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A Comparative Study of the Efficacy of Local/Global and Parametric/Nonparametric Machine Learning Methods for Establishing Structure–Property Linkages in High-Contrast 3D Elastic Composites

  • Patxi Fernandez-Zelaia
  • Yuksel C. Yabansu
  • Surya R. KalidindiEmail author
Technical Article
  • 41 Downloads

Abstract

Reduced-order structure–property (S-P) linkages play a pivotal role in the tailored design of materials for advanced engineering components. There is a critical need to distill these from the simulation datasets aggregated using sophisticated, computationally expensive, physics-based numerical tools (e.g., finite element methods). The recent emergence of materials data science approaches has opened new avenues for addressing this challenge. In this paper, we critically compare the relative merits of the application of four distinct machine learning approaches for their efficacy in extracting microstructure-property linkages from the finite element simulation data aggregated on high-contrast elastic composites with different microstructures. The machine learning approaches selected for the study have included different combinations of local/global and parametric/nonparametric approaches. Furthermore, the nonparametric approaches selected for this study are based on Gaussian Process (GP) models that allow for a formal treatment of uncertainty quantification in the predicted values. The predictive performances of these different approaches have been compared against each other using rigorous cross-validation error metrics. Furthermore, their sensitivity to both the dataset size and dimensionality has been investigated.

Keywords

Nonparametric regression Local approximate Gaussian Process Structure–property linkages High-contrast composites Gaussian Process regression 

Notes

Funding Information

YCY and SRK received support from NSF 1761406. PFZ received financial support of the work from the Morris M. Bryan, Jr. Professorship.

References

  1. 1.
    Materials genome initiative for global competitiveness. National science and technology council executive office of the president (2011)Google Scholar
  2. 2.
    van Schalkwijk W, Scrosati B (2007) Advances in lithium-ion batteries. Springer, BostonGoogle Scholar
  3. 3.
    Reed RC (2008) The superalloys: fundamentals and applications. Cambridge University Press, CambridgeGoogle Scholar
  4. 4.
    Hasegawa R (2000) Present status of amorphous soft magnetic alloys. J Magn Magn Mater 215:240–245Google Scholar
  5. 5.
    Furrer D, Fecht H (1999) Ni-based superalloys for turbine discs. JOM 51(1):14–17Google Scholar
  6. 6.
    Pollock T, Tin S (2006) Nickel-based superalloys for advanced turbine engines: chemistry, microstructure and properties. J Propul Power 22(2):361–374Google Scholar
  7. 7.
    Lu L, Han X, Li J, Hua J, Ouyang M (2013) A review on the key issues for lithium-ion battery management in electric vehicles. J Power Sources 226:272–288Google Scholar
  8. 8.
    Integrated computational materials engineering: a transformational discipline for improved competitiveness and national security. The National Academies Press, Washington (2008)Google Scholar
  9. 9.
    Mueller T, Kusne AG, Ramprasad R (2015) Machine learning in materials science: recent progress and emerging applications. Rev Comput Chem 29:186–273Google Scholar
  10. 10.
    Yang N, Yee J, Zheng B, Gaiser K, Reynolds T, Clemon L, Lu W, Schoenung J, Lavernia E (2017) Process-structure-property relationships for 316l stainless steel fabricated by additive manufacturing and its implication for component engineering. J Therm Spray Tech 26(4):610–626Google Scholar
  11. 11.
    Kalidindi S (2015) Hierarchical materials informatics: novel analytics for materials data. Elsevier, BostonGoogle Scholar
  12. 12.
    Yabansu YC, Steinmetz P, Hötzer J, Kalidindi S, Nestler B (2017) Extraction of reduced-order process-structure linkages from phase-field simulations. Acta Mater 124:182–194Google Scholar
  13. 13.
    Gomberg JA, Medford AJ, Kalidindi S (2017) Extracting knowledge from molecular mechanics simulations of grain boundaries using machine learning. Acta Mater 133:100–108Google Scholar
  14. 14.
    Gorgannejad S, Gahrooei MR, Paynabar K, Neu R (2019) Quantitative prediction of the aged state of ni-base superalloys using pca and tensor regression. Acta Mater 165:259–269Google Scholar
  15. 15.
    Olson GB (1997) Computational design of hierarchically structured materials. Science 277(5330):1237–1242Google Scholar
  16. 16.
    Panchal JH, Kalidindi S, McDowell DL (2013) Key computational modeling issues in integrated computational materials engineering. Comput Aided Des 45(1):4–25Google Scholar
  17. 17.
    Nellippallil AB, Rangaraj V, Gautham B, Singh AK, Allen JK, Mistree F (2017) A goal-oriented, inverse decision-based design method to achieve the vertical and horizontal integration of models in a hot rod rolling process chain. In: ASME 2017 International design engineering technical conferences and computers and information in engineering conference. American Society of Mechanical Engineers, pp v02BT03a003–v02BT03a003Google Scholar
  18. 18.
    Fullwood D, Niezgoda S, Adams BL, Kalidindi S (2010) Microstructure sensitive design for performance optimization. Prog Mater Sci 55(6):477–562Google Scholar
  19. 19.
    Sanchez-Lengeling B, Aspuru-Guzik A (2018) Inverse molecular design using machine learning: Generative models for matter engineering. Science 361(6400):360–365Google Scholar
  20. 20.
    McDowell DL, Kalidindi S (2016) The materials innovation ecosystem: a key enabler for the materials genome initiative. MRS Bulletin 41(4):326–337Google Scholar
  21. 21.
    Mortazavi B, Baniassadi M, Bardon J, Ahzi S (2013) Modeling of two-phase random composite materials by finite element, mori–tanaka and strong contrast methods. Compos Part B Eng 45(1):1117–1125Google Scholar
  22. 22.
    Argatov II, Sabina FJ (2017) A two-phase self-consistent model for the grid indentation testing of composite materials. Int J Eng Sci 121:52–59Google Scholar
  23. 23.
    Duan H, Wang JX, Huang Z, Karihaloo BL (2005) Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. J Mech Phys Solids 53(7):1574–1596Google Scholar
  24. 24.
    Fu SY, Feng XQ, Lauke B, Mai YW (2008) Effects of particle size, particle/matrix interface adhesion and particle loading on mechanical properties of particulate–polymer composites. Compos Part B 39(6):933–961Google Scholar
  25. 25.
    Trofimov A, Drach B, Sevostianov I (2017) Effective elastic properties of composites with particles of polyhedral shapes. Int J Solids Struct 120:157–170Google Scholar
  26. 26.
    Fullwood D, Adams BL, Kalidindi S (2008) A strong contrast homogenization formulation for multi-phase anisotropic materials. J Mech Phys Solids 56(6):2287–2297Google Scholar
  27. 27.
    Pham D, Torquato S (2003) Strong-contrast expansions and approximations for the effective conductivity of isotropic multiphase composites. J Appl Phys 94(10):6591–6602Google Scholar
  28. 28.
    Mikdam A, Makradi A, Ahzi S, Garmestani H, Li DS, Remond Y (2009) Effective conductivity in isotropic heterogeneous media using a strong-contrast statistical continuum theory. J Mech Phys Solids 57(1):76–86Google Scholar
  29. 29.
    Adams BL, Kalidindi S, Fullwood D (2012) Microstructure sensitive design for performance optimization. Butterworth-Heinemann, BostonGoogle Scholar
  30. 30.
    Fernandez-Zelaia P, Joseph VR, Kalidindi S, Melkote SN (2018) Estimating mechanical properties from spherical indentation using bayesian approaches. Mater Des 147:92–105Google Scholar
  31. 31.
    Paulson NH, Priddy MW, McDowell DL, Kalidindi S (2017) Reduced-order structure-property linkages for polycrystalline microstructures based on 2-point statistics. Acta Mater 129:428–438Google Scholar
  32. 32.
    Li X, Xu Y, Chen S (2016) Computational homogenization of effective permeability in three-phase mesoscale concrete. Constr Build Mater 121:100–111Google Scholar
  33. 33.
    Pinz M, Weber G, Lenthe W, Uchic M, Pollock T, Ghosh S (2018) Microstructure and property based statistically equivalent rves for intragranular γ- γ’microstructures of ni-based superalloys. Acta Mater 157:245–258Google Scholar
  34. 34.
    Latypov MI, Kalidindi S (2017) Data-driven reduced order models for effective yield strength and partitioning of strain in multiphase materials. J Comput Phys 346(13):242–261Google Scholar
  35. 35.
    Gupta A, Cecen A, Goyal S, Singh AK, Kalidindi S (2015) Structure–property linkages using a data science approach: application to a non-metallic inclusion/steel composite system. Acta Mater 91:239–254Google Scholar
  36. 36.
    Jung J, Yoon JI, Park HK, Kim JY, Kim HS (2019) Bayesian approach in predicting mechanical properties of materials: Application to dual phase steels. Mater Sci Eng A 743:382–390Google Scholar
  37. 37.
    Iskakov A, Yabansu YC, Rajagopalan S, Kapustina A, Kalidindi S (2018) Application of spherical indentation and the materials knowledge system framework to establishing microstructure-yield strength linkages from carbon steel scoops excised from high-temperature exposed components. Acta Mater 144:758–767Google Scholar
  38. 38.
    Altschuh P, Yabansu YC, Hötzer J, Selzer M, Nestler B, Kalidindi S (2017) Data science approaches for microstructure quantification and feature identification in porous membranes. J Membr Sci 540(1):88–97Google Scholar
  39. 39.
    Mangal A, Holm EA (2018) Applied machine learning to predict stress hotspots i: face centered cubic materials. Int J Plast 111:122–134Google Scholar
  40. 40.
    Friedman J, Hastie T, Tibshirani R (2001) The elements of statistical learning, vol 1. Springer series in statistics. New York, NY, USAGoogle Scholar
  41. 41.
    Cecen A, Dai H, Yabansu YC, Kalidindi S, Song L (2018) Material structure-property linkages using three-dimensional convolutional neural networks. Acta Mater 146:76–84Google Scholar
  42. 42.
    Yang Z, Yabansu YC, Al-Bahrani R, Liao WK, Choudhary AN, Kalidindi SR, Agrawal A (2018) Deep learning approaches for mining structure-property linkages in high contrast composites from simulation datasets. Comput Mater Sci 151:278–287Google Scholar
  43. 43.
    Ryczko K, Mills K, Luchak I, Homenick C, Tamblyn I (2018) Convolutional neural networks for atomistic systems. Comput Mater Sci 149:134–142Google Scholar
  44. 44.
    Kondo R, Yamakawa S, Masuoka Y, Tajima S, Asahi R (2017) Microstructure recognition using convolutional neural networks for prediction of ionic conductivity in ceramics. Acta Mater 141:29–38Google Scholar
  45. 45.
    Fernandez-Zelaia P, Melkote SN (2019) Statistical calibration and uncertainty quantification of complex machining computer models. Int J Mach Tools Manuf 136:45–61Google Scholar
  46. 46.
    Yang Z, Yabansu YC, Jha D, Liao WK, Choudhary AN, Kalidindi SR, Agrawal A (2019) Establishing structure-property localization linkages for elastic deformation of three-dimensional high contrast composites using deep learning approaches. Acta Mater 166:335–345Google Scholar
  47. 47.
    Yabansu YC, Kalidindi S (2015) Representation and calibration of elastic localization kernels for a broad class of cubic polycrystals. Acta Mater 94:26–35Google Scholar
  48. 48.
    Landi G, Niezgoda S, Kalidindi S (2010) Multi-scale modeling of elastic response of three-dimensional voxel-based microstructure datasets using novel dft-based knowledge systems. Acta Mater 58(7):2716–2725Google Scholar
  49. 49.
    Kalidindi S, Niezgoda S, Landi G, Vachhani S, Fast T (2010) A novel framework for building materials knowledge systems. Comput Mater Continua 17(2):103–125Google Scholar
  50. 50.
    Cecen A, Yabansu YC, Kalidindi S (2018) A new framework for rotationally invariant two-point spatial correlations in microstructure datasets. Acta Mater 158:53–64Google Scholar
  51. 51.
    Niezgoda S, Kanjarla AK, Kalidindi S (2013) Novel microstructure quantification framework for databasing, visualization, and analysis of microstructure data. Integr Mater Manuf Innov 2(1):3Google Scholar
  52. 52.
    Niezgoda S, Fullwood D, Kalidindi S (2008) Delineation of the space of 2-point correlations in a composite material system. Acta Mater 56(18):5285–5292Google Scholar
  53. 53.
    Fullwood D, Niezgoda S, Kalidindi S (2008) Microstructure reconstructions from 2-point statistics using phase-recovery algorithms. Acta Mater 56(5):942–948Google Scholar
  54. 54.
    Turner DM, Niezgoda S, Kalidindi S (2016) Efficient computation of the angularly resolved chord length distributions and lineal path functions in large microstructure datasets. Model Simul Mater Sci Eng 24(7):075,002Google Scholar
  55. 55.
    Brough DB, 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(1):36–53Google Scholar
  56. 56.
    Brough DB, Kannan A, Haaland B, Bucknall DG, Kalidindi S (2017) Extraction of process-structure evolution linkages from x-ray scattering measurements using dimensionality reduction and time series analysis. Integr Mater Manuf Innov 6(2):147–159Google Scholar
  57. 57.
    Bishop CM (2006) Pattern recognition and machine learning. Springer, BerlinGoogle Scholar
  58. 58.
    Witten IH, Frank E, Hall MA, Pal CJ (2016) Data mining: practical machine learning tools and techniques. Morgan Kaufmann, CambridgeGoogle Scholar
  59. 59.
    Binois M, Gramacy RB, Ludkovski M (2018) Practical heteroskedastic gaussian process modeling for large simulation experiments. J Comput Graph Stat 27(4):808–821Google Scholar
  60. 60.
    Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc Ser B Methodol 58 (1):267–288Google Scholar
  61. 61.
    Härdle W (1990) Applied nonparametric regression 19. Cambridge University Press, CambridgeGoogle Scholar
  62. 62.
    Kvam PH, Vidakovic B (2007) Nonparametric statistics with applications to science and engineering, vol 653. Wiley, New JerseyGoogle Scholar
  63. 63.
    Cleveland WS (1979) Robust locally weighted regression and smoothing scatterplots. J Am Stat Assoc 74 (368):829–836Google Scholar
  64. 64.
    Cleveland WS, Devlin SJ (1988) Locally weighted regression: an approach to regression analysis by local fitting. J Am Stat Assoc 83(403):596–610Google Scholar
  65. 65.
    Ho TK (1995) Random decision forests. In: 1995 proceedings of the third international conference on document analysis and recognition, vol 1. IEEE, pp 278–282Google Scholar
  66. 66.
    Krige DG (1951) A statistical approach to some basic mine valuation problems on the witwatersrand. J South Afr Inst Min Metall 52(6):119–139Google Scholar
  67. 67.
    Matheron G (1963) Principles of geostatistics. Econ Geol 58(8):1246–1266Google Scholar
  68. 68.
    Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Stat Sci 4(4):409–435Google Scholar
  69. 69.
    Rasmussen CE, Williams CK (2006) Gaussian processes for machine learning, vol 1. MIT Press, CambridgeGoogle Scholar
  70. 70.
    Ba S, Joseph VR et al (2012) Composite gaussian process models for emulating expensive functions. Ann Appl Stat 6(4):1838–1860Google Scholar
  71. 71.
    Joseph VR (2006) Limit kriging. Technometrics 48(4):458–466Google Scholar
  72. 72.
    Tuo R, Wu CJ, Yu D (2014) Surrogate modeling of computer experiments with different mesh densities. Technometrics 56(3):372–380Google Scholar
  73. 73.
    Santner TJ, Williams BJ, Notz WI (2013) The design and analysis of computer experiments. Springer, New YorkGoogle Scholar
  74. 74.
    Chen H, Loeppky JL, Welch WJ (2017) Flexible correlation structure for accurate prediction and uncertainty quantification in bayesian gaussian process emulation of a computer model. SIAM/ASA J Uncertain Quantif 5 (1):598–620Google Scholar
  75. 75.
    Banerjee S, Gelfand AE, Finley AO, Sang H (2008) Gaussian predictive process models for large spatial data sets. J R Stat Soc Ser B Stat Methodol 70(4):825–848Google Scholar
  76. 76.
    Gramacy RB, Lee HKH (2008) Bayesian treed gaussian process models with an application to computer modeling. J Am Stat Assoc 103(483):1119–1130Google Scholar
  77. 77.
    Duvenaud DK, Nickisch H, Rasmussen CE (2011) Additive gaussian processes. In: Advances in neural information processing systems, pp 226–234Google Scholar
  78. 78.
    Gramacy RB, Apley DW (2015) Local gaussian process approximation for large computer experiments. J Comput Graph Stat 24(2):561–578Google Scholar
  79. 79.
    Gramacy RB (2015) lagp: large-scale spatial modeling via local approximate gaussian processes in r. Journal of Statistical Software (available as a vignette in the laGP package)Google Scholar
  80. 80.
    Breiman L (2001) Random forests. Mach Learn 45(1):5–32Google Scholar
  81. 81.
    Chipman HA, George EI, McCulloch RE, et al. (2010) BART: Bayesian additive regression trees. Ann Appl Stat 4(1):266– 298Google Scholar
  82. 82.
    Yabansu YC, Kalidindi SR (2019) Microscale volume elements and their effective/homogenized stiffness parameter for high contrast 3-d elastic composite. https://matin.gatech.edu/resources/309

Copyright information

© The Minerals, Metals & Materials Society 2019

Authors and Affiliations

  1. 1.George W. Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Oak Ridge National LaboratoryOak RidgeUSA
  3. 3.School of Computational Science and EngineeringGeorgia Institute of TechnologyAtlantaUSA

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