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Integrating Materials and Manufacturing Innovation

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12-02-2024 | Thematic Section: Harnessing the Power of Materials Data

MICRO2D: A Large, Statistically Diverse, Heterogeneous Microstructure Dataset

Authors: Andreas E. Robertson, Adam P. Generale, Conlain Kelly, Michael O. Buzzy, Surya R. Kalidindi

Published in: Integrating Materials and Manufacturing Innovation | Issue 1/2024

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Abstract

The availability of large, diverse datasets has enabled transformative advances in a wide variety of technical fields by unlocking data scientific and machine learning techniques. In Materials Informatics for Heterogeneous Microstructures capitalization on these techniques has been limited due to the extreme complexity of generating or curating sizeable heterogeneous microstructure datasets. Historically, this difficulty can be attributed to two main hurdles: quantification (i.e., measuring microstructure diversity) and curation (i.e., generating diverse microstructures). In this paper, we present a framework for curating large, statistically diverse mesoscale microstructure datasets composed of 2-phase microstructures. The framework generates microstructures which are statistically diverse with respect to their n-point statistics—the primary emphasis is on diversity in their 2-point statistics. The framework’s foundation is a proposed set of algorithms for synthesizing salient 2-point statistics and neighborhood distributions. We generate statistically diverse microstructures by using the outputs of these algorithms as inputs to a statistically conditioned Local-Global Decomposition generation procedure. Finally, we demonstrate the proposed framework by curating MICRO2D, a diverse, large-scale, and open source heterogeneous microstructure dataset comprised of 87, 379 2-phase microstructures. The contained microstructures are periodic and \(256 \times 256\) pixels. The dataset also contains salient homogenized elastic and thermal properties computed across a range of constituent contrast ratios for each microstructure. Using MICRO2D, we analyze the statistical and property diversity achievable via the proposed framework. We conclude by discussing important areas of future research in microstructure dataset curation.

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Specifically, PCA is distance preserving only when the entire basis is maintained [112]. However, in practice, truncated PC representations provide useful dimensionality reduction while being approximately distance preserving [87, 88, 92].

We emphasize the similarity of this requirement to that given by Niezgoda et al. [71] above.

The mixture weights must sum to 1. In this work, all weights in a single parameterization were set to the same value.

In this work, we set this value to \(\epsilon =10^{-8}\).

Empirical observations strongly indicate that large parts of the parameter space are not important for many engineering systems (e.g., [94, 123]). For example, in general, peaks closer to zero, i.e., with \(\varvec{\mu }_i\) near zero, are more prevalent and important in real autocorrelations.

This will likely be true even if optimal space filling is accomplished over the parameter space, because of the nonlinear generation transformation step described earlier.

This approximation is a generalization of PYMKS’ standard generative model [125].

The parameterization is numerically implemented as a standard eigenvalue decomposition of the covariance matrix where the eigenvector matrices are the euler rotation matrices.

For example, the class ’VoidSmallBig’ is nonstationary, breaking the stationarity assumption that accompanies many stochastic quantification frameworks. Similarly, the sharp edges in the Voronoi classes and the small features in the NBSA class will be difficult for localization models [126], in particular those utilizing Fourier filters [127].

The exact parameter values—along with all the code necessary to generate the dataset—can be found in the GitHub repository identified at the end of the paper.

In particular, we noticed that if we did not employ volume fraction stratification the final autocorrelation dataset was strongly skewed toward higher volume fractions. We hypothesize that this is a fingerprint of the spacefilling under the \(L_2\)-norm.

The total number of microstructures is less than 100, 000 (i.e., \(10 \times 10,000\)) because several volume fraction and neighborhood combinations resulted in unstable generation, e.g., see NBSA in Table 1.

In the dataset, each class is stored separately to simplify studying subsets of the dataset.

We selected this specific discretization to balance the degree of achievable diversity against practical considerations. This resolution was sufficiently high to allow us to incorporate two important lengthscales: both salient individual features and long range patterns. However, it is sufficiently low to remain inline with the discretizations preferred by the microstructure informatics community (e.g., in Process-Structure–Property modeling [37, 72, 73, 79, 81‐83] and synthetic generation [58, 65, 76, 80, 128]). Additionally, we construct our heuristic strategies to ensure that the chosen discretization is sufficient to represent the generated systems. Primarily, we do this by ensuring that the correlation length of the generated statistics is less than half the domain size and by generating periodic microstructures. It is well established in the micromechanics community that periodic RVEs and SVEs provide highly stable estimates of homogenized properties even using relatively small domains [84, 129]. We note that the proposed framework is not restricted to this discretization and datasets containing smaller, larger, or even 3D microstructures can readily be generated without significantly altering the codebase referenced at the end of this paper. However, more advanced generation strategies will need to be established if one is interested in incorporating more than two feature lengthscales.

Other microstructures, like grain boundary structures, could be generated by the local diffusion model [64, 76].

The TAMU microstructures are rescaled down to \(256 \times 256\) for comparison.

The average relative \(L_2\) reconstruction error of the projection is \(0.0071 \pm 0.0077\) for the spinodal dataset. This is comparable with the reconstruction error of MICRO2D, Appendix B. Therefore, the dataset is well represented by the basis. Additionally, including the spinodal dataset in training the PC basis did not change the structure of the latent space.

We use an analysis congruent to the analysis reported in Robertson et al. [64]. Only the subset of 3-point statistics in which the first shift is equal to 3 are considered.

Additionally, we computed localized elastic strain fields that are not included in the dataset due to the extreme memory cost. Interested readers should contact the authors.

In practice, such second order variability arises in many important material classes and is important to study to achieve desirable properties (e.g., rafting in nickel superalloy [137, 138]).

Jordan MI, Mitchell TM (2015) Machine learning: trends, perspectives, and prospects. Science 349(6245):255–260. https://doi.org/10.1126/science.aaa8415ADSMathSciNetCrossRefPubMed

Vaswani A, Shazeer N, Parmar N, Uskoreit J, Jones L, Gomez A, Kaiser L, Polosukhin I. Attention is all you need, NeurIPS

Goodfellow I, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y Generative adversarial networks, NeurIPS

Chen N, Zhang Y, Zen H, Weiss R, Norouzi M, Chan W (2009) Wavegrad: estimating gradients for waveform generation, https://doi.org/10.48550/arxiv.2009.00713

Mahdavifar S, Ghorbani AA (2019) Application of deep learning to cybersecurity: a survey. Neurocomputing 347:149–176. https://doi.org/10.1016/j.neucom.2019.02.056CrossRef

Cai L, Gao J, Zhao D (2020) A review of the application of deep learning in medical image classification and segmentation. Ann Translat Med 8:713. https://doi.org/10.21037/atm.2020.02.44CrossRef

Jiang W (2021) Applications of deep learning in stock market prediction: recent progress. Expert Syst Appl 184:115537. https://doi.org/10.1016/j.eswa.2021.115537CrossRef

Devlin J, Chang M-W, Lee K, Toutanova K (2019) Bert: pre-training of deep bidirectional transformers for language understanding. arXiv:1810.04805

Song Y, Sohl-Dickstein J, Kigma DP, Kumar A, Ermon S, Poole B (2021) Score-based generative modeling through stochastic differential equations. In: International congress for learning representation, pp 1–36

10.

Ho J, Jain A, Abbeel P. Denoising diffusion probabilistic models. NeurIPS

11.

Ho J, Salimans T, Gritsenko A, Chan W, Norouzi M, Fleet D. Video diffusion models, https://doi.org/10.48550/arxiv.2204.03458

12.

Krizhevsky A, Sutskever I, Hinton GE (2012) Imagenet classification with deep convolutional neural networks, In: Pereira F, Burges C, Bottou L, Weinberger K (eds), Advances in neural information processing systems, vol. 25, Curran Associates, Inc. https://proceedings.neurips.cc/paper_files/paper/2012/file/c399862d3b9d6b76c8436e924a68c45b-Paper.pdf

13.

Hamilton W, Ying Z, Leskovec J (2017) Inductive representation learning on large graphs, In: Guyon I, Luxburg UV, Bengio S, Wallach H, Fergus R, Vishwanathan S, Garnett R (eds), Advances in neural information processing systems, vol. 30, Curran Associates, Inc. https://proceedings.neurips.cc/paper_files/paper/2017/file/5dd9db5e033da9c6fb5ba83c7a7ebea9-Paper.pdf

14.

Wu Y, Schuster M, Chen Z, Le QV, Norouzi M, Macherey W, Krikun M, Cao Y, Gao Q, Macherey K, Klingner J, Shah A, Johnson M, Liu X, Kaiser L, Gouws S, Kato Y, Kudo T, Kazawa H, Stevens K, Kurian G, Patil N, Wang W, Young C, Smith J, Riesa J, Rudnick A, Vinyals O, Corrado G, Hughes M, Dean J (2016) Google’s neural machine translation system: bridging the gap between human and machine translation. arXiv:1609.08144

15.

Jumper J, Evans R, Pritzel A, Green T, Figurnov M, Ronnberger O, Tunyasuvunakool K, Bates R, Zidek A, Potapenko A, Bridgland A, Meyer C, Kohl S, Ballard A, Cowie A, Romera-Paredes B, Nikolov S, Jain R, Adler J, Back T, Peterson S, Reiman D, Clancy E, Zielinski M, Steinegger M, Pacholska M, Berghammer T, Bodenstein S, Silver D, Vinyals O, Senior A, Kavukcuoglu K, Kohli P, Hassabis D (2021) Highly accurate protein structure prediction with alphafold. Nature 596:583–589. https://doi.org/10.1038/s41586-021-03819-2ADSCrossRefPubMedPubMedCentral

16.

Anand N, Achim T. Protein structure and sequence generation with equivariant denoising diffusion probabilistic models, https://doi.org/10.48550/arxiv.2205.15019

17.

Burley SK, Bhikadiya C, Bi C, Bittrich S, Chen L, Crichlow GV, Christie CH, Dalenberg K, Di Costanzo L, Duarte JM, Dutta S, Feng Z, Ganesan S, Goodsell DS, Ghosh S, Green RK, Guranovi V, Guzenko D, Hudson BP, Lawson CL, Liang Y, Lowe R, Namkoong H, Peisach E, Persikova I, Randle C, Rose A, Rose Y, Sali A, Segura J, Sekharan M, Shao C, Tao Y-P, Voigt M, Westbrook JD, Young JY, Zardecki C, Zhuravleva M (2020) RCSB Protein Data Bank: powerful new tools for exploring 3D structures of biological macromolecules for basic and applied research and education in fundamental biology, biomedicine, biotechnology, bioengineering and energy sciences. Nucleic Acids Res 49(D1):D437–D451. https://doi.org/10.1093/nar/gkaa1038CrossRefPubMedCentral

18.

Fersht A (2021) Alphafold: a personal perspective on the impact of machine learning. J Mol Biol 433(20):167088. https://doi.org/10.1016/j.jmb.2021.167088CrossRefPubMed

19.

Zheng S, He J, Liu C, Shi Y, Lu Z, Feng W, Ju F, Wang J, Zhu J, Min Y, Zhang H, Tang S, Hao H, Jin P, Chen C, Noé F, Liu H, Liu T-Y (2023) Towards predicting equilibrium distributions for molecular systems with deep learning. arxiv:2306.05445

20.

Materials genome initiative for global competitiveness

21.

Generale A, Robertson A, Kelly C, Kalidindi S. Inverse stochastic microstructure design, SSRN: preprint https://doi.org/10.2139/ssrn.4590691

22.

Gao Y, Liu Y. Relibaility-based topology optimization with stochastic heterogeneous microstructure properties. Mater Des. https://doi.org/10.1016/j.matdes.2021.109713

23.

Marshall A, Kalidindi S (2021) Autonomous development of a machine-learning model for the plastic response of two-phase composites from micromechanical finite element models. JOM 73:2085–2095. https://doi.org/10.1007/s11837-021-04696-wADSCrossRef

24.

Kalidindi S, Binci M, Fullwood D, Adams B (2006) Elastic properties closures using second-order homogenization theories: case studies in composites of two isotropic constituents. Acta Mater 54:3117–3126. https://doi.org/10.1016/j.actamat.2006.03.005ADSCrossRef

25.

Hasan M, Mao Y, Tavazza F, Choudhary A, Agrawal A, Acar P. Data-driven multi-scale modeling and optimization for elastic properties of cubic microstructures. Integr Mater Manuf Innov. https://doi.org/10.1007/s40192-022-00258-3

26.

Acar P, Sundararaghavan V (2019) Stochastic design optimization of microstructural features using linear programming for robust design. AIAA J 57:448–455ADSCrossRef

27.

Xiong Y, Duong P, Wang D, Park S-I, Ge Q, Raghavan N, Rosen D (2019) Data-driven design space exploration and exploitation for design for additive manufacturing. J Mech Des 141:101101. https://doi.org/10.1115/1.4043587CrossRef

28.

Morris C, Bekker L, Haberman M, Seepersad C (2018) Design exploration of reliably manufacturable materials and structures with applications to negative stiffness metamaterials and microstereolithography. J Mech Des 140:111415. https://doi.org/10.1115/1.4041251CrossRef

29.

Pei Z, Rozman KA, Dogan ÖN, Wen Y, Gao N, Holm EA, Hawk JA, Alman DE, Gao MC (2021) Machine-learning microstructure for inverse material design. Adv Sci 8:2101207. https://doi.org/10.1002/advs.202101207CrossRef

30.

Fung V, Zhang J, Hu G, Ganesh P, Sumpter BG (2021) Inverse design of two-dimensional materials with invertible neural networks. npj Comput Mater 7:200. https://doi.org/10.1038/s41524-021-00670-x

31.

Abram M, Burghardt K, Steeg GV, Galstyan A, Dingreville R. Inferring topological transitions in pattern forming processes with self supervised learning, NPJ: Comput Mater 8. https://doi.org/10.1038/s41524-022-00889-2

32.

Diehl M, Groeber M, Haase C, Molodov D, Roters F, Raabe D (2017) Identifying structure-property relationships through dream. 3d representative volume elements and damask crystal plasticity simulations: An integrated computational materials engineering approach. JOM 69:848–855. https://doi.org/10.1007/s11837-017-2303-0ADSCrossRef

33.

Muir C, Swaminathan B, Almansour A, Sevener K, Smith C, Presby M, Kiser J, Pollock T, Daly S. Damage mechanism identification in composites via machine learning and acoustic emission, NPJ: Comput Mater 7. https://doi.org/10.1038/s41524-021-00565-x

34.

Hashemi S, Kalidindi SR (2023) Gaussian process autoregression models for the evolution of polycrystalline microstructures subjected to arbitrary stretching tensors. Int J Plast 162:103532. https://doi.org/10.1016/j.ijplas.2023.103532CrossRef

35.

Yabansu YC, Steinmetz P, Hötzer J, Kalidindi SR, Nestler B (2017) Extraction of reduced-order process-structure linkages from phase-field simulations. Acta Mater 124:182–194. https://doi.org/10.1016/j.actamat.2016.10.071ADSCrossRef

36.

Dornheim J, Morand L, Zeitvogel S, Iraki T, Link N, Helm D. Deep reinforcement learning methods for structure-guided processing path optimization. J Intell Manuf 33. https://doi.org/10.1007/s10845-021-01805-z

37.

Vlassis NN, Sun W (2023) Denoising diffusion algorithm for inverse design of microstructures with fine-tuned nonlinear material properties. Comput Methods Appl Mech Eng 413:116126. https://doi.org/10.1016/j.cma.2023.116126ADSMathSciNetCrossRef

38.

Jain A, Ong S, Hautier G, Chen W, Richards W, Dacek S, Cholia S, Gunter D, Skinner D, Ceder G, Persson K (2013) Commentary: The materials project: a materials genome approach to accelerating materials innovation. APL Mater 1:011002. https://doi.org/10.1063/1.4812323ADSCrossRef

39.

Groeber M, Jackson M (2014) Dream.3d: a digital representation environment for the analysis of microstructure in 3d, Integrating Materials and Manufacturing. Innovation 3:56–72. https://doi.org/10.1186/2193-9772-3-5CrossRef

40.

Groeber M, Ghosh S, Uchic M, Dimiduk D (2008) A framework for automated analysis and simulation of 3d polycrystalline microstructures. part 2: synthetic microstructure generation. Acta Mater 56:1274–1287. https://doi.org/10.1016/j.actamat.2007.11.040ADSCrossRef

41.

Pilchak AL, Shank J, Tucker JC, Srivatsa S, Fagin PN, Semiatin SL(2016) A dataset for the development, verification, and validation of microstructure-sensitive process models for near-alpha titanium alloys. Integr Mater Manuf Innov, 1–18 https://doi.org/10.1186/s40192-016-0056-1

42.

DeCost BL, Holm EA (2016) A large dataset of synthetic SEM images of powder materials and their ground truth 3d structures. Data Brief 9:727–731. https://doi.org/10.1016/j.dib.2016.10.011CrossRefPubMedPubMedCentral

43.

Kalidindi S, Khosravani A, Yucel B, Shanker A, Blekh A (2019) Data infrastructure elements in support of accelerated materials innovation: ELA, PyMKS, and MATIN. Integr Mater Manuf Innov 8:441–454CrossRef

44.

Hart KA, Rimoli JJ (2020) Microstructpy: a statistical microstructure mesh generator in python. SoftwareX 12:100595. https://doi.org/10.1016/j.softx.2020.100595CrossRef

45.

Song K, Yan Y (2013) A noise robust method based on completed local binary patterns for hot-rolled steel strip surface defects. Appl Surf Sci 285P:858–864. https://doi.org/10.1016/j.apsusc.2013.09.002ADSCrossRef

46.

DeCost BL, Hecht M, Francis T, Webler BA, Picard YN, Holm E (2017) Uhcsdb: ultra high carbon steel micrograph database. Integr Mater Manuf Innov 6:197–205. https://doi.org/10.1007/s40192-017-0097-0CrossRef

47.

Barber Z, Leake J, Clyne T. The doitpoms project: micrograph library. https://www.doitpoms.ac.uk/miclib/index.php

48.

Saal J, Kirklin S, Aykol M, Meredig B, Wolverton C (2013) Materials design and discovery with high-throughput denisty functional theory: the open quantum materials database. JOM 65:1501–1509. https://doi.org/10.1007/s11837-013-0755-4CrossRef

49.

Choudhary K, Garrity KF, Reid ACE, DeCost B, Biacchi AJ, Walker ARH, Trautt Z, Hattrick-Simpers J, Kusne AG, Centrone A, Davydov A, Jiang J, Pachter R, Cheon G, Reed E, Agrawal A, Qian X, Sharma V, Zhuang H, Kalinin SV, Sumpter BG, Pilania G, Acar P, Mandal S, Haule K, Vanderbilt D, Rabe K, Tavazza F, The joint automated repository for various integrated simulations (JARVIS) for data-driven materials design. npj Comput Mater 6. https://doi.org/10.1038/s41524-020-00440-1

50.

Tanifuji M, Matsuda A, Yoshikawa H (2019) Materials data platform: a fair system for data-driven materials science, In: 2019 8th International congress on advanced applied informatics (IIAI-AAI), pp 1021–1022. https://doi.org/10.1109/IIAI-AAI.2019.00206

51.

Ma R, Luo T (2020) PI1M: a benchmark database for polymer informatics. J Chem Inf Model 60(10):4684–4690. https://doi.org/10.1021/acs.jcim.0c00726CrossRefPubMed

52.

Borysov S, Geilhufe R, Balatsky A. Organic materials database: an open-access online database for data mining. PLoS ONE 12. https://doi.org/10.1371/journal.pone.0171501

53.

Kench S, Squires I, Dahari A Microlib: A library of 3d microstructures generated from 2d micrographs using slicegan. Sci Data 9. https://doi.org/10.1038/s41597-022-01744-1

54.

Bargmann S, Klusemann B, Markmann J, Schnabel J, Schneider K, Soyarslan C, Wilmers J (2018) Generation of 3d representative volume elements for heterogeneous materials: a review. Prog Mater Sci 96:322–384. https://doi.org/10.1016/j.pmatsci.2018.02.003CrossRef

55.

Mosser L, Dubrule O, Blunt M (2018) Stochastic reconstruction of oolitic limestone by generative adversarial networks. Transp Porous Med 125:81–103. https://doi.org/10.1007/s11242-018-1039-9CrossRef

56.

Kench S, Cooper S (2021) Generating three-dimensional structures from a two-dimensional slice with generative adversarial network-based dimensionality expansion. Nature Mach Intell 3:299–305. https://doi.org/10.1038/s42256-021-00322-1CrossRef

57.

Fokina D, Muravleva E, Ovchinnikov G, Oseledets I (2020) Microstructure synthesis using style-based generative adversarial networks. Phys Rev E 101:043308. https://doi.org/10.1103/PhysRevE.101.043308ADSCrossRefPubMed

58.

Noguchi S, Inoue J (2021) Stochastic characterization and reconstruction of material microstructures for establishment of process-structure-property linkage using the deep generative model. Phys Rev E 104:025302. https://doi.org/10.1103/PhysRevE.104.025302ADSCrossRefPubMed

59.

Fullwood D, Niezgoda S, Adams B, Kalidindi S (2010) Microstructure sensitive design for performance optimization. Prog Mater Sci 55:477–562. https://doi.org/10.1016/j.pmatsci.2009.08.002CrossRef

60.

Torquato S (2002) Random heterogeneous materials. Springer, New YorkCrossRef

61.

Adams B, Kalidindi S, Fullwood D (2013) Microstructure sensitive design for performance optimization. Butterworth-Heinemann, Waltham

62.

Gao Y, Jiao Y, Liu Y (2021) Ultra-efficient reconstruction of 3d microstructure and distribution of properties of random heterogeneous materials containing multiple phases. Acta Mater 204:116526. https://doi.org/10.1016/j.actamat.2020.116526CrossRef

63.

Robertson A, Kalidindi S (2022) Efficient generation of n-field microstructures from 2-point statistics using multi-output gaussian random fields. Acta Mater 232:117927. https://doi.org/10.1016/j.actamat.2022.117927CrossRef

64.

Robertson AE, Kelly C, Buzzy M, Kalidindi SR (2023) Local-global decompositions for conditional microstructure generation. Acta Mater 253:118966. https://doi.org/10.1016/j.actamat.2023.118966CrossRef

65.

Seibert P, Ambati M, Rabloff A, Kastner M (2021) Reconstructing random heterogeneous media through differentiable optimization. Comput Mater Sci 196:110455. https://doi.org/10.1016/j.commatsci.2021.110455CrossRef

66.

Seibert P, Rabloff A, Ambati M, Kastner M (2022) Descriptor-based reconstruction of three-dimensional microstructures through gradient-based optimization. Acta Mater 227:117667. https://doi.org/10.1016/j.actamat.2022.117667CrossRef

67.

Seibert P, Husert M, Wollner M, Kalina K, Kastner M. Fast reconstruction of microstructures with ellipsoidal inclusions using analytic descriptors, https://doi.org/10.48550/arxiv.2306.08316

68.

Falco S, Jiang J, Cola FD, Petrinic N (2017) Generation of 3d polycrystalline microstructures with a conditioned Laguerre–Voronoi tessellation technique. Comput Mater Sci 136:20–28. https://doi.org/10.1016/j.commatsci.2017.04.018CrossRef

69.

Prasad M, Vajragupta N, Hartmaier A (2019) Kanapy: a python package for generating complex synthetic polycrystalline microstructures. J Open Source Softw 4:1732. https://doi.org/10.21105/joss.01732ADSCrossRef

70.

Mandal S, Lao J, Donegan S, Rollett A (2018) Generation of statistically representative synthetic three-dimensional microstructures. Scripta Mater 146:128–132. https://doi.org/10.1016/j.scriptamat.2017.11.034CrossRef

71.

Niezgoda S, Fullwood D, Kalidindi S (2008) Delineation of the space of 2-point correlations in a composite material system. Acta Mater 56:5285–5292. https://doi.org/10.1016/j.actamat.2008.07.005ADSCrossRef

72.

de Oca Zapiain DM, Stewart J, Dingreville R (2021) Accelerating phase field based microstructure evolution predictions via surrogate models trained by machine learning methods. NPJ Comput Mater 3:1–11. https://doi.org/10.1038/s41524-020-00471-8CrossRef

73.

Attari V, Honarmandi P, Duong T, Sauceda DJ, Allaire D, Arroyave R (2020) Uncertainty propagation in a multiscale calphad-reinforced elastochemical phase-field model. Acta Mater 183:452–470. https://doi.org/10.1016/j.actamat.2019.11.031ADSCrossRef

74.

Hsu T, Epting WK, Kim H, Abernathy HW, Hackett GA, Rollett AD, Salvador PA, Holm EA (2021) Microstructure generation via generative adversarial network for heterogeneous, topoligically complex 3d materials. JOM 73:90–102. https://doi.org/10.1007/s11837-020-04484-yADSCrossRef

75.

NIMS, Nims materials database. https://mits.nims.go.jp/en/

76.

Lee K, Yun G Microstructure reconstruction using diffusion-based generative models

77.

Lin H, Brown LP, Long AC (2011) Modelling and simulating textile structures using texgen, In: Advances in textile engineering, vol. 331 of advanced materials research, pp 44–47. https://doi.org/10.4028/www.scientific.net/AMR.331.44

78.

Krishnamoorthi S, Bandyopadhyay R, Sangid MD (2023) A microstructure-based fatigue model for additively manufactured ti-6al-4v, including the role of prior \(\beta \) boundaries. Int J Plast 163:103569. https://doi.org/10.1016/j.ijplas.2023.103569CrossRef

79.

Du P, Zebrowski A, Zola J, Ganapathysubramanian B, Wodo O. Microstructure design using graphs. Comput Mater 4. https://doi.org/10.1038/s41524-018-0108-5

80.

Dureth C, Seibert P, Rucker D, Handford S, Kastner M, Gude M. Conditional diffusion-based microstructure reconstruction

81.

Jung J, Yoon JI, Park HK, Jo H, Kim HS (2020) Microstructure design using machine learning generated low dimensional and continuous design space. Materialia 11:100690. https://doi.org/10.1016/j.mtla.2020.100690CrossRef

82.

Tang J, Geng X, Li D, Shi Y, Tong J, Xiao H, Peng F (2021) Machine learned-based microstructure prediction during laser sintering of alumina. Sci Rep 11:10724. https://doi.org/10.1038/s41598-021-89816-xADSCrossRefPubMedPubMedCentral

83.

Iyer A, Dey B, Dasgupta A, Chen W. A conditional generative model for predicting material microstructures from processing methods

84.

Kanit T, Forest S, Galliet I, Mounoury V, Jeulin D (2003) Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int J Solids Struct 40(13):3647–3679. https://doi.org/10.1016/S0020-7683(03)00143-4CrossRef

85.

Kim Y, Jung J, Park H, Kim H (2023) Importance of microstructural features in bimodal structure-property linkage. Met Mater Int 29:53–58. https://doi.org/10.1007/s12540-022-01200-0CrossRef

86.

Paulson N, Priddy M, McDowell D, Kalidindi S (2019) Reduced-order microstructure-sensitive protocols to rank-order the transition fatigue resistance of polycrystalline microstructures. Int J Fatigue 119:1. https://doi.org/10.1016/j.ijfatigue.2018.09.011CrossRef

87.

Latypov M, Toth L, Kalidindi S (2019) Materials knowledge system for nonlinear composites. Comput Methods Appl Mech Eng 346:180. https://doi.org/10.1016/j.cma.2018.11.034ADSMathSciNetCrossRef

88.

Paulson N, Priddy M, McDowell D, Kalidindi S (2017) Reduced-order structure-property linkages for polycrystalline microstructures based on 2-point statistics. Acta Mater 129:428. https://doi.org/10.1016/j.actamat.2017.03.009ADSCrossRef

89.

Kaundinya PR, Choudhary K, Kalidindi SR. Machine learning approaches for feature engineering of the crystal structure: application to the prediction of the formation energy of cubic compounds, https://doi.org/10.48550/arXiv.2105.11319

90.

Generale A, Kalidindi S (2021) Reduced-order models for microstructure-sensitive effective thermal conductivity of woven ceramic matrix composites with residual porosity. Compos Struct 274:114399. https://doi.org/10.1016/j.compstruct.2021.114399CrossRef

91.

Fast T, Wodo O, Ganapathysubramanian B, Kalidindi S (2016) Microstructure taxonomy based on spatial correlations: application to microstructure coarsening. Acta Mater 108:176. https://doi.org/10.1016/j.actamat.2016.01.046ADSCrossRef

92.

Harrington G, Kelly C, Attari V, Arroyave R, Kalidindi S (2022) Application of a chained-ann for learning the process-structure mapping in \(mg_2si_xsn_{1-x}\) spinodal decomposition. Integr Mater Manuf Innov 11:433–449. https://doi.org/10.1007/s40192-022-00274-3CrossRef

93.

Barry MC, Gissinger JR, Chandross M, Wise KE, Kalidindi SR, Kumar S (2023) Voxelized atomic structure framework for materials design and discovery. Comput Mater Sci 230:112431. https://doi.org/10.1016/j.commatsci.2023.112431CrossRef

94.

Yabansu YC, Iskakov A, Kapustina A, Rajagopalan S, Kalidindi S. Application of gaussian process regression models for capturing the evolution of microstructure statistics in aging of nickel-based superalloys. Acta Mater 178

95.

Altschuh P, Yabansu YC, Hötzer J, Selzer M, Nestler B, Kalidindi SR (2017) Data science approaches for microstructure quantification and feature identification in porous membranes. J Membr Sci 540:88–97. https://doi.org/10.1016/j.memsci.2017.06.020CrossRef

96.

Latypov M, Kalidindi S (2017) Data-driven reduced order models for effective yield strength and partitioning of strain in multiphase materials. J Comput Phys 346:242–261. https://doi.org/10.1016/j.jcp.2017.06.013ADSMathSciNetCrossRef

97.

Wilson A, Adams R (2013) Gaussian process kernels for pattern discovery and extrapolation, In: Proceedings of the 30th international conference on machine learning, vol 28 of proceedings of machine learning research, PMLR, pp 1067–1075

98.

Lazaro-Gredilla M, Quinonero-Candela J, Rasmussen C, Figueiras-Vidal A (2010) Sparse spectrum gaussian process regression. J Mach Learn Res, 1865–1881

99.

Soutis C (2005) Fibre reinforced composites in aircraft construction. Prog Aerosp Sci 41:143–151. https://doi.org/10.1016/j.paerosci.2005.02.004CrossRef

100.

Brown Jr WF (1955) Solid mixture permittivities. J Chem Phys 23:1514–1517

101.

Kroner E (1977) Bounds for effective elastic moduli of disordered materials. J Mech Phys Solids 25:137–155ADSCrossRef

102.

Safdari M, Baniassadi M, Garmestani H, Al-Haik M (2012) A modified strong-constrast expansion for estimating the effective thermal conductivity of multiphase heterogeneous materials. J Appl Phys 112:114318ADSCrossRef

103.

Torquato S (1997) Effective stiffness tensor of composite media: 1. Exact series expansions. J Mech Phys Solids 45:1421–1448ADSMathSciNetCrossRef

104.

Torquato S (1998) Effective stiffness tensor of composite media: 2. Applications to isotropic dispersions. J Mech Phys Solids 46:1411–1440ADSMathSciNetCrossRef

105.

Fullwood D, Adams B, Kalidindi S (2008) A strong contrast homogenization formulation for multi-phase anistropic materials. J Mech Phys Solids 56:2287–2297ADSMathSciNetCrossRef

106.

Hashemi S, Kalidindi S (2021) A machine learning framework for the temporal evolution of microstructure during static recrystallization of polycrystalline materials simulated by cellular automaton. Comput Mater Sci 188:110132. https://doi.org/10.1016/j.commatsci.2020.110132CrossRef

107.

Fullwood D, Adams B, Kalidindi S (2007) Generalized pareto front methods applied to second-order material property closures. Comput Mater Sci 38:788–799. https://doi.org/10.1016/j.commatsci.2006.05.016CrossRef

108.

Mann A, Kalidindi S (2022) Development of a robust cnn model for capturing microstructure-property linkages and building property closures supporting material design. Front Mater 9:851085. https://doi.org/10.3389/fmats.2022.851085ADSCrossRef

109.

Rossin J, Leser P, Pusch K, Frey C, Vogel S, Saville A, Torbet C, Clarke A, Daly S, Pollock T (2022) Single crystal elastic constants of additively manufactured components determined by resonant ultrasound spectroscopy. Mater Charact 192:112244. https://doi.org/10.1016/j.matchar.2022.112244CrossRef

110.

Kroner E (1972) Statistical continuum mechanics. Springer, New York

111.

Niezgoda S, Yabansu Y, Kalidindi S (2011) Understanding and visualizing microstructure and microstructure variance as a stochastic process. Acta Mater 59:6387–6400. https://doi.org/10.1016/j.actamat.2011.06.051ADSCrossRef

112.

Shlens J (2020) A tutorial of principal component analysis. Accessed 28 Nov 2020. https://www.cs.princeton.edu/picasso/mats/PCA-Tutorial-Intuition_jp.pdf

113.

Kennard RW, Stone LA (1969) Computer aided design of experiments. Technometrics 11(1):137–148. https://doi.org/10.1080/00401706.1969.10490666CrossRef

114.

Mak S, Joseph V (2018) Minimax and minimax projection designs using clustering. J Comput Graph Stat 27:166–178. https://doi.org/10.1080/10618600.2017.1302881MathSciNetCrossRef

115.

Huang C, Joseph V, Ray D (2021) Constrained minimum energy designs. Stat Comput 31:80. https://doi.org/10.1007/s11222-021-10054-2MathSciNetCrossRef

116.

Fullwood D, Niezgoda S, Kalidindi S (2008) Microstructure reconstruction from 2-point statistics using phase recovery algorithms. Acta Mater 56:942–948. https://doi.org/10.1016/j.actamat.2007.10.044ADSCrossRef

117.

Jiao Y, Stillinger F, Torquato S (2007) Modeling heterogeneous materials via two-point correlation functions: basic principles. Phys Rev E 76:031110. https://doi.org/10.1103/PhysRevE.76.031110ADSMathSciNetCrossRef

118.

Jiao Y, Stillinger F, Torquato S (2009) A superior descriptor of random textures and its predictive capacity. PNAS 106:17634–17639. https://doi.org/10.1073/pnas.0905919106ADSCrossRefPubMedPubMedCentral

119.

Niezgoda SR, Turner DM, Fullwood DT, Kalidindi SR (2010) Optimized structure based representative volume element sets reflecting the ensemble-averaged 2-point statistics. Acta Mater 58(13):4432–4445. https://doi.org/10.1016/j.actamat.2010.04.041ADSCrossRef

120.

Helton J, Davis F (2003) Latin hypercube sampling and propogation of uncertainty in analyses of complex systems. Reliab Eng Syst Saf, 23–69. https://doi.org/10.1016/S0951-8320(03)00058-9

121.

Swayer S (2023) Wishart distributions and inverse-wishart sampling. Accessed 4 Oct 2023. https://www.math.wustl.edu/~sawyer/hmhandouts/Wishart.pdf

122.

Odell PL, Feiveson AH (1966) A numerical procedure to generate a sample covariance matrix. J Am Stat Assoc 61(313):199–203. https://doi.org/10.1080/01621459.1966.10502018MathSciNetCrossRef

123.

Cecen A (2017) Calculation, utilization, and inference of spatial statistics in practical spatio-temporal data. Georgia Tech Library, Atlanta

124.

Cecen A, Yucel B, Kalidindi S (2021) A generalized and modular framework for digital generation of composite microstructures. J Compos Sci 5:1–20. https://doi.org/10.3390/jcs5080211CrossRef

125.

Brough D, Wheeler D, Kalidindi S (2017) Materials knowledge systems in python: a data science framework for accelerated development of hierarchical materials. Integr Mater Manuf Innov 6:36–53. https://doi.org/10.1007/s40192-017-0089-0CrossRefPubMedPubMedCentral

126.

Kelly C, Kalidindi S (2021) Recurrent localization networks applied to the Lippmann–Schwinger equation. Comput Mater Sci 192:110356. https://doi.org/10.1016/j.commatsci.2021.110356CrossRef

127.

You H, Zhang Q, Ross C, Lee C, Yu Y (2022) Learning deep implicit fourier neural operators (ifnos) with applications to heterogeneous material modeling. Comput Methods Appl Mech Eng 398:115296. https://doi.org/10.1016/j.cma.2022.115296ADSMathSciNetCrossRef

128.

Chun S, Roy S, Nguyen Y, Choi J, Udaykumar H, Baek S (2020) Deep learning for synthetic microstructure generation in a materials-by-design framework for heterogeneous energetic materials. Sci Rep 10:13307. https://doi.org/10.1038/s41598-020-70149-0ADSCrossRefPubMedPubMedCentral

129.

Ostoja-Starzewski M, Kale S, Karimi P, Malyarenko A, Raghavan B, Ranganathan S, Zhang J (2016) Chapter two-scaling to RVE in random media, vol 49 of Advances in Applied Mechanics, pp 111–211. https://doi.org/10.1016/bs.aams.2016.07.001

130.

Zerhouni O, Brisard S, Danas K. Quantifying the effects of two-point correlations on the effective elasticity of specific classes of random porous materials with and without connectivity. Int J Eng Sci. https://doi.org/10.1016/j.ijengsci.2021.103520

131.

Li S (1999) On the unit cell for micromechanical analysis of fibre-reinforced composites. Proc R Soc A 455:815–838. https://doi.org/10.1098/rspa.1999.0336ADSMathSciNetCrossRef

132.

Li S (2001) General unit cells for micromechanical analyses of unidirectional composites. Compos A Appl Sci Manuf 32(6):815–826. https://doi.org/10.1016/S1359-835X(00)00182-2CrossRef

133.

Landi G, Niezgoda N, Kalidindi S (2010) Multi-scale modeling of elastic propoerties of three-dimensional voxel-based microstructure datasets using novel DFT-based knowledge systems. Acta Mater 58:2716–2725. https://doi.org/10.1016/j.actamat.2010.01.007ADSCrossRef

134.

Fast T, Kalidindi SR (2011) Formulation and calibration of higher-order elastic localization relationships using the MKS approach. Acta Mater 59:4595–4605. https://doi.org/10.1016/j.actamat.2011.04.005ADSCrossRef

135.

Proust G, Kalidindi S (2006) Procedures for construction of anisotropic elastic-plastic property closures for face-centered cubic polycrystals using first-order bounding relations. J Mech Phys Solids 54:1744–1762. https://doi.org/10.1016/j.jmps.2006.01.010ADSMathSciNetCrossRef

136.

Hill R (1963) Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 11:357–372ADSCrossRef

137.

Yang M, Zhang J, Wei H, Zhao Y, Gui W, Su H, Jin T, Liu L. Study of \(\gamma \)’ rafting under different stress states: a phase field simulation considering viscoplasticity. J Alloys Compounds. https://doi.org/10.1016/j.jallcom.2018.07.317

138.

Blesgen T, Chenchiah I. Cahn–Hilliard equations incorporating elasticity: analysis and comparison to experiments. Philos Trans R Soc. https://doi.org/10.1098/rsta.2012.0342

139.

Chen W, Fuge M (2017) Beyond the known: detecting novel feasible domains over unbounded design space. J Mech Des 139:111405. https://doi.org/10.1115/1.4037306CrossRef

140.

Chen W, Fuge M (2019) Synthesizing designs with interpart dependencies using hierarchical generative adversarial networks. J Mech Des 141:111403. https://doi.org/10.1115/1.4044076CrossRef

141.

Wang S, Generale AP, Kalidindi SR, Joseph VR (2023) Sequential designs for filling output spaces. Technometrics, 1–12 https://doi.org/10.1080/00401706.2023.2231042

142.

Ahrendt P (2023) The multivariate gaussian probability. Accessed 4 Oct 2023. https://d1wqtxts1xzle7.cloudfront.net/49874923/The_Multivariate_Gaussian_Probability_Di20161026-27105-77g7a0-libre.pdf?1477466954= &response-content-disposition=inline%3B+filename%3DThe_multivariate_gaussian_probability_di.pdf &Expires=1696429097 &Signature=EbY-smInGeeMVvC0qsTaERE9jTZTSJF8NC9MZl0fOkqTiBgWVcmYqZ~u-8vaYnjyuJyCgV-40kYMMHThOOAhgEGQ8~2dzZG~TV7Rn69mTy1I1ieWafwrsatRpsj3CB6KIbhRn6Y2MgwENUL0RVxnycgT2uiSJiAAoucqbOw5cxBO9H2OrgzgT2SywfSb2hxmr~GLayEwsCWUA~QRgm4AYcbK-YwWebZcZ6RkMOCMotDks-aCd66kbFpBz8bdM3avpmNpYJRWn9jxUFhDhJOnhz0OFdidp~fN96dS-J7~hSJDeK4dGDBE03b5sUd4Px7YrFf4jCCD6KOn1ldefSJR9w__ &Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA

143.

Chawla M (2011) PCA and ICA processing methods for removal of artifacts and noise in electrocardiograms: a survey and comparison. Appl Soft Comput 11(2):2216–2226. https://doi.org/10.1016/j.asoc.2010.08.001CrossRef

144.

Hastie T, Tibshirani R, Friedman J (2016) The elements of statistical learning. Springer, New York

145.

Vetterli M, Kovacevic J, Goyal V (2014) Foundations of signal processing. Cambridge University Press, CambridgeCrossRef

146.

Berryman J (1987) Relationship between specific surface area and spatial correlation functions for anistropic porous media. J Math Phys 28:244–245ADSMathSciNetCrossRef

147.

Blair S, Berge P, Berryman J (1996) Using two-point correlation functions to characterize microgeometry and estimate permeabilities of sandstone and porous glass. J Geophys Res 101:20359–20375. https://doi.org/10.1029/96JB00879ADSCrossRef

Title: MICRO2D: A Large, Statistically Diverse, Heterogeneous Microstructure Dataset
Authors: Andreas E. Robertson
Adam P. Generale
Conlain Kelly
Michael O. Buzzy
Surya R. Kalidindi
Publication date: 12-02-2024
Publisher: Springer International Publishing
Published in: Integrating Materials and Manufacturing Innovation / Issue 1/2024
Print ISSN: 2193-9764
Electronic ISSN: 2193-9772
DOI: https://doi.org/10.1007/s40192-023-00340-4

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MICRO2D: A Large, Statistically Diverse, Heterogeneous Microstructure Dataset

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