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On the Need to Determine Accurately the Impact of Higher-Order Sensitivities on Model Sensitivity Analysis, Uncertainty Quantification and Best-Estimate Predictions

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  • Dan Gabriel Cacuci

    (Center for Nuclear Science and Energy, University of South Carolina, Columbia, SC 29208, USA)

Abstract

This work aims at underscoring the need for the accurate quantification of the sensitivities (i.e., functional derivatives) of the results (a.k.a. “responses”) produced by large-scale computational models with respect to the models’ parameters, which are seldom known perfectly in practice. The large impact that can arise from sensitivities of order higher than first has been highlighted by the results of a third-order sensitivity and uncertainty analysis of an OECD/NEA reactor physics benchmark, which will be briefly reviewed in this work to underscore that neglecting the higher-order sensitivities causes substantial errors in predicting the expectation and variance of model responses. The importance of accurately computing the higher-order sensitivities is further highlighted in this work by presenting a text-book analytical example from the field of neutron transport, which impresses the need for the accurate quantification of higher-order response sensitivities by demonstrating that their neglect would lead to substantial errors in predicting the moments (expectation, variance, skewness, kurtosis) of the model response’s distribution in the phase space of model parameters. The incorporation of response sensitivities in methodologies for uncertainty quantification, data adjustment and predictive modeling currently available for nuclear engineering systems is also reviewed. The fundamental conclusion highlighted by this work is that confidence intervals and tolerance limits on results predicted by models that only employ first-order sensitivities are likely to provide a false sense of confidence, unless such models also demonstrate quantitatively that the second- and higher-order sensitivities provide negligibly small contributions to the respective tolerance limits and confidence intervals. The high-order response sensitivities to parameters underlying large-scale models can be computed most accurately and most efficiently by employing the high-order comprehensive adjoint sensitivity analysis methodology, which overcomes the curse of dimensionality that hampers other methods when applied to large-scale models involving many parameters.

Suggested Citation

  • Dan Gabriel Cacuci, 2021. "On the Need to Determine Accurately the Impact of Higher-Order Sensitivities on Model Sensitivity Analysis, Uncertainty Quantification and Best-Estimate Predictions," Energies, MDPI, vol. 14(19), pages 1-38, October.
  • Handle: RePEc:gam:jeners:v:14:y:2021:i:19:p:6318-:d:649320
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    References listed on IDEAS

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    1. Dan G. Cacuci & Ruixian Fang & Jeffrey A. Favorite, 2020. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark. VI: Overall Impact of 1st- and 2nd-Order Sensitivities o," Energies, MDPI, vol. 13(7), pages 1-37, April.
    2. Dan Gabriel Cacuci, 2019. "Towards Overcoming the Curse of Dimensionality: The Third-Order Adjoint Method for Sensitivity Analysis of Response-Coupled Linear Forward/Adjoint Systems, with Applications to Uncertainty Quantificat," Energies, MDPI, vol. 12(21), pages 1-34, November.
    3. Ruixian Fang & Dan Gabriel Cacuci, 2020. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: IV. Effects of Imprecisely Known Source Parameters," Energies, MDPI, vol. 13(6), pages 1-49, March.
    4. Ruixian Fang & Dan G. Cacuci, 2020. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: V. Computation of Mixed 2nd-Order Sensitivities Involvin," Energies, MDPI, vol. 13(10), pages 1-50, May.
    5. D. G. Cacuci & R. Fang & J. A. Favorite & M. C. Badea & F. Di Rocco, 2019. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: III. Effects of Imprecisely Known Microscopic Fission Cr," Energies, MDPI, vol. 12(21), pages 1-67, October.
    6. Dan G. Cacuci & Ruixian Fang & Jeffrey A. Favorite, 2019. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: I. Effects of Imprecisely Known Microscopic Total and Ca," Energies, MDPI, vol. 12(21), pages 1-43, November.
    7. Ruixian Fang & Dan Gabriel Cacuci, 2019. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: II. Effects of Imprecisely Known Microscopic Scattering ," Energies, MDPI, vol. 12(21), pages 1-33, October.
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    Cited by:

    1. Dan Gabriel Cacuci, 2022. "Overview of Arbitrarily High-Order Adjoint Sensitivity and Uncertainty Quantification Methodology for Large-Scale Systems," Energies, MDPI, vol. 15(18), pages 1-44, September.
    2. Yizhen Wang & Menglei Cui & Jiong Guo & Han Zhang & Yingjie Wu & Fu Li, 2023. "Decay Branch Ratio Sampling Method with Dirichlet Distribution," Energies, MDPI, vol. 16(4), pages 1-17, February.

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