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

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

Energies, 2022, vol. 15, issue 18, 1-44

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.

Keywords: high-order sensitivities; adjoint operators; reactor physics benchmark; limit cycle oscillations; period-doubling bifurcations; chaotic dynamics; uncertainty analysis; large-scale systems; predictive modeling (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
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