Fourth-Order Comprehensive Adjoint Sensitivity Analysis (4th-CASAM) of Response-Coupled Linear Forward/Adjoint Systems: I. Theoretical Framework

The most general quantities of interest (called “responses”) produced by the computational model a linear physical system can depend on both forward and adjoint state functions that describe respective system. This work presents Fourth-Order Comprehensive Adjoint Sensitivity Analysis Methodology (4th-CASAM) for systems, which enables efficient computation exact expressions 1st-, 2nd-, 3rd- 4th-order sensitivities generic response, functions, with respect to all parameters underlying forward/adjoint systems. Among best known such responses are various Lagrangians, including Schwinger Roussopoulos functionals, analyzing ratios reaction rates, Rayleigh quotient eigenvalues and/or separation constants, etc., require simultaneous consideration systems when computing them their (i.e., functional derivatives) parameters. Evidently, encompass, as particular cases, may just or pertaining under consideration. also compares CPU-times needed 4th-CASAM versus other deterministic methods (e.g., finite-difference schemes) response These comparisons underscore fact is only practically implementable methodology obtaining subsequently free methodologically-introduced approximations) 2nd, parameters, coupled By enabling practical any makes it possible compare relative values order, in order assess important actually be neglected, thus future investigations convergence (multivariate) Taylor series expansion terms parameter variations, well investigating range validity variances/covariance, skewness, kurtosis, etc.) derived from Taylor-expansion function model’s presented this provides basis significant advances towards overcoming “curse dimensionality” sensitivity analysis, uncertainty quantification predictive modeling.