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Simulation and Modeling Methodologies, Technologies and Applications pp 211–222Cite as

Quasi-Monte Carlo and RBF Metamodeling for Quantile Estimation in River Bed Morphodynamics

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 319))

Abstract

Four generic methods for quantile estimation have been compared: Monte Carlo (MC), Monte Carlo with Harrel-Davis weighting (WMC), quasi-Monte Carlo with Sobol sequence (QMC) and quasi-random splines (QRS). The methods are combined with RBF metamodel and applied to the analysis of morphodynamic—hydrodynamic simulations of the river bed evolution. The following results have been obtained. Harrel-Davis weighting gives a moderate 10–20 % improvement of precision at small number of samples N ~ 100. Quasi-Monte Carlo methods provide significant improvement of quantile precision, e.g. the number of function evaluations necessary to achieve rms ~ 10−4 precision is reduced from 1,000,000 for MC to 100,000 for QMC and to 6,000 for QRS. On the other hand, RBF metamodeling of bulky data allows to speed up the computation of one complete result in the considered problem from 45 min (on 32CPU) to 20 s (on 1CPU), providing rapid quantile estimation for the whole set of bulky data.

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Acknowledgments

We are grateful to Rebekka Kopmann from Federal Waterways Engineering and Research Institute, Karlsruhe, Germany for providing us with simulation data. We also thank Slawomir Koziel and Leifur Leifsson from Reykjavik University for fruitful discussions at the conference SIMULTECH 2013, Reykjavik, Iceland.

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Authors and Affiliations

  1. Fraunhofer Institute for Algorithms and Scientific Computing, Sankt Augustin, Germany

    Tanja Clees, Igor Nikitin, Lialia Nikitina & Sabine Pott

Authors
  1. Tanja Clees
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  2. Igor Nikitin
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  3. Lialia Nikitina
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  4. Sabine Pott
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Corresponding author

Correspondence to Igor Nikitin .

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Editors and Affiliations

  1. Department of Computer Science, Monmouth University, West Long Branch, New Jersey, USA

    Mohammad S. Obaidat

  2. School of Science and Engineering, Reykjavik University, Reykjavik, Iceland

    Slawomir Koziel

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  4. School of Science and Engineering, Reykjavik University, Reykjavik, Iceland

    Leifur Leifsson

  5. Faculty of Engineering, University of Ottawa, Ottawa, Ontario, Canada

    Tuncer Ören

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Clees, T., Nikitin, I., Nikitina, L., Pott, S. (2015). Quasi-Monte Carlo and RBF Metamodeling for Quantile Estimation in River Bed Morphodynamics. In: Obaidat, M., Koziel, S., Kacprzyk, J., Leifsson, L., Ören, T. (eds) Simulation and Modeling Methodologies, Technologies and Applications. Advances in Intelligent Systems and Computing, vol 319. Springer, Cham. https://doi.org/10.1007/978-3-319-11457-6_15

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  • DOI: https://doi.org/10.1007/978-3-319-11457-6_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11456-9

  • Online ISBN: 978-3-319-11457-6

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