Data-Driven Computing

  • Trenton Kirchdoerfer
  • Michael OrtizEmail author
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 46)


Data-Driven Computing is a new field of computational analysis which uses provided data to directly produce predictive outcomes. Recent works in this developing field have established important properties of Data-Driven solvers, accommodated noisy data sets and demonstrated both quasi-static and dynamic solutions within mechanics. This work reviews this initial progress and advances some of the many possible improvements and applications that might best advance the field. Possible method improvements discuss incorporation of data quality metrics, and adaptive data additions while new applications focus on multi-scale analysis and the need for public databases to support constitutive data collaboration.


  1. 1.
    D. Agarwal, Y.W. Cheah, D. Fay, J. Fay, D. Guo, T. Hey, M. Humphrey, K. Jackson, J. Li, C. Poulain, Y. Ryu, C. van Ingen, Data-intensive science: the terapixel and modisazure projects. Int. J. High Perform. Comput. Appl. 25(3), 304–316 (2011)Google Scholar
  2. 2.
    D.A. Agarwal, B. Faybishenko, V.L. Freedman, H. Krishnan, G. Kushner, C. Lansing, E. Porter, A. Romosan, A. Shoshani, H. Wainwright, A. Weidmer, K.S. Wu, A science data gateway for environmental management. Concur. Comput. Pract. Exp. 28(7), 1994–2004 (2016)Google Scholar
  3. 3.
    R. Agarwal, V. Dhar, Big data, data science, and analytics: the opportunity and challenge for is research. Inf. Syst. Res. 25(3), 443–448 (2014)Google Scholar
  4. 4.
    B. Baesens, Analytics in a Big Data World : The Essential Guide to Data Science and its Applications (Wiley & SAS business series. John Wiley & Sons Inc, Hoboken, New Jersey, 2014)Google Scholar
  5. 5.
    T. Kirchdoerfer, M. Ortiz, Data-driven computational mechanics. Comput. Method Appl. Mech. Eng. 304, 81–101 (2016)Google Scholar
  6. 6.
    T. Kirchdoerfer, M. Ortiz, Data driven computing with noisy material data sets. Submitted for publication, Feb. 2017 (arXiv:1702.01574 [physics.comp-ph])
  7. 7.
    C.M. Breneman, L.C. Brinson, L.S. Schadler, B. Natarajan, M. Krein, K. Wu, L. Morkowchuk, Y. Li, H. Deng, H.Y. Xu, Stalking the materials genome: a data-driven approach to the virtual design of nanostructured polymers. Adv. Funct. Mat. 23(46), 5746–5752 (2013)Google Scholar
  8. 8.
    S. Broderick, K. Rajan, Informatics derived materials databases for multifunctional properties. Sci. Technol. Adv. Mat. 16(1) (2015)Google Scholar
  9. 9.
    S. Broderick, C. Suh, J. Nowers, B. Vogel, S. Mallapragada, B. Narasimhan, K. Rajan, Informatics for combinatorial materials science. Jom 60(3), 56–59 (2008)Google Scholar
  10. 10.
    G. Ceder, D. Morgan, C. Fischer, K. Tibbetts, S. Curtarolo, Data-mining-driven quantum mechanics for the prediction of structure. Mrs Bulletin 31(12), 981–985 (2006)CrossRefGoogle Scholar
  11. 11.
    S. Curtarolo, D. Morgan, K. Persson, J. Rodgers, G. Ceder, Predicting crystal structures with data mining of quantum calculations. Phys. Rev. Lett. 91(13) (2003)Google Scholar
  12. 12.
    A. Gupta, A. Cecen, S. Goyal, A.K. Singh, S.R. Kalidindi, Structure-property linkages using a data science approach: application to a non-metallic inclusion/steel composite system. Acta Materialia 91, 239–254 (2015)Google Scholar
  13. 13.
    S.R. Kalidindi, Data science and cyberinfrastructure: critical enablers for accelerated development of hierarchical materials. Int. Mater. Rev. 60(3), 150–168 (2015)Google Scholar
  14. 14.
    S.R. Kalidindi, M. De Graef, Materials data science: current status and future outlook. Annu. Rev. Mater. Res. 45(45), 171–193 (2015)Google Scholar
  15. 15.
    S.R. Kalidindi, J.A. Gomberg, Z.T. Trautt, C.A. Becker, Application of data science tools to quantify and distinguish between structures and models in molecular dynamics datasets. Nanotechnology 26(34) (2015)Google Scholar
  16. 16.
    S.R. Kalidindi, S.R. Niezgoda, A.A. Salem, Microstructure informatics using higher-order statistics and efficient data-mining protocols. Jom 63(4), 34–41 (2011)CrossRefGoogle Scholar
  17. 17.
    Z.K. Liu, L.Q. Chen, K. Rajan, Linking length scales via materials informatics. Jom 58(11), 42–50 (2006)CrossRefGoogle Scholar
  18. 18.
    D. Morgan, G. Ceder, S. Curtarolo, High-throughput and data mining with ab initio methods. Meas. Sci. Technol. 16(1), 296–301 (2005)Google Scholar
  19. 19.
    K. Rajan, Materials informatics. Mater. Today 8(10), 38–45 (2005)Google Scholar
  20. 20.
    K. Rajan, Materials informatics part i: a diversity of issues. Jom 60(3), 50–50 (2008)Google Scholar
  21. 21.
    K. Rajan, Informatics and integrated computational materials engineering: part ii. Jom 61(1), 47–47 (2009)Google Scholar
  22. 22.
    K. Rajan, Materials informatics how do we go about harnessing the “big data” paradigm? Mater. Today 15(11), 470–470 (2012)Google Scholar
  23. 23.
    K. Rajan, Materials informatics: the materials “gene” and big data. Annual Rev. Mater. Res. 45(45), 153–169 (2015)Google Scholar
  24. 24.
    K. Rajan, M. Zaki, K. Bennett, Informatics based design of materials. Abstr. Pap. Am. Chem. Soc. 221, U464–U464 (2001)Google Scholar
  25. 25.
    C.M. Bishop, Pattern Recognition and Machine Learning (Information science and statistics. Springer, New York, 2006)Google Scholar
  26. 26.
    I. Steinwart, A. Christmann, Support Vector Machines, 1st edn. (Information science and statistics. Springer, New York, 2008)Google Scholar
  27. 27.
    M.A. Aguilo, L. Swiler, A. Urbina, An overview of inverse material identification within the frameworks of deterministic and stochastic parameter estimation. Int. J. Uncertain. Quantif. 3(4), 289–319 (2013)Google Scholar
  28. 28.
    B. Banerjee, T.F. Walsh, W. Aquino, M. Bonnet, Large scale parameter estimation problems in frequency-domain elastodynamics using an error in constitutive equation functional. Comput. Method. Appl. Mech. Eng. 253, 60–72 (2013)Google Scholar
  29. 29.
    M. Ben Azzouna, P. Feissel, P. Villon, Robust identification of elastic properties using the modified constitutive relation error. Comput. Method. Appl. Mech. Eng. 295, 196–218 (2015)Google Scholar
  30. 30.
    M. Bonnet, W. Aquino, Three-dimensional transient elastodynamic inversion using the modified error in constitutive relation, in 4th International Workshop on New Computational Methods for Inverse Problems (NCMIP2014) 542 (2014)Google Scholar
  31. 31.
    L. Chamoin, P. Ladeveze, J. Waeytens, Goal-oriented updating of mechanical models using the adjoint framework. Comput. Mech. 54(6), 1415–1430 (2014)Google Scholar
  32. 32.
    P. Feissel, O. Allix, Modified constitutive relation error identification strategy for transient dynamics with corrupted data: the elastic case. Comput. Method. Appl. Mech. Eng. 196(13–16), 1968–1983 (2007)Google Scholar
  33. 33.
    S. Guchhait, B. Banerjee, Constitutive error based material parameter estimation procedure for hyperelastic material. Comput. Method. Appl. Mech. Eng. 297, 455–475 (2015)Google Scholar
  34. 34.
    F. Latourte, A. Chrysochoos, S. Pagano, B. Wattrisse, Elastoplastic behavior identification for heterogeneous loadings and materials. Exp. Mech. 48(4), 435–449 (2008)Google Scholar
  35. 35.
    T. Merzouki, H. Nouri, F. Roger, Direct identification of nonlinear damage behavior of composite materials using the constitutive equation gap method. Int. J. Mech. Sci. 89, 487–499 (2014)Google Scholar
  36. 36.
    H.M. Nguyen, O. Allix, P. Feissel, A robust identification strategy for rate-dependent models in dynamics. Inverse Probl. 24(6) (2008)Google Scholar
  37. 37.
    N. Promma, B. Raka, M. Grediac, E. Toussaint, J.B. Le Cam, X. Balandraud, F. Hild, Application of the virtual fields method to mechanical characterization of elastomeric materials. Int. J. Solid Struct. 46(3–4), 698–715 (2009)Google Scholar
  38. 38.
    J.E. Warner, M.I. Diaz, W. Aquino, M. Bonnet, Inverse material identification in coupled acoustic-structure interaction using a modified error in constitutive equation functional. Comput. Mech. 54(3), 645–659 (2014)Google Scholar
  39. 39.
    The materials project.
  40. 40.
    The NIST materials genome initiative.
  41. 41.
    The NoMaD repository.
  42. 42.
    The knowledgebase of interatomic models.
  43. 43.
    A.I. Khinchin, Mathematical Foundations of Information Theory, New dover edn. (Dover Publications, New York, 1957)Google Scholar
  44. 44.
    C.E. Shannon, A mathematical theory of communication. Bell Syst. Tech. J. 27(3), 379–423 (1948)Google Scholar
  45. 45.
    C.E. Shannon, A mathematical theory of communication. Bell Syst. Tech. J. 27(4), 623–656 (1948)Google Scholar
  46. 46.
    C.E. Shannon, Communication theory of secrecy systems. Bell Syst. Tech. J. 28(4), 656–715 (1949)Google Scholar
  47. 47.
    M. Arroyo, M. Ortiz, Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods. Int. J. Num. Method Eng. 65(13), 2167–2202 (2006)Google Scholar
  48. 48.
    C.J. Cyron, M. Arroyo, M. Ortiz, Smooth, second order, non-negative meshfree approximants selected by maximum entropy. Int. J. Num. Method Eng. 79(13), 1605–1632 (2009)Google Scholar
  49. 49.
    A.R. Newman, Confidence, pedigree, and security classification for improved data fusion, in Proceedings of the Fifth International Conference on Information Fusion, vol. II (2002), pp. 1408–1415Google Scholar
  50. 50.
    S. Conti, G. Dolzmann, B. Kirchheim, S. Muller, Sufficient conditions for the validity of the cauchy-born rule close to so(n). J. Eur. Math. Soc. 8(3), 515–530 (2006)Google Scholar
  51. 51.
    M. Flucher, A. Garroni, S. Muller, Concentration of low energy extremals: identification of concentration points. Calc. Var. Partial Diff. Equ. 14(4), 483–516 (2002)Google Scholar
  52. 52.
    A. Garroni, S. Muller, Concentration phenomena for the volume functional in unbounded domains: identification of concentration points. J. Func. Anal. 199(2), 386–410 (2003)Google Scholar
  53. 53.
    S. Luckhaus, L. Mugnai, On a mesoscopic many-body hamiltonian describing elastic shears and dislocations. Continuum Mech. Thermodyn. 22(4), 251–290 (2010)Google Scholar
  54. 54.
    B. Runnels, I.J. Beyerlein, S. Conti, M. Ortiz, An analytical model of interfacial energy based on a lattice-matching interatomic energy. J. Mech. Phys. Solid 89, 174–193 (2016)Google Scholar
  55. 55.
    B. Runnels, I.J. Beyerlein, S. Conti, M. Ortiz, A relaxation method for the energy and morphology of grain boundaries and interfaces. J. Mech. Phys. Solid 94, 388–408 (2016)Google Scholar
  56. 56.
    S.Y. Kim, N. Kumar, P. Persson, J. Sofo, A.C.T. van Duin, J.D. Kubicki, Development of a reaxff reactive force field for titanium dioxide/water systems. Langmuir 29(25), 7838–7846 (2013)CrossRefGoogle Scholar
  57. 57.
    J.P. Larentzos, B.M. Rice, E.F.C. Byrd, N.S. Weingarten, J.V. Lill, Parameterizing complex reactive force fields using multiple objective evolutionary strategies (moes). part 1: Reaxff models for cyclotrimethylene trinitramine (rdx) and 1,1-diamino-2,2-dinitroethene (fox-7). J. Chem. Theory Comput. 11(2), 381–391 (2015)Google Scholar
  58. 58.
    J. Ludwig, D.G. Vlachos, A.C.T. van Duin, W.A. Goddard, Dynamics of the dissociation of hydrogen on stepped platinum surfaces using the reaxff reactive force field. J. Phys. Chem. B 110(9), 4274–4282 (2006)Google Scholar
  59. 59.
    G. Psofogiannakis, A.C.T. van Duin, Development of a reaxff reactive force field for si/ge/h systems and application to atomic hydrogen bombardment of si, ge, and sige (100) surfaces. Surf. Sci. 646, 253–260 (2016)Google Scholar
  60. 60.
    O. Rahaman, A.C.T. van Duin, V.S. Bryantsev, J.E. Mueller, S.D. Solares, W.A. Goddard, D.J. Doren, Development of a reaxff reactive force field for aqueous chloride and copper chloride. J. Phys. Chem. A 114(10), 3556–3568 (2010)Google Scholar
  61. 61.
    W.X. Song, S.J. Zhao, Development of the reaxff reactive force field for aluminum-molybdenum alloy. J. Mater. Res. 28(9), 1155–1164 (2013)Google Scholar
  62. 62.
    B. Zhang, A.C.T. van Duin, J.K. Johnson, Development of a reaxff reactive force field for tetrabutylphosphonium glycinate/\({\rm CO_2}\) mixtures. J. Phys. Chem. B 118(41), 12008–12016 (2014)Google Scholar
  63. 63.
    M.I. Espanol, D.M. Kochmann, S. Conti, M. Ortiz, A gamma-convergence analysis of the quasicontinuum method. Multiscale Model. Simul. 11(3), 766–794 (2013)Google Scholar
  64. 64.
    J. Knap, M. Ortiz, An analysis of the quasicontinuum method. J. Mech. Phys. Solid 49(9), 1899–1923 (2001)Google Scholar
  65. 65.
    E.B. Tadmor, M. Ortiz, R. Phillips, Quasicontinuum analysis of defects in solids. Philos. Mag. A 73(6), 1529–1563 (1996) (Physics of Condensed Matter Structure Defects and Mechanical Properties)Google Scholar
  66. 66.
    E.B. Tadmor, R. Phillips, M. Ortiz, Mixed atomistic and continuum models of deformation in solids. Langmuir 12(19), 4529–4534 (1996)CrossRefGoogle Scholar
  67. 67.
    A.S. Argon, G. Xu, M. Ortiz, Kinetics of dislocation emission from crack tips and the brittle to ductile transition of cleavage fracture. Fract. Instab. Dyn. Scaling Ductile/Brittle Beh. 409, 29–44Google Scholar
  68. 68.
    A.S. Argon, G. Xu, M. Ortiz, Kinetics of the crack-tip-governed brittle to ductile transitions in intrinsically brittle solids. Cleavage Fract. 125–135Google Scholar
  69. 69.
    S. Conti, A. Garroni, S. Muller, Singular kernels, multiscale decomposition of microstructure, and dislocation models. Arch. Ration. Mech. Anal. 199(3), 779–819 (2011)Google Scholar
  70. 70.
    A. Garroni, S. Muller, Gamma-limit of a phase-field model of dislocations. Siam J. Math. Anal. 36(6), 1943–1964 (2005)Google Scholar
  71. 71.
    A. Garroni, S. Muller, A variational model for dislocations in the line tension limit. Arch. Ration. Mech. Anal. 181(3), 535–578 (2006)Google Scholar
  72. 72.
    M. Koslowski, A.M. Cuitino, M. Ortiz, A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals. J. Mech. Phys. Solid 50(12), 2597–2635 (2002)Google Scholar
  73. 73.
    M. Koslowski, M. Ortiz, A multi-phase field model of planar dislocation networks. Model. Simul. Mater. Sci. Eng. 12(6), 1087–1097 (2004)Google Scholar
  74. 74.
    G. Xu, A.S. Argon, M. Ortiz, Nucleation of dislocations from crack tips under mixed-modes of loading—implications for brittle against ductile behavior of crystals. Philos. Mag. A 72(2), 415–451 (1995) (Physics of Condensed Matter Structure Defects and Mechanical Properties)Google Scholar
  75. 75.
    J.P. Hirth, J. Lothe, Theory of Dislocations, 2nd edn. (Wiley, New York, 1982)Google Scholar
  76. 76.
    V.V. Bulatov, W. Cai, Nodal effects in dislocation mobility. Phys. Rev. Lett. 89(11) (2002)Google Scholar
  77. 77.
    V.V. Bulatov, L.L. Hsiung, M. Tang, A. Arsenlis, M.C. Bartelt, W. Cai, J.N. Florando, M. Hiratani, M. Rhee, G. Hommes, T.G. Pierce, T.D. de la Rubia, Dislocation multi-junctions and strain hardening. Nature 440(7088), 1174–1178 (2006)CrossRefGoogle Scholar
  78. 78.
    S. Conti, M. Ortiz, Dislocation microstructures and the effective behavior of single crystals. Arch. Ration. Mech. Anal. 176(1), 103–147 (2005)Google Scholar
  79. 79.
    T. Hochrainer, S. Sandfeld, M. Zaiser, P. Gumbsch, Continuum dislocation dynamics: towards a physical theory of crystal plasticity. J. Mech. Phys. Solid 63, 167–178 (2014)Google Scholar
  80. 80.
    D. Weygand, J. Senger, C. Motz, W. Augustin, V. Heuveline, P. Gumbsch, High performance computing and discrete dislocation dynamics: Plasticity of micrometer sized specimens. High Perform. Comput. Sci. Eng ’08 507–523 (2009)Google Scholar
  81. 81.
    G. Dal Maso, An Introduction to \(\Gamma \)-convergence, in Progress in nonlinear differential equations and their applications (Birkhauser, Boston, MA, 1993)Google Scholar
  82. 82.
  83. 83.
    A. Azevedo, M.F. Santos, Integration of Data Mining in Business Intelligence Systems (Business Science Reference, Hershey, 2015)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.California Institute of TechnologyPasadenaUSA

Personalised recommendations