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A Bayesian framework for materials knowledge systems

  • Artificial Intelligence Prospective
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Abstract

This prospective offers a new Bayesian framework that could guide the systematic application of the emerging toolsets of machine learning in the efforts to address two of the central bottlenecks encountered in materials innovation: (i) the capture of core materials knowledge in reduced-order forms that allow one to rapidly explore the vast materials design spaces, and (ii) objective guidance in the selection of experiments or simulations needed to identify the governing physics in the materials phenomena of interest. The framework builds on recent advances in the low-dimensional representation of the statistics describing the material’s hierarchical structure.

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References

  1. Materials Genome Initiative for Global Competitiveness. National Science and Technology Council, Editor. 2011.

  2. D.L. McDowell and S.R. Kalidindi: The materials innovation ecosystem: a key enabler for the Materials Genome Initiative. MRS Bull. 41, 326–337 (2016).

    Article  Google Scholar 

  3. M. Drosback: Materials genome initiative: advances and initiatives. JOM 66, 334–335 (2014).

    Article  Google Scholar 

  4. G.B. Olson and C.J. Kuehmann: Materials genomics: from CALPHAD to flight. Scr. Mater. 70, 25–30 (2014).

    Article  CAS  Google Scholar 

  5. J.C. Zhao: High-throughput experimental tools for the materials genome initiative. Chin. Sci. Bull. 59, 1652–1661 (2014).

    Article  Google Scholar 

  6. C.M. Breneman, L.C. Brinson, L.S. Schadler, B. Natarajan, M. Krein, K. Wu, L. Morkowchuk, Y. Li, H. Deng and H. Xu: Stalking the materials genome: a data-driven approach to the virtual design of nanostructured polymers. Adv. Funct. Mater. 23, 5746–5752 (2013).

    Article  CAS  Google Scholar 

  7. A. Jain, S.P. Ong, G. Hautier, W. Chen, W.D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder and K.A. Persson: Commentary: the materials project: a materials genome approach to accelerating materials innovation. APL Mater. 1, 011002 (2013).

    Article  Google Scholar 

  8. S. Ramakrishna, T.-Y. Zhang, W.-C. Lu, Q. Qian, J.S.C. Low, J.H.R. Yune, D.Z.L. Tan, S. Bressan, S. Sanvito and S.R. Kalidindi: Materials informatics. J. Intell. Manuf. 10.1007/s10845-018-1392-0 (2018).

    Google Scholar 

  9. S.R. Kalidindi, A.J. Medford, and D.L. McDowell: Vision for data and informatics in the future materials innovation ecosystem. JOM 68, 2126–2137 (2016).

    Article  Google Scholar 

  10. S.R. Kalidindi: Hierarchical Materials Informatics (Butterworth Heinemann, Waltham, MA, 2015).

    Google Scholar 

  11. P. Voorhees and G. Spanos: Modeling Across Scales: A Roadmapping Study for Connecting Materials Models and Simulations Across Length and Time Scales. Tech. rep. (The Minerals, Metals & Materials Society (TMS), Pittsburgh, PA, 2015).

    Google Scholar 

  12. E.B. Gulsoy, A.J. Shahani, J.W. Gibbs, J.L. Fife and P.W. Voorhees: Four-dimensional morphological evolution of an aluminum silicon alloy using propagation-based phase contrast X-ray tomographic microscopy. Mater. Trans. 55, 161–164 (2014).

    Article  CAS  Google Scholar 

  13. M.D. Uchic, M.A. Groeber, and A.D. Rollett: Automated serial sectioning methods for rapid collection of 3-D microstructure data. JOM 63, 25–29 (2011).

    Article  Google Scholar 

  14. J.F. Bingert, R.M. Suter, J. Lind, S.F. Li, R. Pokharel and C.P. Trujillo: High-energy diffraction microscopy characterization of spall damage. In Tom Proulx, Bo Song, Dan Casem and Jamie Kimberley (eds.), Dynamic Behavior of Materials (Springer, New York, NY, 1, 2014), pp. 397–403.

    Google Scholar 

  15. U. Lienert, S.F. Li, C.M. Hefferan, J. Lind, R.M. Suter, J.V. Bernier, N.R. Barton, M.C. Brandes, M.J. Mills, M.P. Miller, B. Jakobsen and W. Pantleon: High-energy diffraction microscopy at the advanced photon source. JOM Journal of the Minerals, Metals and Materials Society 63, 70–77 (2011).

    Article  Google Scholar 

  16. S.R. Kalidindi, D.B. Brough, S. Li, A. Cecen, A.L. Blekh, F.Y.P. Congo and C. Campbell: Role of materials data science and informatics in accelerated materials innovation. MRS Bull. 41, 596–602 (2016).

    Article  Google Scholar 

  17. S.R. Kalidindi and M.D. Graef: Materials data science: current status and future outlook. Annu. Rev. Mater. Res. 45, 171–193 (2015).

    Article  CAS  Google Scholar 

  18. K. Rajan: Materials informatics. Mater. Today 8, 38–45 (2005).

    Article  CAS  Google Scholar 

  19. D.B. Brough, D. Wheeler, and S.R. Kalidindi: Materials knowledge systems in python—a data science framework for accelerated development of hierarchical materials. Integr.Mater.Manuf. Innovation 6, 36–53 (2017).

    Article  Google Scholar 

  20. C. Kim, A. Chandrasekaran, T.D. Huan, D. Das and R. Ramprasad: Polymer genome: a data-powered polymer informatics platform for property predictions. J. Phys. Chem. C 122, 17575–17585 (2018).

    Article  CAS  Google Scholar 

  21. S.R. Kalidindi: Data science and cyberinfrastructure: critical enablers for accelerated development of hierarchical materials. Int. Mater. Rev. 60, 150–168 (2015).

    Article  CAS  Google Scholar 

  22. G. Linden, B. Smith, and J. York: Amazon. com recommendations: itemtoitem collaborative filtering. IEEE Internet Comput. 7, 76–80 (2003).

    Article  Google Scholar 

  23. J.A. Cruz and D.S. Wishart: Applications of machine learning in cancer prediction and prognosis. Cancer Inform. 2, 59–78 (2006).

    Article  Google Scholar 

  24. M. Bojarski, D. Del Testa, D. Dworakowski, B. Firner, B. Flepp, P. Goyal, L.D. Jackel, M. Monfort, U. Muller and J. Zhang: End to end learning for self-driving cars. arXiv preprint arXiv:1604.07316, 2016.

    Google Scholar 

  25. Y. Kajikawa, Y. Sugiyama, H. Mima and K. Matsushima: Causal knowledge extraction by natural language processing in material science: a case study in chemical vapor deposition. Data Sci. J. 5, 108–118 (2006).

    Article  CAS  Google Scholar 

  26. E. Kim, K. Huang, A. Tomala, S. Matthews, E. Strubell, A. Saunders, A. McCallum and E. Olivetti: Machine-learned and codified synthesis parameters of oxide materials. Sci. Data 4, 170127 (2017).

    Article  CAS  Google Scholar 

  27. J. Nunez-Iglesias, R. Kennedy, T. Parag, J. Shi and D.B. Chklovskii: Machine learning of hierarchical clustering to segment 2D and 3D images. PLoS One 8, e71715 (2013).

    Article  CAS  Google Scholar 

  28. A. Chowdhury, E. Kautz, B. Yener and D. Lewis: Image driven machine learning methods for microstructure recognition. Comput. Mater. Sci. 123, 176–187 (2016).

    Article  Google Scholar 

  29. P. Raccuglia, K.C. Elbert, P.D.F. Adler, C. Falk, M.B. Wenny, A. Mollo, M. Zeller, S.A. Friedler, J. Schrier and A.J. Norquist: Machine-learning-assisted materials discovery using failed experiments. Nature 533, 73 (2016).

    Article  CAS  Google Scholar 

  30. B. Meredig, A. Agrawal, S. Kirklin, J.E. Saal, J.W. Doak, A. Thompson, K. Zhang, A. Choudhary and C. Wolverton: Combinatorial screening for new materials in unconstrained composition space with machine learning. Phys. Rev. B 89, 094104 (2014).

    Article  Google Scholar 

  31. Y. Liu, T. Zhao, W. Ju and S. Shi: Materials discovery and design using machine learning. J. Materiomics 3, 159–177 (2017).

    Article  Google Scholar 

  32. R. Ramprasad, R. Batra, G. Pilania, A. Mannodi-Kanakkithodi and C. Kim: Machine learning in materials informatics: recent applications and prospects. npj Comput. Mater. 3, 54 (2017).

    Article  Google Scholar 

  33. G. Pilania, A. Mannodi-Kanakkithodi, B.P. Uberuaga, R. Ramprasad, J.E. Gubernatis and T. Lookman: Machine learning bandgaps of double perovskites. Sci. Rep. 6, 19375 (2016).

    Article  CAS  Google Scholar 

  34. G. Pilania et al.: Accelerating materials property predictions using machine learning. Sci. Rep. 3, 2810 (2013).

    Article  Google Scholar 

  35. Y.C. Yabansu, P. Steinmetz, J. Hötzer, S.R. Kalidindi and B. Nestler: Extraction of reduced-order process–structure linkages from phase-field simulations. Acta Mater. 124, 182–194 (2017).

    Article  CAS  Google Scholar 

  36. E. Popova, T.M. Rodgers, X. Gong, A. Cecen, J.D. Madison and S.R. Kalidindi: Process-structure linkages using a data science approach: application to simulated additive manufacturing data. Integr. Mater. Manuf. Innovation, 6, 54–68 (2017).

    Article  Google Scholar 

  37. A. Iskakov, Y.C. Yabansu, S. Rajagopalan, A. Kapustina and S.R. Kalidindi: 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, 758–767 (2017).

    Article  Google Scholar 

  38. N.H. Paulson, M.W. Priddy, D.L. McDowell and S.R. Kalidindi: Reducedorder structure–property linkages for polycrystalline microstructures based on 2-point statistics. Acta Mater. 129, 428–438 (2017).

    Article  CAS  Google Scholar 

  39. M.W. Priddy, N.H. Paulson, S.R. Kalidindi and D.L. McDowell: Strategies for rapid parametric assessment of microstructure-sensitive fatigue for HCP polycrystals. Int. J. Fatigue 104, 231–242 (2017).

    Article  CAS  Google Scholar 

  40. H.K.D.H. Bhadeshia: Neural networks and information in materials science. Stat. Anal. Data. Min. 1, 296–305 (2009).

    Article  Google Scholar 

  41. A. Jain, K.A. Persson, and G. Ceder: Research update: the materials genome initiative: data sharing and the impact of collaborative ab initio databases. APL Mater. 4, 053102 (2016).

    Article  Google Scholar 

  42. C. Hu, C. Ouyang, J. Wu, X. Zhang and C. Zhao: NON-structured materials science data sharing based on semantic annotation. Data Sci. J. 8, 52–61 (2009).

    Article  CAS  Google Scholar 

  43. D.L. McDowell and G.B. Olson: Concurrent design of hierarchical materials and structures. Sci. Model. Simul. 15, 207–240 (2008).

    Article  CAS  Google Scholar 

  44. G.B. Olson: Pathways of discovery designing a new material world. Science 228, 933–998 (2000).

    Google Scholar 

  45. G.B. Olson: Computational design of hierarchically structured materials. Science 277, 1237–1242 (1997).

    Article  CAS  Google Scholar 

  46. G.B. Olson: Systems design of hierarchically structured materials: advanced steels. J. Comput. Aided Mater. Des. 4, 143–156 (1997).

    Article  Google Scholar 

  47. D.L. McDowell, J.H. Panchal, H.-J. Choi, C.C. Seepersad, J.K. Allen and F. Mistree: Integrated Design of Multiscale, Multifunctional Materials and Products (Elsevier, Burlington, MA, 2009).

    Google Scholar 

  48. B.L. Adams, S.R. Kalidindi, and D.T. Fullwood: Microstructure Sensitive Design for Performance Optimization (Elsevier Science, Oxford, 2012).

    Google Scholar 

  49. J.A. Gomberg, A.J. Medford, and S.R. Kalidindi: Extracting knowledge from molecular mechanics simulations of grain boundaries using machine learning. Acta Mater. 133(Supplement C), 100–108 (2017).

    Article  CAS  Google Scholar 

  50. R. Bostanabad, Y. Zhang, X. Li, T. Kearney, L.C. Brinson, D.W. Apley, W. K. Liu and W. Chen: Computational microstructure characterization and reconstruction: review of the state-of-the-art techniques. Prog. Mater. Sci. 95, 1–41 (2018).

    Article  CAS  Google Scholar 

  51. P.I. Frazier and J. Wang: Bayesian optimization for materials design. In Turab Lookman, Francis J. Alexander, Krishna Rajan (eds.), Information Science for Materials Discovery and Design (Springer, New York, NY, 2016), pp. 45–75.

    Chapter  Google Scholar 

  52. P. Angelikopoulos, C. Papadimitriou, and P. Koumoutsakos: X-TMCMC: adaptive kriging for Bayesian inverse modeling. Comput. Methods. Appl. Mech. Eng. 289, 409–428 (2015).

    Article  Google Scholar 

  53. A. Gelman, J. Carlin, H. Stern, D. Dunson, A. Vehtari and D. Rubin: Bayesian Data Analysis, 3rd ed. (Chapman & Hall/CRC Texts in Statistical Science). (Chapman and Hall/CRC, Boca Raton, FL, 2014).

    Google Scholar 

  54. D. Gamerman and H.F. Lopes: Markov Chain Monte Carlo: Stochastic Simulation for Bayesian inference (CRC Press, New York, NY, 2006).

    Book  Google Scholar 

  55. G.E. Box and G.C. Tiao: Bayesian inference in statistical analysis (John Wiley & Sons, 2011).

    Google Scholar 

  56. J.M. Whitney: Structural Analysis of Laminated Anisotropic plates (CRC Press, Lancaster, PA, 1987).

    Google Scholar 

  57. E. Kroner: Statistical modelling. In Modelling Small Deformations of Polycrystals, edited by J. Gittus and J. Zarka (Elsevier Science Publishers: London, 1986), pp. 229–291.

    Chapter  Google Scholar 

  58. H. Garmestani, S. Lin, B.L. Adams and S. Ahzi: Statistical continuum theory for large plastic deformation of polycrystalline materials. J. Mech. Phys. Solids 49, 589–607 (2001).

    Article  Google Scholar 

  59. Y.C. Yabansu and S.R. Kalidindi: Representation and calibration of elastic localization kernels for a broad class of cubic polycrystals. Acta Mater. 94, 26–35 (2015).

    Article  CAS  Google Scholar 

  60. H.F. Alharbi and S.R. Kalidindi: Crystal plasticity finite element simulations using a database of discrete Fourier transforms. Int. J. Plast. 66, 71–84 (2015).

    Article  Google Scholar 

  61. F. Roters, P. Eisenlohr, L. Hantcherli, D.D. Tjahjanto, T.R. Bieler and D. Raabe: Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: theory, experiments, applications. Acta Mater. 58, 1152–1211 (2010).

    Article  CAS  Google Scholar 

  62. A. Lahiri and A. Choudhury: Revisiting Jackson-Hunt calculations: unified theoretical analysis for generic multi-phase growth in a multicomponent system. Acta Mater. 133(Supplement C), 316–332 (2017).

    Article  CAS  Google Scholar 

  63. A. Yamanaka, K. McReynolds, and P.W. Voorhees: Phase field crystal simulation of grain boundary motion, grain rotation and dislocation reactions in a BCC bicrystal. Acta Mater. 133(Supplement C), 160–171 (2017).

    Article  CAS  Google Scholar 

  64. A. Arsenlis and M. Tang: Simulations on the growth of dislocation density during stage 0 deformation in BCC metals. Modelling Simul. Mater. Sci. Eng. 11, 251–264 (2003).

    Article  Google Scholar 

  65. P. Hähner and M. Zaiser: Dislocation dynamics and work hardening of fractal dislocation cell structures. Mater. Sci. Eng., A 272, 443–454 (1999).

    Article  Google Scholar 

  66. S.I. Rao, D.M. Dimiduk, J.A. El-Awady, T.A. Parthasarathy, M.D. Uchic and C. Woodward: Atomistic simulations of cross-slip nucleation at screw dislocation intersections in face-centered cubic nickel. Philos. Mag. 89, 3351–3369 (2009).

    Article  CAS  Google Scholar 

  67. A. Leonardi and D.L. Bish: Interactions of lattice distortion fields in nanopolycrystalline materials revealed by molecular dynamics and X-ray powder diffraction. Acta Mater. 133(Supplement C), 380–392 (2017).

    Article  CAS  Google Scholar 

  68. L. Yang, D. Zhang, and G.E. Karniadakis: Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations. arXiv e-prints, 2018.

    Google Scholar 

  69. X. Huan and Y.M. Marzouk: Simulation-based optimal Bayesian experimental design for nonlinear systems. J. Comput. Phys. 232, 288–317 (2013).

    Article  CAS  Google Scholar 

  70. D.J.C. MacKay: Introduction to Gaussian process. Neural Networks and Machine Learning 84–92 (1998).

    Google Scholar 

  71. C.E. Rasmussen: Evaluation of Gaussian Processes and Other Methods for non-Linear Regression (University of Toronto, Toronto, ON, Canada).

  72. M.B. Christopher: Pattern Recognition and Machine Learning (Springer-Verlag, New York, 2006).

    Google Scholar 

  73. D.J.C. MacKay: Bayesian interpolation. Neural Comput. 4, 415–447 (1992).

    Article  Google Scholar 

  74. D.J.C. MacKay: Hyperparameters: Optimize, or Integrate Out? 1996.

    Google Scholar 

  75. A. Gelman: Bayesian Data Analysis, 2nd ed. (Chapman & Hall/CRC, Boca Raton, FL, 2004).

    Google Scholar 

  76. H. Haario, E. Saksman, and J. Tamminen: Componentwise adaptation for high dimensional MCMC. Comput. Stat. 20, 265–273 (2005).

    Article  Google Scholar 

  77. L.J Huang, L. Geng, B. Wang and LZ. Wu: Effects of volume fraction on the microstructure and tensile properties of in situ TiBw/Ti6Al4V composites with novel network microstructure. Mater. Des. 45, 532–538 (2013).

    Article  CAS  Google Scholar 

  78. X. Xu, S. van der Zwaag, and W. Xu: The effect of ferrite–martensite morphology on the scratch and abrasive wear behaviour of a dual phase construction steel. Wear 348–349, 148–157 (2016).

    Article  Google Scholar 

  79. Q. Wang, Y. Li, S. Li, R. Xiang, N. Xu and S. OuYang: Effects of critical particle size on properties and microstructure of porous purging materials. Mater. Lett. 197, 48–51 (2017).

    Article  CAS  Google Scholar 

  80. R. Li, R. Xin, Q. Liu, A. Chapuis, S. Liu, G. Fu and L. Zong: Effect of grain size, texture and density of precipitates on the hardness and tensile yield stress of Mg-14Gd-0.5Zr alloys. Mater. Des. 114, 450–458 (2017).

    Article  CAS  Google Scholar 

  81. S. Kar, T. Searles, E. Lee, G.B. Viswanathan, H.L. Fraser, J. Tiley and R. Banerjee: Modeling the tensile properties in β-processed α/β Ti alloys. Metall. Mater. Trans. A 37, 559–566 (2006).

    Article  Google Scholar 

  82. S.M. Qidwai, D.M. Turner, S.R. Niezgoda, A.C. Lewis, A.B. Geltmacher, D.J. Rowenhorst and S.R. Kalidindi: Estimating response of polycrystalline materials using sets of weighted statistical volume elements (WSVEs). Acta Mater. 60, 5284–5299 (2012).

    Article  CAS  Google Scholar 

  83. D.J. Rowenhorst, A.C. Lewis, and G. Spanos: Three-dimensional analysis of grain topology and interface curvature in a β-titanium alloy. Acta Mater. 58, 5511–5519 (2010).

    Article  CAS  Google Scholar 

  84. N.H. Paulson, M.W. Priddy, D.L. McDowell and S.R. Kalidindi: Data-driven reduced-order models for rank-ordering the high cycle fatigue performance of polycrystalline microstructures. Mater. Des. 154, 170–183 (2018).

    Article  CAS  Google Scholar 

  85. B.L. Adams, G. Xiang, and S.R. Kalidindi: Finite approximations to the second-order properties closure in single phase polycrystals. Acta Mater. 53, 3563–3577 (2005).

    Article  CAS  Google Scholar 

  86. D.T. Fullwood, S.R. Niezgoda, B.L. Adams and S.R. Kalidindi: Microstructure sensitive design for performance optimization. Prog. Mater. Sci. 55, 477–562 (2010).

    Article  CAS  Google Scholar 

  87. X. Dong et al.: Dependence of mechanical properties on crystal orientation of semi-crystalline polyethylene structures. Polymer 55, 4248–4257 (2014).

    Article  CAS  Google Scholar 

  88. D.T. Fullwood, S.R. Niezgoda, and S.R. Kalidindi: Microstructure reconstructions from 2-point statistics using phase-recovery algorithms. Acta Mater. 56, 942–948 (2008).

    Article  CAS  Google Scholar 

  89. D.M. Turner and S.R. Kalidindi: Statistical construction of 3-D microstructures from 2-D exemplars collected on oblique sections. Acta Mater. 102, 136–148 (2016).

    Article  CAS  Google Scholar 

  90. V. Sundararaghavan: Reconstruction of three-dimensional anisotropic microstructures from two-dimensional micrographs imaged on orthogonal planes. Integr. Mater. Manuf. Innovation 3, 19 (2014).

    Article  Google Scholar 

  91. S. Mika, B. Schölkopf, A.J. Smola, K.-R. Müller, M. Scholz and G. Rätsch: Kernel PCA and de-noising in feature spaces. In Advances in Neural Information Processing Systems (Massachusetts Institute of Technology, Cambridge, MA, 1999), pp. 536–542.

    Google Scholar 

  92. S.T. Roweis and L.K. Saul: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000).

    Article  CAS  Google Scholar 

  93. Z. Zhang and H. Zha: Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM J. Sci. Comput. 26, 313–338 (2004).

    Article  Google Scholar 

  94. T. Fast and S.R. Kalidindi: Formulation and calibration of higher-order elastic localization relationships using the MKS approach. Acta Mater. 59, 4595–4605 (2011).

    Article  CAS  Google Scholar 

  95. D. Montes de Oca Zapiain, E. Popova, and S.R. Kalidindi: Prediction of microscale plastic strain rate fields in two-phase composites subjected to an arbitrary macroscale strain rate using the materials knowledge system framework. Acta Mater. 141(Supplement C), 230–240 (2017).

    Article  Google Scholar 

  96. D. Montes de Oca Zapiain, E. Popova, F. Abdeljawad, J.W. Foulk, S.R. Kalidindi and H. Lim: Reduced-order microstructure-sensitive models for damage initiation in two-phase composites. Integr. Mater. Manuf. Innovation 7, 97–115 (2018).

    Article  Google Scholar 

  97. N.H. Paulson, M.W. Priddy, D.L. McDowell and S.R. Kalidindi: Reducedorder microstructure-sensitive protocols to rank-order the transition fatigue resistance of polycrystalline microstructures. Int. J. Fatigue 119, 1–10 (2019).

    Article  CAS  Google Scholar 

  98. A. Cecen, H. Dai, Y.C. Yabansu, S.R. Kalidindi and L. Song: Material structure–property linkages using three-dimensional convolutional neural networks. Acta Mater. 146, 76–84 (2018).

    Article  CAS  Google Scholar 

  99. Z. Yang, Y.C. Yabansu, R. Al-Bahrani, W. Liao, A.N. Choudhary, S.R. Kalidindi and A. Agrawal: Deep learning approaches for mining structure–property linkages in high contrast composites from simulation datasets. Comput. Mater. Sci. 151, 278–287 (2018).

    Article  CAS  Google Scholar 

  100. N. Lubbers, T. Lookman, and K. Barros: Inferring low-dimensional microstructure representations using convolutional neural networks. Phys. Rev. E 96, 052111 (2017).

    Article  Google Scholar 

  101. G.E.P. Box, G.M. Jenkins, G.C. Reinsel and G.M. Ljung: Time Series Analysis: Forecasting and Control (John Wiley & Sons, Hoboken, NJ, 2015).

    Google Scholar 

  102. P.J. Brockwell, R.A. Davis, and M.V. Calder: Introduction to Time Series and Forecasting (Springer, New York, NY, 2, 2002).

  103. J.D. Hamilton: Time Series analysis (Princeton University Press, 2, Princeton, NJ, 1994).

    Book  Google Scholar 

  104. R. Tibshirani: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B (Methodol.), 58, 267–288 (1996).

    Google Scholar 

  105. A.E. Hoerl and R.W. Kennard: Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12, 55–67 (1970).

    Article  Google Scholar 

  106. M.I. Latypov, L.S. Toth, and S.R. Kalidindi: Materials knowledge system for nonlinear composites. Comput. Methods. Appl. Mech. Eng. 346, 180–196 (2018).

    Article  Google Scholar 

  107. J. Lee Rodgers and W.A. Nicewander: Thirteen ways to look at the correlation coefficient. Am. Stat. 42, 59–66 (1988).

    Article  Google Scholar 

  108. D.B. Brough, A. Kannan, B. Haaland, D.G. Bucknall and S.R. Kalidindi: Extraction of process-structure evolution linkages from X-ray scattering measurements using dimensionality reduction and time series analysis. Integr. Mater. Manuf. Innovation, 6, 147–159 (2017).

    Article  Google Scholar 

  109. Q. Li, L. Gu, G. Augenbroe, C.F.J. Wu and J. Brown: A Generic Approach to Calibrate Building Energy Models under Uncertainty Using Bayesian Inference. In Building Simulation Conference. Hyderabad, India, 2015.

    Google Scholar 

  110. P. Nikolaev, D. Hooper, F. Webber, R. Rao, K. Decker, M. Krein, J. Poleski, R. Barto and B. Maruyama: Autonomy in materials research: a case study in carbon nanotube growth. npj Comput. Mater. 2, 16031 (2016).

    Article  Google Scholar 

  111. J.H. Panchal, S.R. Kalidindi, and D.L. McDowell: Key computational modeling issues in integrated computational materials engineering. Computer-Aided Design 45, 4–25 (2013).

    Article  Google Scholar 

  112. S. Pathak and S.R. Kalidindi: Spherical nanoindentation stress–strain curves. Mater. Sci., Eng. R., Rep. 91, 1–36 (2015).

    Article  Google Scholar 

  113. J.S. Weaver and S.R. Kalidindi: Mechanical characterization of Ti-6Al-4V titanium alloy at multiple length scales using spherical indentation stress–strain measurements. Mater. Des. 111, 463–472 (2016).

    Article  CAS  Google Scholar 

  114. A. Khosravani, L. Morsdorf, C.C. Tasan and S.R. Kalidindi: Multiresolution mechanical characterization of hierarchical materials: spherical nanoindentation on martensitic Fe-Ni-C steels. Acta Mater. 153, 257–269 (2018).

    Article  CAS  Google Scholar 

  115. D. Patel and S. Kalidindi: Estimating the slip resistance from spherical nanoindentation and orientation measurements in polycrystalline samples of cubic metals. Int. J. Plast. 92, 19 (2017).

    Article  CAS  Google Scholar 

  116. D.K. Patel and S.R. Kalidindi: Correlation of spherical nanoindentation stress–strain curves to simple compression stress–strain curves for elastic-plastic isotropic materials using finite element models. Acta Mater. 112, 295–302 (2016).

    Article  CAS  Google Scholar 

  117. D.K. Patel, H.F. Al-Harbi, and S.R. Kalidindi: Extracting single-crystal elastic constants from polycrystalline samples using spherical nanoindentation and orientation measurements. Acta Mater. 79, 108–116 (2014).

    Article  CAS  Google Scholar 

  118. S. Pathak, D. Stojakovic, and S.R. Kalidindi: Measurement of the local mechanical properties in polycrystalline samples using spherical nanoindentation and orientation imaging microscopy. Acta Mater. 57, 3020–3028 (2009).

    Article  CAS  Google Scholar 

  119. A. Castillo and S.R. Kalidindi: Accelerated extraction of crystal level elastic parameters via Bayesian framework. Front. Mater. (2019), submitted.

    Google Scholar 

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Acknowledgments

The author acknowledges support for this work from NIST 70NANB18H039 (Program Manager: Dr. James Warren). The author is grateful to Dave Rowenhorst (NRL), Yuksel Yabansu (GT), Marat Latypov (UCSB), and Andrew Castillo (GT) for the figures used in this paper.

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Correspondence to Surya R. Kalidindi.

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Kalidindi, S.R. A Bayesian framework for materials knowledge systems. MRS Communications 9, 518–531 (2019). https://doi.org/10.1557/mrc.2019.56

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