Skip to main content
SpringerLink
Log in

Unlocking Large Scale Uncertainty Quantification with In Transit Iterative Statistics

  • Conference paper
  • First Online:
In Situ Visualization for Computational Science

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

Multi-run numerical simulations using supercomputers are increasingly used by physicists and engineers for dealing with input data and model uncertainties. Most of the time, the input parameters of a simulation are modeled as random variables, then simulations are run a (possibly large) number of times with input parameters varied according to a specific design of experiments. Uncertainty quantification for numerical simulations is a hard computational problem, currently bounded by the large size of the produced results. This book chapter is about using in situ techniques to enable large scale uncertainty quantification studies. We provide a comprehensive description of Melissa, a file avoiding, adaptive, fault-tolerant, and elastic framework that computes in transit statistical quantities of interest. Melissa currently implements the on-the-fly computation of the statistics necessary for the realization of large scale uncertainty quantification studies: moment-based statistics (mean, standard deviation, higher orders), quantiles, Sobol’ indices, and threshold exceedance.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    https://melissa-sa.github.io.

  2. 2.

    https://melissa-sa.github.io/.

References

  1. Archambeau, F., Méchitoua, N., Sakiz, M.: Code_saturne: a finite volume code for the computation of turbulent incompressible flows. Int. J. Finite Vol. 1 (2004)

    Google Scholar 

  2. Baudin, M., Boumhaout, K., Delage, T., Iooss, B., Martinez, J.M.: Numerical stability of sobol’ indices estimation formula. In: Proceedings of the 8th International Conference on Sensitivity Analysis of Model Output (SAMO 2016). Le Tampon, Réunion Island, France (2016)

    Google Scholar 

  3. Baudin, M., Dutfoy, A., Iooss, B., Popelin, A.: Open TURNS: an industrial software for uncertainty quantification in simulation. In: Ghanem, R., Higdon, D., Owhadi, H. (eds.) Springer Handbook on Uncertainty Quantification, pp. 2001–2038. Springer (2017)

    Google Scholar 

  4. Bect, J., Ginsbourger, D., Li, L., Picheny, V., Vazquez, E.: Sequential design of computer experiments for the estimation of a probability of failure. Stat. Comput. 22, 773–793 (2012)

    Article  MathSciNet  Google Scholar 

  5. Bennett, J., Grout, R., Pébay, P., Roe, D., Thompson, D.: Numerically stable, single-pass, parallel statistics algorithms. In: Cluster Computing and Workshops, 2009. CLUSTER’09. IEEE International Conference on, pp. 1–8. IEEE (2009)

    Google Scholar 

  6. Bennett, J.C., Abbasi, H., Bremer, P.T., Grout, R., Gyulassy, A., Jin, T., Klasky, S., Kolla, H., Parashar, M., Pascucci, V., et al.: Combining in-situ and in-transit processing to enable extreme-scale scientific analysis. In: High Performance Computing, Networking, Storage and Analysis (SC), 2012 International Conference for, pp. 1–9. IEEE (2012)

    Google Scholar 

  7. Bennett, J.C., Krishnamoorthy, V., Liu, S., Grout, R.W., Hawkes, E.R., Chen, J.H., Shepherd, J., Pascucci, V., Bremer, P.T.: Feature-based statistical analysis of combustion simulation data. IEEE Trans. Vis. Comput. Graph. 17(12), 1822–1831 (2011)

    Article  Google Scholar 

  8. Cannamela, C., Garnier, J., Iooss, B.: Controlled stratification for quantile estimation. Ann. Appl. Stat. 2, 1554–1580 (2008)

    Article  MathSciNet  Google Scholar 

  9. Chan, T.F., Golub, G.H., LeVeque, R.J.: Updating formulae and a pairwise algorithm for computing sample variances. In: COMPSTAT 1982 5th Symposium held at Toulouse 1982, pp. 30–41. Springer (1982)

    Google Scholar 

  10. David, H., Nagaraja, H.: Order Statistics, 3rd edn. Wiley, New-York (2003)

    Book  Google Scholar 

  11. de Rocquigny, E., Devictor, N., Tarantola, S. (eds.): Uncertainty in Industrial Practice. Wiley (2008)

    Google Scholar 

  12. Finch, T.: Incremental calculation of weighted mean and variance. Technical report. University of Cambridge (2009)

    Google Scholar 

  13. Fournier, Y., Bonelle, J., Moulinec, C., Shang, Z., Sunderland, A., Uribe, J.: Optimizing code_saturne computations on petascale systems. Comput. Fluids 45(1), 103–108 (2011). 22nd International Conference on Parallel Computational Fluid Dynamics (ParCFD 2010)ParCFD

    Google Scholar 

  14. Gamboa, F., Janon, A., Klein, T., Lagnoux, A.: Sensitivity analysis for multidimensional and functional outputs. Electron. J. Stat. 8(1), 575–603 (2014)

    Article  MathSciNet  Google Scholar 

  15. Gilquin, L., Arnaud, E., Prieur, C., Monod, H.: Recursive estimation procedure of sobol’ indices based on replicated designs. Submitted, http://hal.univ-grenoble-alpes.fr/hal-01291769 (2017)

  16. Glynn, P.W.: Importance sampling for monte carlo estimation of quantiles. In: Proceedings of Second International Workshop on Mathematical Methods in Stochastic Simulation and Experimental Design, pp. 180–185. Publishing House of Saint Petersburg University (1996)

    Google Scholar 

  17. Hesterberg, T., Nelson, B.: Control variates for probability and quantile estimation. Manag. Sci. 44, 1295–1312 (1998)

    Article  Google Scholar 

  18. Higdon, D., Gattiker, J., Williams, B., Rightley, M.: Computer model calibration using high-dimensional output. J. Am. Stat. Assoc. 103, 571–583 (2008)

    Article  MathSciNet  Google Scholar 

  19. Homma, T., Saltelli, A.: Importance measures in global sensitivity analysis of non linear models. Reliab. Eng. Syst. Saf. 52, 1–17 (1996)

    Article  Google Scholar 

  20. Iooss, B.: Estimation itérative en propagation d’incertitudes : réglage robuste de l’algorithme de Robbins-Monro. Preprint, https://hal.archives-ouvertes.fr/hal-02511787 (2020)

  21. 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, pp. 101–122. Springer (2015)

    Google Scholar 

  22. Iooss, B., Marrel, A.: Advanced methodology for uncertainty propagation in computer experiments with large number of inputs. Nucl. Technol. 205, 1588–1606 (2019)

    Article  Google Scholar 

  23. Janon, A., Klein, T., Lagnoux, A., Nodet, M., Prieur, C.: Asymptotic normality and efficiency of two sobol index estimators. ESAIM: Probab. Stat. 18, 342–364 (2014)

    Google Scholar 

  24. Lakshminarasimhan, S., Jenkins, J., Arkatkar, I., Gong, Z., Kolla, H., Ku, S.H., Ethier, S., Chen, J., Chang, C.S., Klasky, S., et al.: Isabela-qa: query-driven analytics with isabela-compressed extreme-scale scientific data. In: Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis, p. 31. ACM (2011)

    Google Scholar 

  25. Lampitella, P., Inzoli, F., Colombo, E.: Note on a formula for one-pass, parallel computations of arbitrary-order, weighted, multivariate central moments (2015)

    Google Scholar 

  26. Le Gratiet, L., Iooss, B., Browne, T., Blatman, G., Cordeiro, S., Goursaud, B.: Model assisted probability of detection curves: new statistical tools and progressive methodology. J. Nondestruct. Eval. 36, 8 (2017)

    Article  Google Scholar 

  27. Lemaire, M., Chateauneuf, A., Mitteau, J.C.: Structural Reliability. Wiley (2009)

    Google Scholar 

  28. Marrel, A., De Lozzo, M.: Sensitivity analysis with dependence and variance-based measures for spatio-temporal numerical simulators. In: Stochastic Environmental Research and Risk Assessment, In Press (2017)

    Google Scholar 

  29. Marrel, A., Iooss, B., Jullien, M., Laurent, B., Volkova, E.: Global sensitivity analysis for models with spatially dependent outputs. Environmetrics 22, 383–397 (2011)

    Article  MathSciNet  Google Scholar 

  30. Marrel, A., Perot, N., Mottet, C.: Development of a surrogate model and sensitivity analysis for spatio-temporal numerical simulators. Stoch. Environ. Res. Risk Assess. 29, 959–974 (2015)

    Article  Google Scholar 

  31. Marrel, A., Saint-Geours, N.: Sensitivity analysis of spatial and/or temporal phenomena. In: Ghanem, R., Higdon, D., Owhadi, H. (eds.) Springer Handbook on Uncertainty Quantification. Springer (2017)

    Google Scholar 

  32. Morio, J., Balesdent, M.: Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems. Woodhead Publishing (2016)

    Google Scholar 

  33. Nanty, S., Helbert, C., Marrel, A., Pérot, N., Prieur, C.: Uncertainty quantification for functional dependent random variables. Comput. Stat. (2016). https://doi.org/10.1007/s00180-016-0676-0

  34. Pébay, P.: Formulas for robust, one-pass parallel computation of covariances and arbitrary-order statistical moments. Sandia Report SAND2008-6212, Sandia National Laboratories 94 (2008)

    Google Scholar 

  35. Pébay, P., Thompson, D., Bennett, J., Mascarenhas, A.: Design and performance of a scalable, parallel statistics toolkit. In: 2011 IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum (IPDPSW), pp. 1475–1484. IEEE (2011)

    Google Scholar 

  36. Popelin, A.L., Iooss, B.: Visualization tools for uncertainty and sensitivity analyses on thermal-hydraulic transients. In: Joint International Conference on Supercomputing in Nuclear Applications and Monte Carlo 2013 (SNA + MC 2013). Paris, France (2013)

    Google Scholar 

  37. Prieur, C., Tarantola, S.: Variance-based sensitivity analysis: theory and estimation algorithms. In: Ghanem, R., Higdon, D., Owhadi, H. (eds.) Springer Handbook on Uncertainty Quantification. Springer (2017)

    Google Scholar 

  38. Ribés, A., Pouderoux, J., Popelin, A.L., Iooss, B.: Visualizing statistical analysis of curves datasets in Paraview. In: 2014 IEEE Conference on Visual Analytics Science and Technology (VAST). Paris, France (2014)

    Google Scholar 

  39. Ribés, A., Terraz, T., Fournier, Y., Iooss, B., Raffin, B.: Large scale in transit computation of quantiles for ensemble runs. Unpublished Technical Report (2019). arXiv: 1905.04180

  40. Ribés, A., Pouderoux, J., Iooss, B.: A visual sensitivity analysis for parameter-augmented ensembles of curves. J. Verif. Valid. Uncertain. Quantif. December 2019 4(4), 041007 (2020, February 11). https://doi.org/10.1115/1.4046020

  41. Robbins, H., Monro, S.: A stochastic approximation method. Ann. Math. Stat. 22, 400–407 (1951)

    Article  MathSciNet  Google Scholar 

  42. Saltelli, A., Chan, K., Scott, E. (eds.): Sensitivity Analysis. Wiley Series in Probability and Statistics. Wiley (2000)

    Google Scholar 

  43. Smith, R.: Uncertainty quantification. SIAM (2014)

    Google Scholar 

  44. Sobol, I.: Sensitivity estimates for non linear mathematical models. Math. Model. Comput. Exp. 1, 407–414 (1993)

    MATH  Google Scholar 

  45. Terraz, T., Ribés, A., Fournier, Y., Iooss, B., Raffin, B.: Melissa: large scale in transit sensitivity analysis avoiding intermediate files. In: International Conference for High Performance Computing, Networking, Storage and Analysis (SC’17). Denver (2017)

    Google Scholar 

  46. Tukey, J.W.: Exploratory Data Analysis, vol. 2. Reading, Mass (1977)

    MATH  Google Scholar 

  47. Welford, B.: Note on a method for calculating corrected sums of squares and products. Technometrics 4(3), 419–420 (1962)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. EDF R&D, Palaiseau, France

    Alejandro Ribés

  2. Université Grenoble Alpes, Inria, CNRS, Grenoble INP, LIG, 38000, Grenoble, France

    Théophile Terraz & Bruno Raffin

  3. EDF R&D, Chatou, France

    Yvan Fournier & Bertrand Iooss

Authors
  1. Alejandro Ribés
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Théophile Terraz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yvan Fournier
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Bertrand Iooss
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Bruno Raffin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alejandro Ribés .

Editor information

Editors and Affiliations

  1. Computer and Information Science, University of Oregon, Eugene, OR, USA

    Hank Childs

  2. Extreme-Scale Data Science and Analytics, Sandia National Laboratories, Livermore, CA, USA

    Janine C. Bennett

  3. Scientific Visualization Lab, University of Kaiserslautern, Kaiserslautern, Germany

    Christoph Garth

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ribés, A., Terraz, T., Fournier, Y., Iooss, B., Raffin, B. (2022). Unlocking Large Scale Uncertainty Quantification with In Transit Iterative Statistics. In: Childs, H., Bennett, J.C., Garth, C. (eds) In Situ Visualization for Computational Science. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-030-81627-8_6

Download citation

Publish with us

Policies and ethics

Search

Navigation