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Overview of Arbitrarily High-Order Adjoint Sensitivity and Uncertainty Quantification Methodology for Large-Scale Systems

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  • Dan Gabriel Cacuci

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

Abstract

This work reviews from a unified viewpoint the concepts underlying the “n th -Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems” (n th -CASAM-L) and the “n th -Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (n th -CASAM-N) methodologies. The practical application of the n th -CASAM-L methodology is illustrated for an OECD/NEA reactor physics benchmark, while the practical application of the n th -CASAM-N methodology is illustrated for a nonlinear model of reactor dynamics that exhibits periodic and chaotic oscillations. As illustrated both by the general theory and by the examples reviewed in this work, both the n th -CASAM-L and n th -CASAM-N methodologies overcome the curse of dimensionality in sensitivity analysis. The availability of efficiently and exactly computed sensitivities of arbitrarily high order can lead to major advances in all areas that need such high-order sensitivities, including data assimilation, model calibration, uncertainty reduction, and predictive modeling.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:18:p:6590-:d:910546
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    References listed on IDEAS

    as
    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, 2021. "High-Order Deterministic Sensitivity Analysis and Uncertainty Quantification: Review and New Developments," Energies, MDPI, vol. 14(20), pages 1-53, October.
    3. 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.
    4. Dan Gabriel Cacuci, 2021. "The n th -Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (n th -CASAM-L): I. Mathematical Framework," Energies, MDPI, vol. 14(24), pages 1-42, December.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Dan Gabriel Cacuci, 2021. "Fourth-Order Comprehensive Adjoint Sensitivity Analysis (4th-CASAM) of Response-Coupled Linear Forward/Adjoint Systems: I. Theoretical Framework," Energies, MDPI, vol. 14(11), pages 1-45, June.
    10. 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.
    11. 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.
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