang PS, Paluszny A, Zimmerman RW (2014) Permeability tensor of three-dimensional fractured porous rock and a comparison to trace map predictions. J Geophys Res Solid Earth 119(8):6288\u20136307","journal-title":"J Geophys Res Solid Earth"},{"issue":"1","key":"1827_CR66","doi-asserted-by":"crossref","first-page":"16","DOI":"10.3390\/fluids5010016","volume":"5","author":"RS Vianna","year":"2020","unstructured":"Vianna RS, Cunha AM, Azeredo RBV, Leiderman R, Pereira A (2020) Computing effective permeability of porous media with fem and micro-ct: an educational approach. Fluids 5(1):16","journal-title":"Fluids"},{"key":"1827_CR67","doi-asserted-by":"crossref","first-page":"113670","DOI":"10.1016\/j.cma.2021.113670","volume":"377","author":"T Kumar","year":"2021","unstructured":"Kumar T, Sridhara S, Prabhune B, Suresh K (2021) Spectral decomposition for graded multi-scale topology optimization. Comput Methods Appl Mech Eng 377:113670","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"3","key":"1827_CR68","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1007\/s00158-020-02748-4","volume":"63","author":"A Chandrasekhar","year":"2021","unstructured":"Chandrasekhar A, Suresh K (2021) Tounn: topology optimization using neural networks. Struct Multidiscip Optim 63(3):1135\u20131149","journal-title":"Struct Multidiscip Optim"},{"key":"1827_CR69","doi-asserted-by":"crossref","first-page":"103017","DOI":"10.1016\/j.cad.2021.103017","volume":"136","author":"A Chandrasekhar","year":"2021","unstructured":"Chandrasekhar A, Suresh K (2021) Multi-material topology optimization using neural networks. Comput Aided Des 136:103017","journal-title":"Comput Aided Des"},{"key":"1827_CR70","unstructured":"Rahaman N, Baratin A, Arpit D, Draxler F, Lin M, Hamprecht F, Bengio Y, Courville A (2019) On the spectral bias of neural networks. In: International conference on machine learning. PMLR, pp 5301\u20135310"},{"key":"1827_CR71","first-page":"7537","volume":"33","author":"M Tancik","year":"2020","unstructured":"Tancik M, Srinivasan P, Mildenhall B, Fridovich-Keil S, Raghavan N, Singhal U, Ramamoorthi R, Barron J, Ng R (2020) Fourier features let networks learn high frequency functions in low dimensional domains. Adv Neural Inf Process Syst 33:7537\u20137547","journal-title":"Adv Neural Inf Process Syst"},{"key":"1827_CR72","doi-asserted-by":"crossref","first-page":"103277","DOI":"10.1016\/j.cad.2022.103277","volume":"150","author":"A Chandrasekhar","year":"2022","unstructured":"Chandrasekhar A, Suresh K (2022) Approximate length scale filter in topology optimization using Fourier enhanced neural networks. Comput Aided Des 150:103277","journal-title":"Comput Aided Des"},{"key":"1827_CR73","unstructured":"Maas AL, Hannun AY, Ng AY et\u00a0al (2013) Rectifier nonlinearities improve neural network acoustic models. In: Proceedings of icml. Atlanta, Georgia, USA, vol\u00a030, p\u00a03"},{"key":"1827_CR74","volume-title":"Constrained optimization and Lagrange multiplier methods","author":"DP Bertsekas","year":"2014","unstructured":"Bertsekas DP (2014) Constrained optimization and Lagrange multiplier methods. Academic Press, New York"},{"key":"1827_CR75","doi-asserted-by":"crossref","unstructured":"Liu DC, Nocedal J (1989) On the limited memory BFGS method for large scale optimization: Mathematical programming, Springer 45(1-3):503\u2013528","DOI":"10.1007\/BF01589116"},{"issue":"6","key":"1827_CR76","doi-asserted-by":"crossref","first-page":"4355","DOI":"10.1007\/s00158-021-03025-8","volume":"64","author":"A Chandrasekhar","year":"2021","unstructured":"Chandrasekhar A, Sridhara S, Suresh K (2021) Auto: a framework for automatic differentiation in topology optimization. Struct Multidiscip Optim 64(6):4355\u20134365","journal-title":"Struct Multidiscip Optim"},{"key":"1827_CR77","unstructured":"Paszke A, Gross S, Massa F, Lerer A, Bradbury J, Chanan G, Killeen T, Lin Z, Gimelshein N, Antiga L, Desmaison A, Kopf A, Yang E, DeVito Z, Raison M, Tejani A, Chilamkurthy S, Steiner B, Fang L, Bai J, Chintala S (2019) Pytorch: an imperative style, high-performance deep learning library. In: Wallach H, Larochelle H, Beygelzimer A, d\u2019 Alch\u00e9-Buc F, Fox E, Garnett R (eds) Advances in neural information processing systems 32. Curran Associates, Inc., pp 8024\u20138035"},{"key":"1827_CR78","unstructured":"Glorot X, Bengio Y (2010) Understanding the difficulty of training deep feedforward neural networks. In: Proceedings of the thirteenth international conference on artificial intelligence and statistics. JMLR workshop and conference Proceedings, pp 249\u2013256"},{"key":"1827_CR79","unstructured":"Ioffe S, Szegedy C (2015) Batch normalization: accelerating deep network training by reducing internal covariate shift. In: International conference on machine learning. pmlr, pp 448\u2013456"},{"issue":"1","key":"1827_CR80","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1007\/BF01214002","volume":"16","author":"O Sigmund","year":"1998","unstructured":"Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim 16(1):68\u201375","journal-title":"Struct Optim"},{"key":"1827_CR81","doi-asserted-by":"crossref","DOI":"10.1007\/b98874","volume-title":"Numerical optimization","author":"J Nocedal","year":"1999","unstructured":"Nocedal J, Wright SJ (1999) Numerical optimization. Springer, Berlin"},{"key":"1827_CR82","volume-title":"ANSYS engineering analysis system: user\u2019s manual","author":"GJ DeSalvo","year":"1979","unstructured":"DeSalvo GJ, Swanson JA (1979) ANSYS engineering analysis system: user\u2019s manual. Swanson Analysis Systems, Houston"},{"issue":"8","key":"1827_CR83","doi-asserted-by":"crossref","first-page":"1987","DOI":"10.3390\/en13081987","volume":"13","author":"A Ghasemi","year":"2020","unstructured":"Ghasemi A, Elham A (2020) A novel topology optimization approach for flow power loss minimization across fin arrays. Energies 13(8):1987","journal-title":"Energies"},{"issue":"6","key":"1827_CR84","doi-asserted-by":"crossref","first-page":"4829","DOI":"10.1007\/s00366-022-01716-4","volume":"38","author":"X Liang","year":"2022","unstructured":"Liang X, Li A, Rollett AD, Zhang YJ (2022) An isogeometric analysis-based topology optimization framework for 2d cross-flow heat exchangers with manufacturability constraints. Eng Comput 38(6):4829\u20134852","journal-title":"Eng Comput"},{"issue":"5","key":"1827_CR85","doi-asserted-by":"crossref","first-page":"1905","DOI":"10.1007\/s00158-018-1967-6","volume":"57","author":"SB Dilgen","year":"2018","unstructured":"Dilgen SB, Dilgen CB, Fuhrman DR, Sigmund O, Lazarov BS (2018) Density based topology optimization of turbulent flow heat transfer systems. Struct Multidiscip Optim 57(5):1905\u20131918","journal-title":"Struct Multidiscip Optim"},{"key":"1827_CR86","unstructured":"Foret P, Kleiner A, Mobahi H, Neyshabur B (2020) Sharpness-aware minimization for efficiently improving generalization. arXiv preprint arXiv:2010.01412"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-023-01827-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-023-01827-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-023-01827-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,21]],"date-time":"2024-04-21T02:43:54Z","timestamp":1713667434000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-023-01827-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,17]]},"references-count":86,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["1827"],"URL":"https:\/\/doi.org\/10.1007\/s00366-023-01827-6","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,17]]},"assertion":[{"value":"16 September 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 April 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 May 2023","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 they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"The Python code pertinent to this paper is available at (github.com\/UW-ERSL\/FluTO).","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Replication of results"}}]}}