Exploiting Task-Based Parallelism in Bayesian Uncertainty Quantification

  • Panagiotis E. Hadjidoukas
  • Panagiotis Angelikopoulos
  • Lina Kulakova
  • Costas Papadimitriou
  • Petros Koumoutsakos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9233)


We introduce a task-parallel framework for non-intrusive Bayesian Uncertainty Quantification and Propagation of complex and computationally demanding physical models on massively parallel computing architectures. The framework incorporates Laplace asymptotic approximations and stochastic algorithms along with distributed numerical differentiation. Sampling is based on the Transitional Markov Chain Monte Carlo algorithm and its variants while the optimization tasks associated with the asymptotic approximations are treated via the Covariance Matrix Adaptation Evolution Strategy. Exploitation of task-based parallelism is based on a platform-agnostic adaptive load balancing library that orchestrates scheduling of multiple physical model evaluations on computing platforms that range from multicore systems to hybrid GPU clusters. Experimental results using representative applications demonstrate the flexibility and excellent scalability of the proposed framework.


Task-based parallelism Bayesian uncertainty quantification 


  1. 1.
    Owhadi, H., Scovel, C., Sullivan, T., McKerns, M., Ortiz, M.: Optimal uncertainty quantification. SIAM Rev. 55(2), 271–345 (2013)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Beck, J.L., Yuen, K.V.: Model selection using response measurements: Bayesian probabilistic approach. J. Eng. Mech. 130(2), 192–203 (2004)CrossRefGoogle Scholar
  3. 3.
    Papadimitriou, C., Beck, J.L., Katafygiotis, L.S.: Asymptotic expansions for reliability and moments of uncertain systems. J. Eng. Mech. 123(12), 1219–1229 (1997)CrossRefGoogle Scholar
  4. 4.
    Chen, M.H., Shao, Q.M., Ibrahim, J.G.: Monte Carlo Methods in Bayesian Computation. Springer, New York (2000)CrossRefMATHGoogle Scholar
  5. 5.
    Wu, S., Beck, J.L., Heaton, T.H.: Earthquake probability-based automated decision-making framework for earthquake early warning applications. Comp. Aid. Civ. Infr. Eng. 28, 737–752 (2013)Google Scholar
  6. 6.
    Adams, B., Bohnhoff, W., Dalbey, K., Eddy, J., Eldred, M., Gay, D., Haskell, K., Hough, P., Swiler, L.: DAKOTA, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Sandia Technical report (2013)Google Scholar
  7. 7.
    Lawrence Livermore National Laboratory. The PSUADE UQ project. http://computation.llnl.gov/casc/uncertainty_quantification/
  8. 8.
    Prudencio, E., Cheung, S.H.: Parallel adaptive multilevel sampling algorithms for the Bayesian analysis of mathematical models. Int. J. Unc. Quan. 2(3), 215–237 (2012)MathSciNetMATHGoogle Scholar
  9. 9.
    Hadjidoukas, P.E., Lappas, E., Dimakopoulos, V.V.: A runtime library for platform-independent task parallelism. In: 20th International Conference on Parallel, Distributed and Network-Based Processing, pp. 229–236 (2012)Google Scholar
  10. 10.
    Ching, J.Y., Chen, Y.C.: Transitional markov chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging. J. Eng. Mech. 133(7), 816–832 (2007)CrossRefGoogle Scholar
  11. 11.
    Chiachio, M., Beck, J., Chiachio, J., Rus, G.: Approximate Bayesian computation by subset simulation. SIAM J. Sci. Comput. 36, A1339–A1358 (2014)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Hansen, N., Muller, S.D., Koumoutsakos, P.: Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol. Comp. 11(1), 1–18 (2003)CrossRefGoogle Scholar
  13. 13.
    Beck, J.L., Katafygiotis, L.S.: Updating models and their uncertainties. I: Bayesian statistical framework. J. Eng. Mech. 124(4), 455–461 (1998)CrossRefGoogle Scholar
  14. 14.
    Galbally, D., Fidkowski, K., Willcox, K., Ghattas, O.: Non-linear model reduction for uncertainty quantification in large-scale inverse problems. Int. J. Num. Meth. Eng. 81(12), 1581–1608 (2010)MathSciNetMATHGoogle Scholar
  15. 15.
    Hadjidoukas, P.E., Angelikopoulos, P., Voglis, C., Papageorgiou, D.G., Lagaris, I.E.: NDL-v2.0: A new version of the numerical differentiation library for parallel architectures. Comput. Phys. Comm. 185(7), 2217–2219 (2014)CrossRefGoogle Scholar
  16. 16.
    Angelikopoulos, P., Papadimitriou, C., Koumoutsakos, P.: Data driven, predictive molecular dynamics for nanoscale flow simulations under uncertainty. J. Phys. Chem. B 117(47), 14808–14816 (2013)CrossRefGoogle Scholar
  17. 17.
    Rick, S.: A reoptimization of the five-site water potential (TIP5P) for use with Ewald sums. J. Chem. Phys. 120, 6085–6093 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Panagiotis E. Hadjidoukas
    • 1
  • Panagiotis Angelikopoulos
    • 1
  • Lina Kulakova
    • 1
  • Costas Papadimitriou
    • 2
  • Petros Koumoutsakos
    • 1
  1. 1.Computational Science and Engineering LaboratoryETH ZürichZurichSwitzerland
  2. 2.Department of Mechanical EngineeringUniversity of ThessalyVolosGreece

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