Cacuci, D.G. (2022) Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): I. Mathematical Framework. American Journal of Computational Mathematics (AJCM), 12, 44-78.
https://doi.org/10.4236/ajcm.2022.121005

has been cited by the following article:

• TITLE: Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): II. Paradigm Application to a Bernoulli Model Comprising Uncertain Parameters

  AUTHORS: Dan Gabriel Cacuci

  KEYWORDS: Fifth-Order Sensitivity Analysis of Bernoulli Model, Uncertain Model Parameters, Uncertain Model Domain Boundaries, Uncertain Model Boundary Conditions

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.12 No.1, March 22, 2022

  ABSTRACT: This work presents the application of the recently developed “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N)” to a simplified Bernoulli model. The 5th-CASAM-N builds upon and incorporates all of the lower-order (i.e., the first-, second-, third-, and fourth-order) adjoint sensitivities analysis methodologies. The Bernoulli model comprises a nonlinear model response, uncertain model parameters, uncertain model domain boundaries and uncertain model boundary conditions, admitting closed-form explicit expressions for the response sensitivities of all orders. Illustrating the specific mechanisms and advantages of applying the 5th-CASAM-N for the computation of the response sensitivities with respect to the uncertain parameters and boundaries reveals that the 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.