{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T06:49:13Z","timestamp":1778741353657,"version":"3.51.4"},"reference-count":82,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,7,22]],"date-time":"2024-07-22T00:00:00Z","timestamp":1721606400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,7,22]],"date-time":"2024-07-22T00:00:00Z","timestamp":1721606400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["KA 3309\/18-1"],"award-info":[{"award-number":["KA 3309\/18-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002957","name":"Technische Universit\u00e4t Dresden","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100002957","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2025,2]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Reconstructing microstructures from statistical descriptors is a key enabler of computer-based inverse materials design. In the Yeong\u2013Torquato algorithm and other common methods, the problem is approached by formulating it as an optimization problem in the space of possible microstructures. In this case, the error between the desired microstructure and the current reconstruction is measured in terms of a descriptor. As an alternative, descriptors can be regarded as constraints defining subspaces or regions in the microstructure space. Given a set of descriptors, a valid microstructure can be obtained by sequentially projecting onto these subspaces. This is done in the Portilla\u2013Simoncelli algorithm, which is well known in the field of texture synthesis. Noting the algorithm\u2019s potential, the present work aims at introducing it to microstructure reconstruction. After exploring its capabilities and limitations in 2D, a dimensionality expansion is developed for reconstructing 3D volumes from 2D reference data. The resulting method is extremely efficient, as it allows for high-resolution reconstructions on conventional laptops. Various numerical experiments are conducted to demonstrate its versatility and scalability. Finally, the method is validated by comparing homogenized mechanical properties of original and reconstructed 3D microstructures.<\/jats:p>","DOI":"10.1007\/s00366-024-02026-7","type":"journal-article","created":{"date-parts":[[2024,7,22]],"date-time":"2024-07-22T17:01:59Z","timestamp":1721667719000},"page":"589-607","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fast descriptor-based 2D and 3D microstructure reconstruction using the Portilla\u2013Simoncelli algorithm"],"prefix":"10.1007","volume":"41","author":[{"given":"Paul","family":"Seibert","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Ra\u00dfloff","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karl","family":"Kalina","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Markus","family":"K\u00e4stner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,22]]},"reference":[{"issue":"5330","key":"2026_CR1","doi-asserted-by":"publisher","first-page":"1237","DOI":"10.1126\/science.277.5330.1237","volume":"277","author":"GB Olson","year":"1997","unstructured":"Olson GB (1997) Computational Design of Hierarchically Structured Materials. Science 277(5330):1237. https:\/\/doi.org\/10.1126\/science.277.5330.1237","journal-title":"Science"},{"key":"2026_CR2","doi-asserted-by":"publisher","unstructured":"W.\u00a0Chen, A.\u00a0Iyer, R.\u00a0Bostanabad, Data-centric design of microstructural materials systems, Engineering p. S209580992200056X (2022). https:\/\/doi.org\/10.1016\/j.eng.2021.05.022. https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S209580992200056X","DOI":"10.1016\/j.eng.2021.05.022"},{"key":"2026_CR3","doi-asserted-by":"publisher","unstructured":"Bargmann S, Klusemann B, Markmann J, Schnabel JE, Schneider K, Soyarslan C, Wilmers J (2018) Generation of 3D representative volume elements for heterogeneous materials: A review. Progress in Materials Science 96:322 https:\/\/doi.org\/10.1016\/j.pmatsci.2018.02.003. https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0079642518300161","DOI":"10.1016\/j.pmatsci.2018.02.003"},{"key":"2026_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.pmatsci.2018.01.005","volume":"95","author":"R Bostanabad","year":"2018","unstructured":"Bostanabad R, Zhang Y, Li X, Kearney T, Brinson LC, Apley DW, Liu WK, Chen W (2018) Computational microstructure characterization and reconstruction: Review of the state-of-the-art techniques. Progress in Materials Science 95:1. https:\/\/doi.org\/10.1016\/j.pmatsci.2018.01.005","journal-title":"Progress in Materials Science"},{"key":"2026_CR5","doi-asserted-by":"publisher","unstructured":"Sahimi M, Tahmasebi P (2021) Reconstruction, optimization, and design of heterogeneous materials and media: Basic principles, computational algorithms, and applications. Physics Reports 939:1 https:\/\/doi.org\/10.1016\/j.physrep.2021.09.003. https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0370157321003719","DOI":"10.1016\/j.physrep.2021.09.003"},{"key":"2026_CR6","doi-asserted-by":"crossref","unstructured":"R.\u00a0Cang, Y.\u00a0Xu, S.\u00a0Chen, Y.\u00a0Liu, Y.\u00a0Jiao, M.Y. Ren, Microstructure Representation and Reconstruction of Heterogeneous Materials via Deep Belief Network for Computational Material Design, arXiv:1612.07401 [cond-mat, stat] pp. 1\u201329 (2017). ArXiv: 1612.07401","DOI":"10.1115\/1.4036649"},{"key":"2026_CR7","doi-asserted-by":"publisher","unstructured":"M.\u00a0Faraji\u00a0Niri, J.\u00a0Mafeni\u00a0Mase, J.\u00a0Marco, Performance Evaluation of Convolutional Auto Encoders for the Reconstruction of Li-Ion Battery Electrode Microstructure, Energies 15(12), 4489 (2022). https:\/\/doi.org\/10.3390\/en15124489. https:\/\/www.mdpi.com\/1996-1073\/15\/12\/4489","DOI":"10.3390\/en15124489"},{"key":"2026_CR8","doi-asserted-by":"publisher","unstructured":"X.\u00a0Li, Z.\u00a0Yang, L.C. Brinson, A.\u00a0Choudhary, A.\u00a0Agrawal, W.\u00a0Chen, A Deep Adversarial Learning Methodology for Designing Microstructural Material Systems, in Volume 2B: 44th Design Automation Conference (American Society of Mechanical Engineers, Quebec City, Quebec, Canada, 2018), pp. 1\u201314. https:\/\/doi.org\/10.1115\/DETC2018-85633","DOI":"10.1115\/DETC2018-85633"},{"key":"2026_CR9","unstructured":"A.\u00a0Iyer, B.\u00a0Dey, A.\u00a0Dasgupta, W.\u00a0Chen, A.\u00a0Chakraborty, A Conditional Generative Model for Predicting Material Microstructures from Processing Methods, arXiv:1910.02133 [cond-mat, stat] (2019). arxiv:1910.02133"},{"key":"2026_CR10","doi-asserted-by":"publisher","unstructured":"J.\u00a0Feng, X.\u00a0He, Q.\u00a0Teng, C.\u00a0Ren, C.\u00a0Honggang, Y.\u00a0Li, Reconstruction of porous media from extremely limited information using conditional generative adversarial networks, Physical Review E 100, 033308 (2019). https:\/\/doi.org\/10.13140\/RG.2.2.32567.98727. Publisher: Unpublished","DOI":"10.13140\/RG.2.2.32567.98727"},{"issue":"4","key":"2026_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1103\/PhysRevE.101.043308","volume":"101","author":"D Fokina","year":"2020","unstructured":"Fokina D, Muravleva E, Ovchinnikov G, Oseledets I (2020) Microstructure synthesis using style-based generative adversarial networks. Physical Review E 101(4):1. https:\/\/doi.org\/10.1103\/PhysRevE.101.043308","journal-title":"Physical Review E"},{"key":"2026_CR12","doi-asserted-by":"crossref","unstructured":"Y.\u00a0Li, X.\u00a0He, W.\u00a0Zhu, H.\u00a0Kwak, Digital Rock Reconstruction Using Wasserstein GANs with Gradient Penalty, IPTC (2022)","DOI":"10.2523\/IPTC-21884-MS"},{"key":"2026_CR13","doi-asserted-by":"publisher","unstructured":"J.W. Lee, N.H. Goo, W.B. Park, M.\u00a0Pyo, K.S. Sohn, Virtual microstructure design for steels using generative adversarial networks, Engineering Reports 3(1) (2021). https:\/\/doi.org\/10.1002\/eng2.12274. https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/eng2.12274","DOI":"10.1002\/eng2.12274"},{"key":"2026_CR14","doi-asserted-by":"publisher","unstructured":"H.\u00a0Amiri, I.\u00a0Vasconcelos, Y.\u00a0Jiao, P.E. Chen, O.\u00a0Pl\u00fcmper, Quantifying complex microstructures of earth materials: Reconstructing higher-order spatial correlations using deep generative adversarial networks. preprint, Geology (2022). https:\/\/doi.org\/10.1002\/essoar.10510988.1. http:\/\/www.essoar.org\/doi\/10.1002\/essoar.10510988.1","DOI":"10.1002\/essoar.10510988.1"},{"key":"2026_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.petrol.2019.106794","volume":"186","author":"R Shams","year":"2020","unstructured":"Shams R, Masihi M, Boozarjomehry RB, Blunt MJ (2020) Coupled generative adversarial and auto-encoder neural networks to reconstruct three-dimensional multi-scale porous media. Journal of Petroleum Science and Engineering 186:1. https:\/\/doi.org\/10.1016\/j.petrol.2019.106794","journal-title":"Journal of Petroleum Science and Engineering"},{"key":"2026_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2020.113043","volume":"368","author":"J Feng","year":"2020","unstructured":"Feng J, Teng Q, Li B, He X, Chen H, Li Y (2020) An end-to-end three-dimensional reconstruction framework of porous media from a single two-dimensional image based on deep learning. Computer Methods in Applied Mechanics and Engineering 368:113043. https:\/\/doi.org\/10.1016\/j.cma.2020.113043","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"2026_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.commatsci.2020.110018","volume":"186","author":"F Zhang","year":"2021","unstructured":"Zhang F, Teng Q, Chen H, He X, Dong X (2021) Slice-to-voxel stochastic reconstructions on porous media with hybrid deep generative model. Computational Materials Science 186:110018. https:\/\/doi.org\/10.1016\/j.commatsci.2020.110018","journal-title":"Computational Materials Science"},{"key":"2026_CR18","doi-asserted-by":"crossref","unstructured":"Y.\u00a0Zhang, P.\u00a0Seibert, A.\u00a0Otto, A.\u00a0Ra\u00dfloff, M.\u00a0Ambati, M.\u00a0Kastner, DA-VEGAN: Differentiably Augmenting VAE-GAN for microstructure reconstruction from extremely small data sets, arXiv:0904.3664 [cs] (2023)","DOI":"10.1016\/j.commatsci.2023.112661"},{"issue":"1","key":"2026_CR19","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1146\/annurev.matsci.32.110101.155324","volume":"32","author":"S Torquato","year":"2002","unstructured":"Torquato S (2002) Statistical Description of Microstructures. Annual Review of Materials Research 32(1):77. https:\/\/doi.org\/10.1146\/annurev.matsci.32.110101.155324","journal-title":"Annual Review of Materials Research"},{"issue":"1","key":"2026_CR20","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1103\/PhysRevE.57.495","volume":"57","author":"CLY Yeong","year":"1998","unstructured":"Yeong CLY, Torquato S (1998) Reconstructing random media. Physical Review E 57(1):495. https:\/\/doi.org\/10.1103\/PhysRevE.57.495","journal-title":"Physical Review E"},{"issue":"4","key":"2026_CR21","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1007\/s11004-008-9209-x","volume":"41","author":"SK Alexander","year":"2009","unstructured":"Alexander SK, Fieguth P, Ioannidis MA, Vrscay ER (2009) Hierarchical Annealing for Synthesis of Binary Images. Mathematical Geosciences 41(4):357. https:\/\/doi.org\/10.1007\/s11004-008-9209-x","journal-title":"Mathematical Geosciences"},{"issue":"6","key":"2026_CR22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.92.063303","volume":"92","author":"LM Pant","year":"2015","unstructured":"Pant LM, Mitra SK, Secanell M (2015) Multigrid hierarchical simulated annealing method for reconstructing heterogeneous media. Physical Review E 92(6):063303. https:\/\/doi.org\/10.1103\/PhysRevE.92.063303","journal-title":"Physical Review E"},{"issue":"26","key":"2026_CR23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.121.265501","volume":"121","author":"MV Karsanina","year":"2018","unstructured":"Karsanina MV, Gerke KM (2018) Hierarchical Optimization: Fast and Robust Multiscale Stochastic Reconstructions with Rescaled Correlation Functions. Physical Review Letters 121(26):265501. https:\/\/doi.org\/10.1103\/PhysRevLett.121.265501","journal-title":"Physical Review Letters"},{"issue":"5","key":"2026_CR24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.105.055301","volume":"105","author":"D Chen","year":"2022","unstructured":"Chen D, Xu Z, Wang X, He H, Du Z, Nan J (2022) Fast reconstruction of multiphase microstructures based on statistical descriptors. Physical Review E 105(5):055301. https:\/\/doi.org\/10.1103\/PhysRevE.105.055301","journal-title":"Physical Review E"},{"issue":"6","key":"2026_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1103\/PhysRevE.63.066701","volume":"63","author":"MG Rozman","year":"2001","unstructured":"Rozman MG, Utz M (2001) Efficient reconstruction of multiphase morphologies from correlation functions. Physical Review E 63(6):1. https:\/\/doi.org\/10.1103\/PhysRevE.63.066701","journal-title":"Physical Review E"},{"key":"2026_CR26","doi-asserted-by":"publisher","unstructured":"A.\u00a0Adam, F.\u00a0Wang, X.\u00a0Li, Efficient reconstruction and validation of heterogeneous microstructures for energy applications, International Journal of Energy Research p. er.8578 (2022). https:\/\/doi.org\/10.1002\/er.8578. https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/er.8578","DOI":"10.1002\/er.8578"},{"issue":"2","key":"2026_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1103\/PhysRevE.90.023306","volume":"90","author":"LM Pant","year":"2014","unstructured":"Pant LM, Mitra SK, Secanell M (2014) Stochastic reconstruction using multiple correlation functions with different-phase-neighbor-based pixel selection. Physical Review E 90(2):1. https:\/\/doi.org\/10.1103\/PhysRevE.90.023306","journal-title":"Physical Review E"},{"key":"2026_CR28","doi-asserted-by":"publisher","unstructured":"Gerke KM, Karsanina MV, Vasilyev RV, Mallants D (2014) Improving pattern reconstruction using directional correlation functions. EPL (Europhysics Letters) 106(6):66002 https:\/\/doi.org\/10.1209\/0295-5075\/106\/66002. https:\/\/iopscience.iop.org\/article\/10.1209\/0295-5075\/106\/66002","DOI":"10.1209\/0295-5075\/106\/66002"},{"key":"2026_CR29","doi-asserted-by":"publisher","unstructured":"Shao Q, Makradi A, Fiorelli D, Mikdam A, Huang W, Hu H, Belouettar S (2022) Material Twin for composite material microstructure generation and reconstruction. Composites Part C: Open Access 7:100216 https:\/\/doi.org\/10.1016\/j.jcomc.2021.100216. https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S2666682021001080","DOI":"10.1016\/j.jcomc.2021.100216"},{"issue":"1\u20132","key":"2026_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0920-4105(02)00160-2","volume":"35","author":"M Talukdar","year":"2002","unstructured":"Talukdar M, Torsaeter O, Ioannidis M, Howard J (2002) Stochastic reconstruction, 3D characterization and network modeling of chalk. Journal of Petroleum Science and Engineering 35(1\u20132):1. https:\/\/doi.org\/10.1016\/S0920-4105(02)00160-2","journal-title":"Journal of Petroleum Science and Engineering"},{"issue":"2","key":"2026_CR31","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1111\/jmi.12077","volume":"252","author":"Z Jiang","year":"2013","unstructured":"Jiang Z, Chen W, Burkhart C (2013) Efficient 3D porous microstructure reconstruction via Gaussian random field and hybrid optimization. Journal of Microscopy 252(2):135. https:\/\/doi.org\/10.1111\/jmi.12077","journal-title":"Journal of Microscopy"},{"issue":"9","key":"2026_CR32","doi-asserted-by":"publisher","first-page":"861","DOI":"10.1134\/S1064229312090049","volume":"45","author":"KM Gerke","year":"2012","unstructured":"Gerke KM, Karsanina MV, Skvortsova EB (2012) Description and reconstruction of the soil pore space using correlation functions. Eurasian Soil Science 45(9):861. https:\/\/doi.org\/10.1134\/S1064229312090049","journal-title":"Eurasian Soil Science"},{"issue":"7","key":"2026_CR33","doi-asserted-by":"publisher","first-page":"2135","DOI":"10.1007\/s00603-018-1451-z","volume":"51","author":"XP Zhou","year":"2018","unstructured":"Zhou XP, Xiao N (2018) 3D Numerical Reconstruction of Porous Sandstone Using Improved Simulated Annealing Algorithms. Rock Mechanics and Rock Engineering 51(7):2135. https:\/\/doi.org\/10.1007\/s00603-018-1451-z","journal-title":"Rock Mechanics and Rock Engineering"},{"key":"2026_CR34","doi-asserted-by":"publisher","DOI":"10.1016\/j.commatsci.2021.110455","volume":"196","author":"P Seibert","year":"2021","unstructured":"Seibert P, Ambati M, Ra\u00dfloff A, K\u00e4stner M (2021) Reconstructing random heterogeneous media through differentiable optimization. Computational Materials Science 196:110455","journal-title":"Computational Materials Science"},{"key":"2026_CR35","doi-asserted-by":"publisher","unstructured":"Seibert P, Ra\u00dfloff A, Ambati M, K\u00e4stner M (2022) Descriptor-based reconstruction of three-dimensional microstructures through gradient-based optimization. Acta Materialia 227:117667 https:\/\/doi.org\/10.1016\/j.actamat.2022.117667. https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1359645422000520","DOI":"10.1016\/j.actamat.2022.117667"},{"key":"2026_CR36","doi-asserted-by":"publisher","unstructured":"Seibert P, Ra\u00dfloff A, Kalina KA, Gussone J, Bugelnig K, Diehl M, K\u00e4stner M (2023) Two-stage 2D-to-3D reconstruction of realistic microstructures: Implementation and numerical validation by effective properties. Computer Methods in Applied Mechanics and Engineering 412:116098 https:\/\/doi.org\/10.1016\/j.cma.2023.116098. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0045782523002220","DOI":"10.1016\/j.cma.2023.116098"},{"issue":"3","key":"2026_CR37","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1007\/s40192-022-00273-4","volume":"11","author":"P Seibert","year":"2022","unstructured":"Seibert P, Ra\u00dfloff A, Kalina K, Ambati M, K\u00e4stner M (2022) Microstructure Characterization and Reconstruction in Python: MCRpy. Integrating Materials and Manufacturing Innovation 11(3):450. https:\/\/doi.org\/10.1007\/s40192-022-00273-4","journal-title":"Integrating Materials and Manufacturing Innovation"},{"issue":"1","key":"2026_CR38","doi-asserted-by":"publisher","first-page":"13461","DOI":"10.1038\/s41598-018-31571-7","volume":"8","author":"X Li","year":"2018","unstructured":"Li X, Zhang Y, Zhao H, Burkhart C, Brinson LC, Chen W (2018) A Transfer Learning Approach for Microstructure Reconstruction and Structure-property Predictions. Scientific Reports 8(1):13461. https:\/\/doi.org\/10.1038\/s41598-018-31571-7","journal-title":"Scientific Reports"},{"key":"2026_CR39","doi-asserted-by":"publisher","unstructured":"Bhaduri A, Gupta A, Olivier A, Graham-Brady L (2021) An efficient optimization based microstructure reconstruction approach with multiple loss functions. Computational Materials Science 199:110709 https:\/\/doi.org\/10.1016\/j.commatsci.2021.110709. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0927025621004365","DOI":"10.1016\/j.commatsci.2021.110709"},{"key":"2026_CR40","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2020.102906","volume":"128","author":"R Bostanabad","year":"2020","unstructured":"Bostanabad R (2020) Reconstruction of 3D Microstructures from 2D Images via Transfer Learning. Computer-Aided Design 128:102906. https:\/\/doi.org\/10.1016\/j.cad.2020.102906","journal-title":"Computer-Aided Design"},{"issue":"052111","key":"2026_CR41","first-page":"1","volume":"96","author":"N Lubbers","year":"2017","unstructured":"Lubbers N, Lookman T, Barros K (2017) Inferring low-dimensional microstructure representations using convolutional neural networks. Physical Review E 96(052111):1","journal-title":"Physical Review E"},{"key":"2026_CR42","doi-asserted-by":"publisher","unstructured":"Reck P, Seibert P, Ra\u00dfloff A, K\u00e4stner M, Peterseim D (2023) Scattering transform in microstructure reconstruction. PAMM 23(3):e202300169 https:\/\/doi.org\/10.1002\/pamm.202300169. https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/pamm.202300169","DOI":"10.1002\/pamm.202300169"},{"key":"2026_CR43","doi-asserted-by":"publisher","unstructured":"P.\u00a0Seibert, A.\u00a0Ra\u00dfloff, K.\u00a0Kalina, A.\u00a0Safi, P.\u00a0Reck, D.\u00a0Peterseim, B.\u00a0Klusemann, M.\u00a0K\u00e4stner, On the relevance of descriptor fidelity in microstructure reconstruction, PAMM p. e202300116 (2023). https:\/\/doi.org\/10.1002\/pamm.202300116. https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/pamm.202300116","DOI":"10.1002\/pamm.202300116"},{"key":"2026_CR44","doi-asserted-by":"publisher","unstructured":"Henrich M, Fehlemann N, Bexter F, Neite M, Kong L, Shen F, K\u00f6nemann M, D\u00f6lz M, M\u00fcnstermann S (2023) DRAGen \u2013 A deep learning supported RVE generator framework for complex microstructure models. Heliyon 9(8):e19003 https:\/\/doi.org\/10.1016\/j.heliyon.2023.e19003. https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S2405844023062114","DOI":"10.1016\/j.heliyon.2023.e19003"},{"key":"2026_CR45","doi-asserted-by":"publisher","unstructured":"M.A. Groeber, M.A. Jackson, DREAM.3D: A Digital Representation Environment for the Analysis of Microstructure in 3D, Integrating Materials and Manufacturing Innovation 3(1), 56 (2014). https:\/\/doi.org\/10.1186\/2193-9772-3-5","DOI":"10.1186\/2193-9772-3-5"},{"issue":"2","key":"2026_CR46","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/s00466-016-1350-7","volume":"59","author":"M Schneider","year":"2017","unstructured":"Schneider M (2017) The sequential addition and migration method to generate representative volume elements for the homogenization of short fiber reinforced plastics. Computational Mechanics 59(2):247. https:\/\/doi.org\/10.1007\/s00466-016-1350-7","journal-title":"Computational Mechanics"},{"key":"2026_CR47","doi-asserted-by":"publisher","DOI":"10.1007\/s00466-022-02201-x","author":"A Mehta","year":"2022","unstructured":"Mehta A, Schneider M (2022) A sequential addition and migration method for generating microstructures of short fibers with prescribed length distribution. Computational Mechanics. https:\/\/doi.org\/10.1007\/s00466-022-02201-x","journal-title":"Computational Mechanics"},{"key":"2026_CR48","doi-asserted-by":"publisher","unstructured":"C.\u00a0Lauff, M.\u00a0Schneider, J.\u00a0Montesano, T.\u00a0B\u00f6hlke, An orientation corrected shaking method for the microstructure generation of short fiber-reinforced composites with almost planar fiber orientation, Composite Structures p. 117352 (2023). https:\/\/doi.org\/10.1016\/j.compstruct.2023.117352. https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0263822323006980","DOI":"10.1016\/j.compstruct.2023.117352"},{"key":"2026_CR49","doi-asserted-by":"crossref","unstructured":"P.\u00a0Seibert, M.\u00a0Husert, M.P. Wollner, K.A. Kalina, M.\u00a0K\u00e4stner, Fast reconstruction of microstructures with ellipsoidal inclusions using analytical descriptors, ArXiv (2023)","DOI":"10.1016\/j.cad.2023.103635"},{"key":"2026_CR50","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/j.mechmat.2015.03.005","volume":"90","author":"L Scheunemann","year":"2015","unstructured":"Scheunemann L, Balzani D, Brands D, Schr\u00f6der J (2015) Design of 3D statistically similar Representative Volume Elements based on Minkowski functionals. Mechanics of Materials 90:185. https:\/\/doi.org\/10.1016\/j.mechmat.2015.03.005","journal-title":"Mechanics of Materials"},{"key":"2026_CR51","doi-asserted-by":"publisher","unstructured":"Eshlaghi GT, Egels G, Benito S, Stricker M, Weber S, Hartmaier A (2023) Three-dimensional microstructure reconstruction for two-phase materials from three orthogonal surface maps. Frontiers in Materials 10:1220399 https:\/\/doi.org\/10.3389\/fmats.2023.1220399. https:\/\/www.frontiersin.org\/articles\/10.3389\/fmats.2023.1220399\/full","DOI":"10.3389\/fmats.2023.1220399"},{"key":"2026_CR52","unstructured":"L.Y. Wei, S.\u00a0Lefebvre, V.\u00a0Kwatra, G.\u00a0Turk, Eurographics 2009, State of the Art in Example-based Texture Synthesis, State of the Art Report, EG-STAR pp. 93\u2013117 (2009)"},{"key":"2026_CR53","unstructured":"L.\u00a0Gatys, A.S. Ecker, M.\u00a0Bethge, Texture Synthesis Using Convolutional Neural Networks, arXiv:1505.07376 pp. 1\u20139 (2015)"},{"key":"2026_CR54","doi-asserted-by":"publisher","unstructured":"P.\u00a0Seibert, A.\u00a0Ra\u00dfloff, Y.\u00a0Zhang, K.\u00a0Kalina, P.\u00a0Reck, D.\u00a0Peterseim, Reconstructing microstructures from statistical descriptors using neural cellular automata, arXiv:2309.16195 [cond-mat.mtrl-sci] (2023). https:\/\/doi.org\/10.48550\/arXiv.2309.16195","DOI":"10.48550\/arXiv.2309.16195"},{"key":"2026_CR55","doi-asserted-by":"crossref","unstructured":"A.\u00a0Mordvintsev, E.\u00a0Niklasson, E.\u00a0Randazzo, Texture Generation with Neural Cellular Automata, arXiv:2105.07299 (2021)","DOI":"10.1162\/isal_a_00461"},{"key":"2026_CR56","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1023\/A:1026553619983","volume":"40","author":"J Portilla","year":"2000","unstructured":"Portilla J, Simoncelli EP (2000) A Parametric Texture Model Based on Joint Statistics of Complex Wavelet Coefficients. International Journal of Computer Vision 40:49","journal-title":"International Journal of Computer Vision"},{"key":"2026_CR57","doi-asserted-by":"publisher","unstructured":"Robertson AE, Kalidindi SR (2021) Efficient Generation of Anisotropic N-Field Microstructures From 2-Point Statistics Using Multi-Output Gaussian Random Fields. SSRN Electronic Journal https:\/\/doi.org\/10.2139\/ssrn.3949516. https:\/\/www.ssrn.com\/abstract=3949516","DOI":"10.2139\/ssrn.3949516"},{"issue":"4","key":"2026_CR58","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.105.045305","volume":"105","author":"Y Gao","year":"2022","unstructured":"Gao Y, Jiao Y, Liu Y (2022) Ultraefficient reconstruction of effectively hyperuniform disordered biphase materials via non-Gaussian random fields. Physical Review E 105(4):045305. https:\/\/doi.org\/10.1103\/PhysRevE.105.045305","journal-title":"Physical Review E"},{"key":"2026_CR59","doi-asserted-by":"crossref","unstructured":"D.J. Heeger, J.R. Bergen, Pyramid-Based Texture Analysis\/Synthesis, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques (1995)","DOI":"10.1145\/218380.218446"},{"key":"2026_CR60","unstructured":"TetsuyaOdaka\/texture-synthesis-portilla-simoncelli. https:\/\/github.com\/TetsuyaOdaka\/texture-synthesis-portilla-simoncelli"},{"key":"2026_CR61","unstructured":"LabForComputationalVision\/textureSynth (2023). https:\/\/github.com\/LabForComputationalVision\/textureSynth. Original-date: 2016-06-07T18:28:21Z"},{"key":"2026_CR62","doi-asserted-by":"publisher","unstructured":"S.\u00a0Kench, S.J. Cooper, Generating 3D structures from a 2D slice with GAN-based dimensionality expansion, Nat Mach Intell 3, 299 (2021). https:\/\/doi.org\/10.1038\/s42256-021-00322-1. ArXiv: 2102.07708","DOI":"10.1038\/s42256-021-00322-1"},{"key":"2026_CR63","doi-asserted-by":"publisher","unstructured":"Coiffier G, Renard P, Lefebvre S (2020) 3D Geological Image Synthesis From 2D Examples Using Generative Adversarial Networks. Frontiers in Water 2:560598 https:\/\/doi.org\/10.3389\/frwa.2020.560598. https:\/\/www.frontiersin.org\/articles\/10.3389\/frwa.2020.560598\/full","DOI":"10.3389\/frwa.2020.560598"},{"key":"2026_CR64","doi-asserted-by":"publisher","DOI":"10.1016\/j.petrol.2022.110648","volume":"215","author":"J Phan","year":"2022","unstructured":"Phan J, Ruspini L, Kiss G, Lindseth F (2022) Size-invariant 3D generation from a single 2D rock image. Journal of Petroleum Science and Engineering 215:110648","journal-title":"Journal of Petroleum Science and Engineering"},{"key":"2026_CR65","doi-asserted-by":"publisher","unstructured":"K.H. Lee, G.J. Yun, Microstructure reconstruction using diffusion-based generative models, Mechanics of Advanced Materials and Structures pp. 1\u201319 (2023). https:\/\/doi.org\/10.1080\/15376494.2023.2198528. https:\/\/www.tandfonline.com\/doi\/full\/10.1080\/15376494.2023.2198528","DOI":"10.1080\/15376494.2023.2198528"},{"key":"2026_CR66","doi-asserted-by":"publisher","unstructured":"C.\u00a0D\u00fcreth, P.\u00a0Seibert, D.\u00a0R\u00fccker, S.\u00a0Handford, M.\u00a0K\u00e4stner, M.\u00a0Gude, Conditional diffusion-based microstructure reconstruction, Materials Today Communications p. 105608 (2023). https:\/\/doi.org\/10.1016\/j.mtcomm.2023.105608. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S2352492823002982","DOI":"10.1016\/j.mtcomm.2023.105608"},{"key":"2026_CR67","doi-asserted-by":"publisher","unstructured":"J.\u00a0Song, C.\u00a0Meng, S.\u00a0Ermon. Denoising Diffusion Implicit Models (2022). https:\/\/doi.org\/10.48550\/arXiv.2010.02502. arxiv:2010.02502. ArXiv:2010.02502 [cs]","DOI":"10.48550\/arXiv.2010.02502"},{"key":"2026_CR68","doi-asserted-by":"publisher","unstructured":"K.H. Lee, G.J. Yun, Multi-plane denoising diffusion-based dimensionality expansion for 2D-to-3D reconstruction of microstructures with harmonized sampling, Preprint (2023). https:\/\/doi.org\/10.21203\/rs.3.rs-3309277\/v1","DOI":"10.21203\/rs.3.rs-3309277\/v1"},{"issue":"3","key":"2026_CR69","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1007\/s10596-022-10144-8","volume":"26","author":"Q Zheng","year":"2022","unstructured":"Zheng Q, Zhang D (2022) RockGPT: reconstructing three-dimensional digital rocks from single two-dimensional slice with deep learning. Computational Geosciences 26(3):677. https:\/\/doi.org\/10.1007\/s10596-022-10144-8","journal-title":"Computational Geosciences"},{"key":"2026_CR70","doi-asserted-by":"publisher","unstructured":"Zhang F, He X, Teng Q, Wu X, Cui J, Dong X (2023) PM-ARNN: 2D-TO-3D reconstruction paradigm for microstructure of porous media via adversarial recurrent neural network. Knowledge-Based Systems 264:110333 https:\/\/doi.org\/10.1016\/j.knosys.2023.110333. https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0950705123000837","DOI":"10.1016\/j.knosys.2023.110333"},{"issue":"2","key":"2026_CR71","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.106.025310","volume":"106","author":"F Zhang","year":"2022","unstructured":"Zhang F, Teng Q, He X, Wu X, Dong X (2022) Improved recurrent generative model for reconstructing large-size porous media from two-dimensional images. Physical Review E 106(2):025310. https:\/\/doi.org\/10.1103\/PhysRevE.106.025310","journal-title":"Physical Review E"},{"key":"2026_CR72","doi-asserted-by":"publisher","unstructured":"Turner DM, Kalidindi SR (2016) Statistical construction of 3-D microstructures from 2-D exemplars collected on oblique sections. Acta Materialia 102:136 https:\/\/doi.org\/10.1016\/j.actamat.2015.09.011. https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1359645415006771","DOI":"10.1016\/j.actamat.2015.09.011"},{"key":"2026_CR73","doi-asserted-by":"publisher","unstructured":"Liu L, Yao J, Imani G, Sun H, Zhang L, Yang Y, Zhang K (2023) Reconstruction of 3D multi-mineral shale digital rock from a 2D image based on multi-point statistics. Frontiers in Earth Science https:\/\/doi.org\/10.3389\/feart.2022.1104401. https:\/\/www.frontiersin.org\/articles\/10.3389\/feart.2022.1104401\/full","DOI":"10.3389\/feart.2022.1104401"},{"issue":"5","key":"2026_CR74","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.100.053312","volume":"100","author":"KM Gerke","year":"2019","unstructured":"Gerke KM, Karsanina MV, Katsman R (2019) Calculation of tensorial flow properties on pore level: Exploring the influence of boundary conditions on the permeability of three-dimensional stochastic reconstructions. Physical Review E 100(5):053312. https:\/\/doi.org\/10.1103\/PhysRevE.100.053312","journal-title":"Physical Review E"},{"key":"2026_CR75","doi-asserted-by":"publisher","unstructured":"Briand T, Vacher J, Galerne B, Rabin J (2014) The Heeger & Bergen Pyramid Based Texture Synthesis Algorithm. Image Processing On Line 4:276 https:\/\/doi.org\/10.5201\/ipol.2014.79.https:\/\/www.ipol.im\/pub\/art\/2014\/79\/?utm_source=doi","DOI":"10.5201\/ipol.2014.79"},{"key":"2026_CR76","unstructured":"M.M. McKerns, L.\u00a0Strand, T.\u00a0Sullivan, A.\u00a0Fang, M.A.G. Aivazis, Building a Framework for Predictive Science, arXiv:1202.1056 [cs] (2012). arxiv:1202.1056"},{"key":"2026_CR77","unstructured":"M.\u00a0McKerns, M.\u00a0Aivazis. pathos: a framework for heterogeneous computing (2023). https:\/\/uqfoundation.github.io\/project\/pathos"},{"key":"2026_CR78","unstructured":"C.\u00a0Commons. Creative Commons licence CC BY 4.0 (2021). https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"},{"key":"2026_CR79","doi-asserted-by":"publisher","unstructured":"S.\u00a0Yu, Y.\u00a0Zhang, C.\u00a0Wang, W.k. Lee, B.\u00a0Dong, T.W. Odom, C.\u00a0Sun, W.\u00a0Chen, Characterization and Design of Functional Quasi-Random Nanostructured Materials Using Spectral Density Function, Journal of Mechanical Design 139(7) (2017). https:\/\/doi.org\/10.1115\/1.4036582. https:\/\/asmedigitalcollection.asme.org\/mechanicaldesign\/article\/139\/7\/071401\/383763\/Characterization-and-Design-of-Functional-Quasi","DOI":"10.1115\/1.4036582"},{"key":"2026_CR80","doi-asserted-by":"publisher","unstructured":"J.\u00a0Gussone, K.\u00a0Bugelnig, P.\u00a0Barriobero-Vila, J.C.d. Silva, P.\u00a0Cloetens, J.\u00a0Haubrich, G.\u00a0Requena, (2023). Ptychotomography datasets of an ultrafine eutectic Ti-Fe-based alloy processed by additive manufacturing, https:\/\/doi.org\/10.5281\/zenodo.7660542. https:\/\/zenodo.org\/record\/7660542","DOI":"10.5281\/zenodo.7660542"},{"key":"2026_CR81","doi-asserted-by":"publisher","first-page":"420","DOI":"10.1016\/j.commatsci.2018.04.030","volume":"158","author":"F Roters","year":"2019","unstructured":"Roters F, Diehl M, Shanthraj P, Eisenlohr P, Reuber C, Wong S, Maiti T, Ebrahimi A, Hochrainer T, Fabritius HO, Nikolov S, Fri\u00e1k M, Fujita N, Grilli N, Janssens K, Jia N, Kok P, Ma D, Meier F, Werner E, Stricker M, Weygand D, Raabe D (2019) DAMASK \u2013 The D\u00fcsseldorf Advanced Material Simulation Kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale. Computational Materials Science 158:420. https:\/\/doi.org\/10.1016\/j.commatsci.2018.04.030","journal-title":"Computational Materials Science"},{"key":"2026_CR82","first-page":"145","volume":"21","author":"T B\u00f6hlke","year":"2001","unstructured":"B\u00f6hlke T, Br\u00fcggemann C (2001) Graphical Representation of the Generalized Hooke\u2019s Law. Technische Mechanik 21:145","journal-title":"Technische Mechanik"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-024-02026-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-024-02026-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-024-02026-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T06:41:32Z","timestamp":1740724892000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-024-02026-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,22]]},"references-count":82,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,2]]}},"alternative-id":["2026"],"URL":"https:\/\/doi.org\/10.1007\/s00366-024-02026-7","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-3771211\/v1","asserted-by":"object"}]},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,22]]},"assertion":[{"value":"18 December 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 July 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 July 2024","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 no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}