The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology, Volume I

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 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. To facilitate the understanding of the fundamental concepts underlying C-ASAM, this book first analyzes the less challenging finite-dimensional systems before progressing to infinite dimensional systems which involve boundary and/or initial conditions. The text applies the author's principles to a series of problems, repeating the same examples with each new higher-order level of the methodology. It includes illustrative paradigm problems from several disciplines, such as particle transport and diffusion, and heat transfer. These paradigm problems 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 One, the first of three, addresses systems that are linear in the state variables, but are nonlinear in the model parameters and associated responses. The selected illustrative paradigm problems share these general characteristics. Understanding the application of the C-ASAM to linear systems will greatly facilitate the understanding of the application of the C-ASAM to nonlinear systems, which are covered in Volume Two.