The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology, Volume III: Overcoming the Curse of Dimensionality: Nonlinear Systems

This text describes a comprehensive adjoint sensitivity analysis methodology (C-ASAM), developed by the author, enabling the efficient and exact computation of arbitrarily high-order functional derivatives of model responses to model parameters in large-scale systems. The model’s responses can be either scalar-valued functionals of the model’s parameters and state variables (as customarily encountered, e.g., in optimization problems) or general function-valued responses, which are often of interest but are currently not amenable to efficient sensitivity analysis. The C-ASAM framework is set in linearly increasing Hilbert spaces, each of state-function-dimensionality, as opposed to exponentially increasing parameter-dimensional spaces, thereby breaking the so-called “curse of dimensionality” in sensitivity and uncertainty analysis. The C-ASAM applies to any model; the larger the number of model parameters, the more efficient the C-ASAM becomes for computing arbitrarily high-order response sensitivities. The text includes illustrative paradigm problems which are fully worked-out to enable the thorough understanding of the C-ASAM’s principles and their practical application. The book will be helpful to those working in the fields of sensitivity analysis, uncertainty quantification, model validation, optimization, data assimilation, model calibration, sensor fusion, reduced-order modelling, inverse problems and predictive modelling. It serves as a textbook or as supplementary reading for graduate course on these topics, in academic departments in the natural, biological, and physical sciences and engineering.

This Volume Three, the third of three, covers systems that are nonlinear in the state variables, model parameters and associated responses. The selected illustrative paradigm problems share these general characteristics. A separate Volume One covers systems that are linear in the state variables.

Professor Cacuci’s career spans over 40 years in the field of nuclear science and energy, encompassing both academia and large-scale multidisciplinary research centers. His scientific expertise includes predictive best-estimate analysis of large-scale physical and engineering systems, large scale scientific computations and, within nuclear science and engineering, reactor multi-physics, dynamics, and safety. During the period 1990-2012, Prof. Cacuci served as Director of the Institute of Reactor Safet at the Research Center Karlsruhe and Chaired Professor at the University of Karlsruhe in Germany, and also served as the Scientific Director of The French Alternative Energies and Atomic Energy Commission’s Nuclear Energy Pole. During the period 1984-2019, Prof. Cacuci served as the Editor of “Nuclear Science and Engineering,” a research journal of the American Nuclear Society, and is serving since 2019 as the Founding Editor-in-Chief of the open access MDPI Journal of Nuclear Engineering. He has received many prestigious awards, including four titles of Doctor Honoris Causa, the E. O. Lawrence Award and Gold Medal from the US DOE, the Alexander von Humboldt Prize for Senior Scholars and from the American Nuclear Society, the Arthur Holly Compton Award, the Eugene P. Wigner Award, the Glenn Seaborg Medal, Young Members Engineering Achievement Award, and ANS Fellow.  He is a member of several international and national academies of arts and sciences, has made over 600 presentations worldwide, has authored 46 books, 7 book chapters, over 200 peer-reviewed articles, and has edited the comprehensive Handbook of Nuclear Engineering. Currently, Prof Cacuci serves as the Director of the Center of Economic Excellence in Nuclear Science and Energy and SmartState Endowed Chair Professor of Mechanical Engineering at University of South Carolina.