OpenTURNS: An Industrial Software for Uncertainty Quantification in Simulation

  • Michaël Baudin
  • Anne Dutfoy
  • Bertrand Iooss
  • Anne-Laure Popelin
Living reference work entry


The needs to assess robust performances for complex systems and to answer tighter regulatory processes (security, safety, environmental control, health impacts, etc.) have led to the emergence of a new industrial simulation challenge: to take uncertainties into account when dealing with complex numerical simulation frameworks. Therefore, a generic methodology has emerged from the joint effort of several industrial companies and academic institutions. EDF R&D, Airbus Group, and Phimeca Engineering started a collaboration at the beginning of 2005, joined by IMACS in 2014, for the development of an open-source software platform dedicated to uncertainty propagation by probabilistic methods, named OpenTURNS for open-source treatment of uncertainty, Risk ’N Statistics. OpenTURNS addresses the specific industrial challenges attached to uncertainties, which are transparency , genericity , modularity, and multi-accessibility. This paper focuses on OpenTURNS and presents its main features: OpenTURNS is an open- source software under the LGPL license that presents itself as a C++ library and a Python TUI and which works under Linux and Windows environment. All the methodological tools are described in the different sections of this paper: uncertainty quantification, uncertainty propagation, sensitivity analysis, and metamodeling. A section also explains the generic wrappers’ way to link OpenTURNS to any external code. The paper illustrates as much as possible the methodological tools on an educational example that simulates the height of a river and compares it to the height of a dike that protects industrial facilities. At last, it gives an overview of the main developments planned for the next few years.


OpenTURNS Uncertainty Quantification Propagation Estimation Sensitivity Simulation Probability Statistics Random vectors Multivariate distribution Open source Python module C++ library Transparency Genericity 


  1. 1.
    Airbus, EDF, Phimeca: Developer’s guide, OpenTURNS 1.4 (2014).
  2. 2.
    Au, S., Beck, J.L.: Estimation of small failure probabilities in high dimensions by subset simulation. Probab. Eng. Mech. 16, 263–277 (2001)CrossRefGoogle Scholar
  3. 3.
    Barate, R.: Calcul haute performance avec OpenTURNS, workshop du GdR MASCOT-NUM, Quantification d’incertitude et calcul intensif. (2013)
  4. 4.
    Berg, I.: muparser,, fast Math Parser Library (2014)
  5. 5.
    Berger, J. (ed.): Statistical Decision Theory and Bayesian Analysis. Springer, New York (1985)MATHGoogle Scholar
  6. 6.
    Blatman, G.: Adaptative sparse polynomial chaos expansions for uncertainty propagation and sensitivity anaysis. PhD thesis, Clermont University (2009)Google Scholar
  7. 7.
    Blatman, G., Sudret, B.: Adaptive sparse polynomial chaos expansion based on least angle regression. J. Comput. Phys. 230, 2345–2367 (2011)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Butucea, C., Delmas, J., Dutfoy, A., Fischer, R.: Maximum entropy copula with given diagonal section. J. Multivar. Anal. 137, 61–81 (2015)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Ditlevsen, O., Madsen, H.: Structural Reliability Methods. Wiley, Chichester/New York (1996)Google Scholar
  10. 10.
    Dutfoy, A., Dutka-Malen, I., Pasanisi, A., Lebrun, R., Mangeant, F., Gupta, J.S., Pendola, M., Yalamas, T.: OpenTURNS, an open source initiative to treat uncertainties, Risks’N statistics in a structured industrial approach. In: Proceedings of 41èmes Journées de Statistique, Bordeaux (2009)Google Scholar
  11. 11.
    Fang, K.T., Li, R., Sudjianto, A.: Design and Modeling for Computer Experiments. Chapman & Hall/CRC, Boca Raton (2006)MATHGoogle Scholar
  12. 12.
    gum08: JCGM 100-2008 – Evaluation of measurement data – guide to the expression of uncertainty in measurement. JCGM (2008)Google Scholar
  13. 13.
    Hyndman, R., Shang, H.: Rainbow plots, bagplots, and boxplots for functional data. J. Comput. Graph. Stat. 19, 29–45 (2010)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Iooss, B., Lemaître, P.: A review on global sensitivity analysis methods. In: Meloni, C., Dellino, G. (eds.) Uncertainty Management in Simulation-Optimization of Complex Systems: Algorithms and Applications. Springer, New York (2015)Google Scholar
  15. 15.
    Kurowicka, D., Cooke, R.: Uncertainty Analysis with High Dimensional Dependence Modelling. Wiley, Chichester/Hoboken (2006)CrossRefMATHGoogle Scholar
  16. 16.
    Lebrun, R., Dutfoy, A.: Do rosenblatt and nataf isoprobabilistic transformations really differ? Probab. Eng. Mech. 24, 577–584 (2009)CrossRefGoogle Scholar
  17. 17.
    Lebrun, R., Dutfoy, A.: A generalization of the nataf transformation to distributions with elliptical copula. Probab. Eng. Mech. 24, 172–178 (2009)CrossRefGoogle Scholar
  18. 18.
    Lebrun, R., Dutfoy, A.: An innovating analysis of the nataf transformation from the viewpoint of copula. Probab. Eng. Mech. 24, 312–320 (2009)CrossRefGoogle Scholar
  19. 19.
    Lebrun, R., Dutfoy, A.: A practical approach to dependence modelling using copulas. J. Risk Reliab. 223(04), 347–361 (2009)Google Scholar
  20. 20.
    Lebrun, R., Dutfoy, A.: Copulas for order statistics with prescribed margins. J. Multivar. Anal. 128, 120–133 (2014)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Lemaire, M.: Structural Reliability. Wiley, Hoboken (2009)CrossRefGoogle Scholar
  22. 22.
    Liberty, L.: Ev3: a library for symbolic computation in c++ using n-ary trees, (2003)
  23. 23.
    Marin, J.M., Robert, C. (eds.): Bayesian Core: A Practical Approach to Computational Bayesian Statistics. Springer, New York (2007)MATHGoogle Scholar
  24. 24.
    Marrel, A., Iooss, B., Van Dorpe, F., Volkova, E.: An efficient methodology for modeling complex computer codes with Gaussian processes. Comput. Stat. Data Anal. 52, 4731–4744 (2008)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Munoz-Zuniga, M., Garnier, J., Remy, E.: Adaptive directional stratification for controlled estimation of the probability of a rare event. Reliab. Eng. Syst. Saf. 96, 1691–1712 (2011)CrossRefMATHGoogle Scholar
  26. 26.
    Nash, S.: A survey of truncated-newton methods. J. Comput. Appl. Math. 124, 45–59 (2000)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    OPEN CASCADE S.: Salome: the open source integration platform for numerical simulation. (2006)
  28. 28.
    Pasanisi, A.: Uncertainty analysis and decision-aid: methodological, technical and managerial contributions to engineering and R&D studies. Habilitation Thesis of Université de Technologie de Compiègne, France (2014)
  29. 29.
    Pasanisi, A., Dutfoy, A.: An industrial viewpoint on uncertainty quantification in simulation: stakes, methods, tools, examples. In: Dienstfrey, A., Boisvert, R. (eds.) Uncertainty Quantification in Scientific Computing – 10th IFIP WG 2.5 Working Conference, WoCoUQ 2011, Boulder, 1–4 Aug 2011. IFIP Advances in Information and Communication Technology, vol. 377, pp. 27–45. Springer, Berlin (2012)Google Scholar
  30. 30.
    Rasmussen, C., Williams, C., Dietterich, T.: Gaussian Processes for Machine Learning. MIT, Cambridge (2006)Google Scholar
  31. 31.
    Robert, C.P., Casella, G.: Monte Carlo Statistical Methods. Springer, New York (2004)CrossRefMATHGoogle Scholar
  32. 32.
    Rubinstein, R.: Simulation and the Monte-Carlo Methods. Wiley, New York (1981)CrossRefMATHGoogle Scholar
  33. 33.
    Sacks, J., Welch, W., Mitchell, T., Wynn, H.: Design and analysis of computer experiments. Stat. Sci. 4, 409–435 (1989)MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Saltelli, A.: Making best use of model evaluations to compute sensitivity indices. Comput. Phys. Commun. 145, 280–297 (2002)CrossRefMATHGoogle Scholar
  35. 35.
    Saltelli, A., Tarantola, S., Chan, K.: A quantitative, model-independent method for global sensitivity analysis of model output. Technometrics 41, 39–56 (1999)CrossRefGoogle Scholar
  36. 36.
    Saltelli, A., Chan, K., Scott, E. (eds.): Sensitivity Analysis. Wiley Series in Probability and Statistics. Wiley, Chichester/New York (2000)MATHGoogle Scholar
  37. 37.
    Santner, T., Williams, B., Notz, W.: The Design and Analysis of Computer Experiments. Springer, New York (2003)CrossRefMATHGoogle Scholar
  38. 38.
    Sudret, B.: Global sensitivity analysis using polynomial chaos expansion. Reliab. Eng. Syst. Saf. 93, 964–979 (2008)CrossRefGoogle Scholar
  39. 39.
    Tarantola, A.: Inverse Problem Theory and Methods for Model Parameter Estimation. Society for Industrial and Applied Mathematics, Philadelphia (2005)CrossRefMATHGoogle Scholar
  40. 40.
    Top 500 Supercomputer Sites: Zumbrota, BlueGene/Q, Power BQC 16C 1.60GHz, Custom (2014)

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Michaël Baudin
    • 1
  • Anne Dutfoy
    • 2
  • Bertrand Iooss
    • 3
  • Anne-Laure Popelin
    • 4
  1. 1.Industrial Risk Management DepartmentEDF R&D FranceChatouFrance
  2. 2.Industrial Risk Management DepartmentEDF R&D FranceSaclayFrance
  3. 3.Industrial Risk Management DepartmentEDF R&D FranceChatouFrance
  4. 4.Industrial Risk Management DepartmentEDF R&D FranceChatouFrance

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