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Cacuci, D.G. and Fang, R. (2021) Fourth-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: I. Mathematical Expressions and CPU-Time Comparisons for Computing 1st-, 2nd-and 3rd-Order Sensitivities. American Journal of Computational Mathematics (AJCM), 11, 94-132.
https://doi.org/10.4236/ajcm.2021.112009

has been cited by the following article:

• TITLE: Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): I. Mathematical Framework

  AUTHORS: Dan Gabriel Cacuci

  KEYWORDS: Nonlinear Models of Physical Systems, High-Order Sensitivity Analysis, 1st-Order Sensitivities, 2nd-Order Sensitivities, 3rd-Order Sensitivities, 4th-Order Sensitivities, 5th-Order Sensitivities

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.12 No.1, March 11, 2022

  ABSTRACT: This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5th-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.