Advances in High-Order Sensitivity Analysis

The high-order sensitivities of model responses with respect to model parameters are notoriously difficult to compute for large-scale models involving many parameters. The neglect of higher-order response sensitivities leads to substantial errors in predicting the moments (expectation, variance, skewness, kurtosis) of the model response’s distribution in the phase-space of model parameters. The author expands on his theory of addressing high-order sensitivity analysis.

The mathematical/computational models of physical systems comprise parameters, independent and dependent variables. Since the physical processes themselves are seldom known precisely and since most of the model’s parameters stem from experimental procedures that are also subject to imprecision and/or uncertainties, the results predicted by these models are also imprecise, being affected by the uncertainties underlying the respective model.

In the particular case of sensitivity analysis using conventional methods, the number of large-scale computations increases exponentially. For large-scale models involving many parameters, even the first-order sensitivities are computationally very expensive to determine accurately by conventional methods. Furthermore, the "curse of dimensionality" prohibits the accurate computation of higher-order sensitivities by conventional methods.

Other books by the author, all published by CRC Press, include Sensitivity & Uncertainty Analysis, Volume: Theory (2003), and Sensitivity and Uncertainty Analysis, Volume II: Applications to Large-Scale Systems (Cacuci, et al., 2005), Computational Methods for Data Evaluation and Assimilation (Cacuci, et al.,2014). The Second-Order Adjoint Sensitivity Analysis Methodology (2018), and Advances in High-Order Predictive Modeling Methodologies and Illustrative Problems (2025).

Dan Gabriel Cacuci is a Distinguished Professor Emeritus in the Department of Mechanical Engineering at the University of South Carolina and the Karlsruhe Institute of Technology, Germany. He received his PhD in applied physics, mechanical and nuclear engineering from Columbia University. He is also the recipient of many awards including four honorary doctorates, the Ernest Orlando Lawrence Memorial award from the U.S. Department of Energy and the Arthur Holly Compton, Eugene P. Wigner and the Glenn Seaborg Awards from the American Nuclear Society. He was named an “Inaugural Highly Ranked Scholar” by Scholar GPS, being ranked #2 in the world in the field of Uncertainty Analysis, #5 in the world in the field of Sensitivity Analysis, and ranked in the top 0.05% of all scholars worldwide.