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A Bayesian framework for materials knowledge systems

Published online by Cambridge University Press:  07 May 2019

Surya R. Kalidindi Open the ORCID record for Surya R. Kalidindi [Opens in a new window]
Surya R. Kalidindi*
Affiliation:
Georgia Institute of Technology, Atlanta, GA, USA
*
Address all correspondence to Surya R. Kalidindi at [email protected]
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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.

Type
Artificial Intelligence Prospectives
Information
MRS Communications , Volume 9 , Issue 2 , June 2019 , pp. 518 - 531
Copyright
Copyright © Materials Research Society 2019 

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References

1.Materials Genome Initiative for Global Competitiveness. National Science and Technology Council, Editor. 2011.Google Scholar
2.McDowell, D.L. and Kalidindi, S.R.: The materials innovation ecosystem: a key enabler for the Materials Genome Initiative. MRS Bull. 41, 326–337 (2016).Google Scholar
3.Drosback, M.: Materials genome initiative: advances and initiatives. JOM 66, 334–335 (2014).Google Scholar
4.Olson, G.B. and Kuehmann, C.J.: Materials genomics: from CALPHAD to flight. Scr. Mater. 70, 25–30 (2014).Google Scholar
5.Zhao, J.C.: High-throughput experimental tools for the materials genome initiative. Chin. Sci. Bull. 59, 1652–1661 (2014).Google Scholar
6.Breneman, C.M., Brinson, L.C., Schadler, L.S., Natarajan, B., Krein, M., Wu, K., Morkowchuk, L., Li, Y., Deng, H. and Xu, H.: Stalking the materials genome: a data-driven approach to the virtual design of nanostructured polymers. Adv. Funct. Mater. 23, 5746–5752 (2013).Google Scholar
7.Jain, A., Ong, S.P., Hautier, G., Chen, W., Richards, W.D., Dacek, S., Cholia, S., Gunter, D., Skinner, D., Ceder, G. and Persson, K.A.: Commentary: the materials project: a materials genome approach to accelerating materials innovation. APL Mater. 1, 011002 (2013).Google Scholar
8.Ramakrishna, S., Zhang, T.-Y., Lu, W.-C., Qian, Q., Low, J.S.C., Yune, J.H.R., Tan, D.Z.L., Bressan, S., Sanvito, S. and Kalidindi, S.R.: Materials informatics. J. Intell. Manuf. 10.1007/s10845-018-1392-0 (2018).Google Scholar
9.Kalidindi, S.R., Medford, A.J., and McDowell, D.L.: Vision for data and informatics in the future materials innovation ecosystem. JOM 68, 2126–2137 (2016).Google Scholar
10.Kalidindi, S.R.: Hierarchical Materials Informatics (Butterworth Heinemann, Waltham, MA, 2015).Google Scholar
11.Voorhees, P. and Spanos, G.: 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.Gulsoy, E.B., Shahani, A.J., Gibbs, J.W., Fife, J.L. and Voorhees, P.W.: Four-dimensional morphological evolution of an aluminum silicon alloy using propagation-based phase contrast X-ray tomographic microscopy. Mater. Trans. 55, 161–164 (2014).Google Scholar
13.Uchic, M.D., Groeber, M.A., and Rollett, A.D.: Automated serial sectioning methods for rapid collection of 3-D microstructure data. JOM 63, 25–29 (2011).Google Scholar
14.Bingert, J.F., Suter, R.M., Lind, J., Li, S.F., Pokharel, R. and Trujillo, C.P.: High-energy diffraction microscopy characterization of spall damage. In Proulx, Tom, Song, Bo, Casem, Dan and Kimberley, Jamie (eds.), Dynamic Behavior of Materials (Springer, New York, NY, 1, 2014), pp. 397–403.Google Scholar
15.Lienert, U., Li, S.F., Hefferan, C.M., Lind, J., Suter, R.M., Bernier, J.V., Barton, N.R., Brandes, M.C., Mills, M.J., Miller, M.P., Jakobsen, B. and Pantleon, W.: High-energy diffraction microscopy at the advanced photon source. JOM Journal of the Minerals, Metals and Materials Society 63, 70–77 (2011).Google Scholar
16.Kalidindi, S.R., Brough, D.B., Li, S., Cecen, A., Blekh, A.L., Congo, F.Y.P. and Campbell, C.: Role of materials data science and informatics in accelerated materials innovation. MRS Bull. 41, 596–602 (2016).Google Scholar
17.Kalidindi, S.R. and Graef, M.D.: Materials data science: current status and future outlook. Annu. Rev. Mater. Res. 45, 171–193 (2015).Google Scholar
18.Rajan, K.: Materials informatics. Mater. Today 8, 38–45 (2005).Google Scholar
19.Brough, D.B., Wheeler, D., and Kalidindi, S.R.: Materials knowledge systems in python—a data science framework for accelerated development of hierarchical materials. Integr. Mater. Manuf. Innovation 6, 36–53 (2017).Google Scholar
20.Kim, C., Chandrasekaran, A., Huan, T.D., Das, D. and Ramprasad, R.: Polymer genome: a data-powered polymer informatics platform for property predictions. J. Phys. Chem. C 122, 17575–17585 (2018).Google Scholar
21.Kalidindi, S.R.: Data science and cyberinfrastructure: critical enablers for accelerated development of hierarchical materials. Int. Mater. Rev. 60, 150–168 (2015).Google Scholar
22.Linden, G., Smith, B., and York, J.: Amazon. com recommendations: item-to-item collaborative filtering. IEEE Internet Comput. 7, 76–80 (2003).Google Scholar
23.Cruz, J.A. and Wishart, D.S.: Applications of machine learning in cancer prediction and prognosis. Cancer Inform. 2, 59–78 (2006).Google Scholar
24.Bojarski, M., Del Testa, D., Dworakowski, D., Firner, B., Flepp, B., Goyal, P., Jackel, L.D., Monfort, M., Muller, U. and Zhang, J.: End to end learning for self-driving cars. arXiv preprint arXiv:1604.07316, 2016.Google Scholar
25.Kajikawa, Y., Sugiyama, Y., Mima, H. and Matsushima, K.: Causal knowledge extraction by natural language processing in material science: a case study in chemical vapor deposition. Data Sci. J. 5, 108–118 (2006).Google Scholar
26.Kim, E., Huang, K., Tomala, A., Matthews, S., Strubell, E., Saunders, A., McCallum, A. and Olivetti, E.: Machine-learned and codified synthesis parameters of oxide materials. Sci. Data 4, 170127 (2017).Google Scholar
27.Nunez-Iglesias, J., Kennedy, R., Parag, T., Shi, J. and Chklovskii, D.B.: Machine learning of hierarchical clustering to segment 2D and 3D images. PLoS One 8, e71715 (2013).Google Scholar
28.Chowdhury, A., Kautz, E., Yener, B. and Lewis, D.: Image driven machine learning methods for microstructure recognition. Comput. Mater. Sci. 123, 176–187 (2016).Google Scholar
29.Raccuglia, P., Elbert, K.C., Adler, P.D.F., Falk, C., Wenny, M.B., Mollo, A., Zeller, M., Friedler, S.A., Schrier, J. and Norquist, A.J.: Machine-learning-assisted materials discovery using failed experiments. Nature 533, 73 (2016).Google Scholar
30.Meredig, B., Agrawal, A., Kirklin, S., Saal, J.E., Doak, J.W., Thompson, A., Zhang, K., Choudhary, A. and Wolverton, C.: Combinatorial screening for new materials in unconstrained composition space with machine learning. Phys. Rev. B 89, 094104 (2014).Google Scholar
31.Liu, Y., Zhao, T., Ju, W. and Shi, S.: Materials discovery and design using machine learning. J. Materiomics 3, 159–177 (2017).Google Scholar
32.Ramprasad, R., Batra, R., Pilania, G., Mannodi-Kanakkithodi, A. and Kim, C.: Machine learning in materials informatics: recent applications and prospects. npj Comput. Mater. 3, 54 (2017).Google Scholar
33.Pilania, G., Mannodi-Kanakkithodi, A., Uberuaga, B.P., Ramprasad, R., Gubernatis, J.E. and Lookman, T.: Machine learning bandgaps of double perovskites. Sci. Rep. 6, 19375 (2016).Google Scholar
34.Pilania, G. et al. : Accelerating materials property predictions using machine learning. Sci. Rep. 3, 2810 (2013).Google Scholar
35.Yabansu, Y.C., Steinmetz, P., Hötzer, J., Kalidindi, S.R. and Nestler, B.: Extraction of reduced-order process–structure linkages from phase-field simulations. Acta Mater. 124, 182–194 (2017).Google Scholar
36.Popova, E., Rodgers, T.M., Gong, X., Cecen, A., Madison, J.D. and Kalidindi, S.R.: Process-structure linkages using a data science approach: application to simulated additive manufacturing data. Integr. Mater. Manuf. Innovation, 6, 54–68 (2017).Google Scholar
37.Iskakov, A., Yabansu, Y.C., Rajagopalan, S., Kapustina, A. and Kalidindi, S.R.: 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).Google Scholar
38.Paulson, N.H., Priddy, M.W., McDowell, D.L. and Kalidindi, S.R.: Reduced-order structure–property linkages for polycrystalline microstructures based on 2-point statistics. Acta Mater. 129, 428–438 (2017).Google Scholar
39.Priddy, M.W., Paulson, N.H., Kalidindi, S.R. and McDowell, D.L.: Strategies for rapid parametric assessment of microstructure-sensitive fatigue for HCP polycrystals. Int. J. Fatigue 104, 231–242 (2017).Google Scholar
40.Bhadeshia, H.K.D.H.: Neural networks and information in materials science. Stat. Anal. Data. Min. 1, 296–305 (2009).Google Scholar
41.Jain, A., Persson, K.A., and Ceder, G.: Research update: the materials genome initiative: data sharing and the impact of collaborative ab initio databases. APL Mater. 4, 053102 (2016).Google Scholar
42.Hu, C., Ouyang, C., Wu, J., Zhang, X. and Zhao, C.: NON-structured materials science data sharing based on semantic annotation. Data Sci. J. 8, 52–61 (2009).Google Scholar
43.McDowell, D.L. and Olson, G.B.: Concurrent design of hierarchical materials and structures. Sci. Model. Simul. 15, 207–240 (2008).Google Scholar
44.Olson, G.B.: Pathways of discovery designing a new material world. Science 228, 933–998 (2000).Google Scholar
45.Olson, G.B.: Computational design of hierarchically structured materials. Science 277, 1237–1242 (1997).Google Scholar
46.Olson, G.B.: Systems design of hierarchically structured materials: advanced steels. J. Comput. Aided Mater. Des. 4, 143–156 (1997).Google Scholar
47.McDowell, D.L., Panchal, J.H., Choi, H. -J., Seepersad, C.C., Allen, J.K. and Mistree, F.: Integrated Design of Multiscale, Multifunctional Materials and Products (Elsevier, Burlington, MA, 2009).Google Scholar
48.Adams, B.L., Kalidindi, S.R., and Fullwood, D.T.: Microstructure Sensitive Design for Performance Optimization (Elsevier Science, Oxford, 2012).Google Scholar
49.Gomberg, J.A., Medford, A.J., and Kalidindi, S.R.: Extracting knowledge from molecular mechanics simulations of grain boundaries using machine learning. Acta Mater. 133(Supplement C), 100–108 (2017).Google Scholar
50.Bostanabad, R., Zhang, Y., Li, X., Kearney, T., Brinson, L.C., Apley, D.W., Liu, W.K. and Chen, W.: Computational microstructure characterization and reconstruction: review of the state-of-the-art techniques. Prog. Mater. Sci. 95, 1–41 (2018).Google Scholar
51.Frazier, P.I. and Wang, J.: Bayesian optimization for materials design. In Lookman, Turab, Alexander, Francis J., Rajan, Krishna (eds.), Information Science for Materials Discovery and Design (Springer, New York, NY, 2016), pp. 45–75.Google Scholar
52.Angelikopoulos, P., Papadimitriou, C., and Koumoutsakos, P.: X-TMCMC: adaptive kriging for Bayesian inverse modeling. Comput. Methods. Appl. Mech. Eng. 289, 409–428 (2015).Google Scholar
53.Gelman, A., Carlin, J., Stern, H., Dunson, D., Vehtari, A. and Rubin, D.: Bayesian Data Analysis, 3rd ed. (Chapman & Hall/CRC Texts in Statistical Science). (Chapman and Hall/CRC, Boca Raton, FL, 2014).Google Scholar
54.Gamerman, D. and Lopes, H.F.: Markov Chain Monte Carlo: Stochastic Simulation for Bayesian inference (CRC Press, New York, NY, 2006).Google Scholar
55.Box, G.E. and Tiao, G.C.: Bayesian inference in statistical analysis (John Wiley & Sons, 2011).Google Scholar
56.Whitney, J.M.: Structural Analysis of Laminated Anisotropic plates (CRC Press, Lancaster, PA, 1987).Google Scholar
57.Kroner, E.: Statistical modelling. In Modelling Small Deformations of Polycrystals, edited by Gittus, J. and Zarka, J. (Elsevier Science Publishers: London, 1986), pp. 229–291.Google Scholar
58.Garmestani, H., Lin, S., Adams, B.L. and Ahzi, S.: Statistical continuum theory for large plastic deformation of polycrystalline materials. J. Mech. Phys. Solids 49, 589–607 (2001).Google Scholar
59.Yabansu, Y.C. and Kalidindi, S.R.: Representation and calibration of elastic localization kernels for a broad class of cubic polycrystals. Acta Mater. 94, 26–35 (2015).Google Scholar
60.Alharbi, H.F. and Kalidindi, S.R.: Crystal plasticity finite element simulations using a database of discrete Fourier transforms. Int. J. Plast. 66, 71–84 (2015).Google Scholar
61.Roters, F., Eisenlohr, P., Hantcherli, L., Tjahjanto, D.D., Bieler, T.R. and Raabe, D.: Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: theory, experiments, applications. Acta Mater. 58, 1152–1211 (2010).Google Scholar
62.Lahiri, A. and Choudhury, A.: Revisiting Jackson-Hunt calculations: unified theoretical analysis for generic multi-phase growth in a multi-component system. Acta Mater. 133(Supplement C), 316–332 (2017).Google Scholar
63.Yamanaka, A., McReynolds, K., and Voorhees, P.W.: 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).Google Scholar
64.Arsenlis, A. and Tang, M.: Simulations on the growth of dislocation density during stage 0 deformation in BCC metals. Modelling Simul. Mater. Sci. Eng. 11, 251–264 (2003).Google Scholar
65.Hähner, P. and Zaiser, M.: Dislocation dynamics and work hardening of fractal dislocation cell structures. Mater. Sci. Eng., A 272, 443–454 (1999).Google Scholar
66.Rao, S.I., Dimiduk, D.M., El-Awady, J.A., Parthasarathy, T.A., Uchic, M.D. and Woodward, C.: Atomistic simulations of cross-slip nucleation at screw dislocation intersections in face-centered cubic nickel. Philos. Mag. 89, 3351–3369 (2009).Google Scholar
67.Leonardi, A. and Bish, D.L.: 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).Google Scholar
68.Yang, L., Zhang, D., and Karniadakis, G.E.: Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations. arXiv e-prints, 2018.Google Scholar
69.Huan, X. and Marzouk, Y.M.: Simulation-based optimal Bayesian experimental design for nonlinear systems. J. Comput. Phys. 232, 288–317 (2013).Google Scholar
70.MacKay, D.J.C.: Introduction to Gaussian process. Neural Networks and Machine Learning 84–92 (1998).Google Scholar
71.Rasmussen, C.E.: Evaluation of Gaussian Processes and Other Methods for non-Linear Regression (University of Toronto, Toronto, ON, Canada).Google Scholar
72.Christopher, M.B.: Pattern Recognition and Machine Learning (Springer-Verlag, New York, 2006).Google Scholar
73.MacKay, D.J.C.: Bayesian interpolation. Neural Comput. 4, 415–447 (1992).Google Scholar
74.MacKay, D.J.C.: Hyperparameters: Optimize, or Integrate Out? 1996.Google Scholar
75.Gelman, A.: Bayesian Data Analysis, 2nd ed. (Chapman & Hall/CRC, Boca Raton, FL, 2004).Google Scholar
76.Haario, H., Saksman, E., and Tamminen, J.: Componentwise adaptation for high dimensional MCMC. Comput. Stat. 20, 265–273 (2005).Google Scholar
77.Huang, L.J, Geng, L., Wang, B. and Wu, LZ.: 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).Google Scholar
78.Xu, X., van der Zwaag, S., and Xu, W.: 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).Google Scholar
79.Wang, Q., Li, Y., Li, S., Xiang, R., Xu, N. and OuYang, S.: Effects of critical particle size on properties and microstructure of porous purging materials. Mater. Lett. 197, 48–51 (2017).Google Scholar
80.Li, R., Xin, R., Liu, Q., Chapuis, A., Liu, S., Fu, G. and Zong, L.: 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).Google Scholar
81.Kar, S., Searles, T., Lee, E., Viswanathan, G.B., Fraser, H.L., Tiley, J. and Banerjee, R.: Modeling the tensile properties in β-processed α/β Ti alloys. Metall. Mater. Trans. A 37, 559–566 (2006).Google Scholar
82.Qidwai, S.M., Turner, D.M., Niezgoda, S.R., Lewis, A.C., Geltmacher, A.B., Rowenhorst, D.J. and Kalidindi, S.R.: Estimating response of polycrystalline materials using sets of weighted statistical volume elements (WSVEs). Acta Mater. 60, 5284–5299 (2012).Google Scholar
83.Rowenhorst, D.J., Lewis, A.C., and Spanos, G.: Three-dimensional analysis of grain topology and interface curvature in a β-titanium alloy. Acta Mater. 58, 5511–5519 (2010).Google Scholar
84.Paulson, N.H., Priddy, M.W., McDowell, D.L. and Kalidindi, S.R.: Data-driven reduced-order models for rank-ordering the high cycle fatigue performance of polycrystalline microstructures. Mater. Des. 154, 170–183 (2018).Google Scholar
85.Adams, B.L., Xiang, G., and Kalidindi, S.R.: Finite approximations to the second-order properties closure in single phase polycrystals. Acta Mater. 53, 3563–3577 (2005).Google Scholar
86.Fullwood, D.T., Niezgoda, S.R., Adams, B.L. and Kalidindi, S.R.: Microstructure sensitive design for performance optimization. Prog. Mater. Sci. 55, 477–562 (2010).Google Scholar
87.Dong, X. et al. : Dependence of mechanical properties on crystal orientation of semi-crystalline polyethylene structures. Polymer 55, 4248–4257 (2014).Google Scholar
88.Fullwood, D.T., Niezgoda, S.R., and Kalidindi, S.R.: Microstructure reconstructions from 2-point statistics using phase-recovery algorithms. Acta Mater. 56, 942–948 (2008).Google Scholar
89.Turner, D.M. and Kalidindi, S.R.: Statistical construction of 3-D microstructures from 2-D exemplars collected on oblique sections. Acta Mater. 102, 136–148 (2016).Google Scholar
90.Sundararaghavan, V.: Reconstruction of three-dimensional anisotropic microstructures from two-dimensional micrographs imaged on orthogonal planes. Integr. Mater. Manuf. Innovation 3, 19 (2014).Google Scholar
91.Mika, S., Schölkopf, B., Smola, A.J., Müller, K.-R., Scholz, M. and Rätsch, G.: 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.Roweis, S.T. and Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000).Google Scholar
93.Zhang, Z. and Zha, H.: Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM J. Sci. Comput. 26, 313–338 (2004).Google Scholar
94.Fast, T. and Kalidindi, S.R.: Formulation and calibration of higher-order elastic localization relationships using the MKS approach. Acta Mater. 59, 4595–4605 (2011).Google Scholar
95.Montes de Oca Zapiain, D., Popova, E., and Kalidindi, S.R.: 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).Google Scholar
96.Montes de Oca Zapiain, D., Popova, E., Abdeljawad, F., Foulk, J.W., Kalidindi, S.R. and Lim, H.: Reduced-order microstructure-sensitive models for damage initiation in two-phase composites. Integr. Mater. Manuf. Innovation 7, 97–115 (2018).Google Scholar
97.Paulson, N.H., Priddy, M.W., McDowell, D.L. and Kalidindi, S.R.: Reduced-order microstructure-sensitive protocols to rank-order the transition fatigue resistance of polycrystalline microstructures. Int. J. Fatigue 119, 1–10 (2019).Google Scholar
98.Cecen, A., Dai, H., Yabansu, Y.C., Kalidindi, S.R. and Song, L.: Material structure–property linkages using three-dimensional convolutional neural networks. Acta Mater. 146, 76–84 (2018).Google Scholar
99.Yang, Z., Yabansu, Y.C., Al-Bahrani, R., Liao, W., Choudhary, A.N., Kalidindi, S.R. and Agrawal, A.: Deep learning approaches for mining structure–property linkages in high contrast composites from simulation datasets. Comput. Mater. Sci. 151, 278–287 (2018).Google Scholar
100.Lubbers, N., Lookman, T., and Barros, K.: Inferring low-dimensional microstructure representations using convolutional neural networks. Phys. Rev. E 96, 052111 (2017).Google Scholar
101.Box, G.E.P., Jenkins, G.M., Reinsel, G.C. and Ljung, G.M.: Time Series Analysis: Forecasting and Control (John Wiley & Sons, Hoboken, NJ, 2015).Google Scholar
102.Brockwell, P.J., Davis, R.A., and Calder, M.V.: Introduction to Time Series and Forecasting (Springer, New York, NY, 2, 2002).Google Scholar
103.Hamilton, J.D.: Time Series analysis (Princeton University Press, 2, Princeton, NJ, 1994).Google Scholar
104.Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B (Methodol.), 58, 267–288 (1996).Google Scholar
105.Hoerl, A.E. and Kennard, R.W.: Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12, 55–67 (1970).Google Scholar
106.Latypov, M.I., Toth, L.S., and Kalidindi, S.R.: Materials knowledge system for nonlinear composites. Comput. Methods. Appl. Mech. Eng. 346, 180–196 (2018).Google Scholar
107.Lee Rodgers, J. and Nicewander, W.A.: Thirteen ways to look at the correlation coefficient. Am. Stat. 42, 59–66 (1988).Google Scholar
108.Brough, D.B., Kannan, A., Haaland, B., Bucknall, D.G. and Kalidindi, S.R.: 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).Google Scholar
109.Li, Q., Gu, L., Augenbroe, G., Wu, C.F.J. and Brown, J.: A Generic Approach to Calibrate Building Energy Models under Uncertainty Using Bayesian Inference. In Building Simulation Conference. Hyderabad, India, 2015.Google Scholar
110.Nikolaev, P., Hooper, D., Webber, F., Rao, R., Decker, K., Krein, M., Poleski, J., Barto, R. and Maruyama, B.: Autonomy in materials research: a case study in carbon nanotube growth. npj Comput. Mater. 2, 16031 (2016).Google Scholar
111.Panchal, J.H., Kalidindi, S.R., and McDowell, D.L.: Key computational modeling issues in integrated computational materials engineering. Computer-Aided Design 45, 4–25 (2013).Google Scholar
112.Pathak, S. and Kalidindi, S.R.: Spherical nanoindentation stress–strain curves. Mater. Sci., Eng. R., Rep. 91, 1–36 (2015).Google Scholar
113.Weaver, J.S. and Kalidindi, S.R.: Mechanical characterization of Ti-6Al-4V titanium alloy at multiple length scales using spherical indentation stress–strain measurements. Mater. Des. 111, 463–472 (2016).Google Scholar
114.Khosravani, A., Morsdorf, L., Tasan, C.C. and Kalidindi, S.R.: Multiresolution mechanical characterization of hierarchical materials: spherical nanoindentation on martensitic Fe-Ni-C steels. Acta Mater. 153, 257–269 (2018).Google Scholar
115.Patel, D. and Kalidindi, S.: Estimating the slip resistance from spherical nanoindentation and orientation measurements in polycrystalline samples of cubic metals. Int. J. Plast. 92, 19 (2017).Google Scholar
116.Patel, D.K. and Kalidindi, S.R.: 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).Google Scholar
117.Patel, D.K., Al-Harbi, H.F., and Kalidindi, S.R.: Extracting single-crystal elastic constants from polycrystalline samples using spherical nanoindentation and orientation measurements. Acta Mater. 79, 108–116 (2014).Google Scholar
118.Pathak, S., Stojakovic, D., and Kalidindi, S.R.: Measurement of the local mechanical properties in polycrystalline samples using spherical nanoindentation and orientation imaging microscopy. Acta Mater. 57, 3020–3028 (2009).Google Scholar
119.Castillo, A. and Kalidindi, S.R.: Accelerated extraction of crystal level elastic parameters via Bayesian framework. Front. Mater. (2019), submitted.Google Scholar