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