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.