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Estimation of an improved surrogate model in uncertainty quantification by neural networks

Author

Listed:
  • Benedict Götz

    (Technische Universität Darmstadt)

  • Sebastian Kersting

    (Technische Universität Darmstadt)

  • Michael Kohler

    (Technische Universität Darmstadt)

Abstract

Quantification of uncertainty of a technical system is often based on a surrogate model of a corresponding simulation model. In any application, the simulation model will not describe the reality perfectly, and consequently the surrogate model will be imperfect. In this article, we combine observed data from the technical system with simulated data from the imperfect simulation model in order to estimate an improved surrogate model consisting of multilayer feedforward neural networks, and we show that under suitable assumptions, this estimate is able to circumvent the curse of dimensionality. Based on this improved surrogate model, we show a rate of the convergence result for density estimates. The finite sample size performance of the estimates is illustrated by applying them to simulated data. The practical usefulness of the newly proposed estimates is demonstrated by using them to predict the uncertainty of a lateral vibration attenuation system with piezo-elastic supports.

Suggested Citation

  • Benedict Götz & Sebastian Kersting & Michael Kohler, 2021. "Estimation of an improved surrogate model in uncertainty quantification by neural networks," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(2), pages 249-281, April.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:2:d:10.1007_s10463-020-00748-1
    DOI: 10.1007/s10463-020-00748-1
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    References listed on IDEAS

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    1. Ann-Kathrin Bott & Tina Felber & Michael Kohler, 2015. "Estimation of a density in a simulation model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 271-285, September.
    2. Michael Kohler & Adam Krzyżak & Shashidhar Mallapur & Roland Platz, 2018. "Uncertainty Quantification in Case of Imperfect Models: A Non‐Bayesian Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(3), pages 729-752, September.
    3. Marc C. Kennedy & Anthony O'Hagan, 2001. "Bayesian calibration of computer models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 425-464.
    4. Tina Felber & Michael Kohler & Adam Krzyżak, 2015. "Adaptive density estimation based on real and artificial data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 1-18, March.
    5. Raymond K. W. Wong & Curtis B. Storlie & Thomas C. M. Lee, 2017. "A frequentist approach to computer model calibration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 635-648, March.
    Full references (including those not matched with items on IDEAS)

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