Cacuci, D.G (2021) Fourth-Order Comprehensive Adjoint Sensitivity Analysis (4th-CASAM) of Response-Coupled Linear Forward/Adjoint Systems. I. Theoretical Framework. Energies, 14, Article No. 3335.
https://doi.org/10.3390/en14113335

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.