The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-CASAM-N): Mathematical Framework

This work presents the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-CASAM-N), which enables most efficient computation of exactly determined expressions arbitrarily high-order sensitivities generic nonlinear system responses with respect to model parameters, uncertain boundaries, and internal interfaces in model’s phase space. The mathematical framework underlying nth-CASAM-N is proven be correct by using induction. formulated linearly increasing higher-dimensional Hilbert spaces—as opposed exponentially parameter-dimensional spaces—thus overcoming curse dimensionality sensitivity analysis systems.