How Long to Read The Nth-order Comprehensive Adjoint Sensitivity Analysis Methodology

By Dan Gabriel Cacuci

How Long Does it Take to Read The Nth-order Comprehensive Adjoint Sensitivity Analysis Methodology?

It takes the average reader to read The Nth-order Comprehensive Adjoint Sensitivity Analysis Methodology by Dan Gabriel Cacuci

Assuming a reading speed of 250 words per minute. Learn more

Description

The 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 parameters stem from experimental procedures which are also subject to imprecisions, the results predicted by these models are also imprecise, being affected by the uncertainties underlying the respective model. The functional derivatives (also called "sensitivities") of results (also called "responses") produced by mathematical/computational models are needed for many purposes, including: (i) understanding the model by ranking the importance of the various model parameters; (ii) performing "reduced-order modeling" by eliminating unimportant parameters and/or processes; (iii) quantifying the uncertainties induced in a model response due to model parameter uncertainties; (iv) performing "model validation," by comparing computations to experiments to address the question "does the model represent reality?" prioritizing improvements in the model; (vi) performing data assimilation and model calibration as part of forward "predictive modeling" to obtain best-estimate predicted results with reduced predicted uncertainties; (vii) performing inverse "predictive modeling" designing and optimizing the system. This 3-Volume monograph describes a comprehensive adjoint sensitivity analysis methodology, developed by the author, which enables the efficient and exact computation of arbitrarily high-order sensitivities of model responses in large-scale systems comprising many model parameters. The qualifier "comprehensive" is employed to highlight that the model parameters considered within the framework of this methodology also include the systems uncertain boundaries and internal interfaces in phase-space. The models responses can be either scalar-valued functionals of the models parameters and state variables (e.g., as customarily encountered in optimization problems) or general function-valued responses. Since linear operators admit bona-fide adjoint operators, responses of models that are linear in the state functions (i.e., dependent variables) can depend simultaneously on both the forward and the adjoint state functions. Hence, the sensitivity analysis of such responses warrants the treatment of linear systems in their own right, rather than treating them as particular cases of nonlinear systems. This is in contradistinction to responses for nonlinear systems, which can depend only on the forward state functions, since nonlinear operators do not admit bona-fide adjoint operators (only a linearized form of a nonlinear operator may admit an adjoint operator). Thus, Volume 1 of this book presents the mathematical framework of the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (abbreviated as "nth-CASAM-L"), which is conceived for the most efficient computation of exactly obtained mathematical expressions of arbitrarily-high-order (nth-order) sensitivities of a generic system response with respect to all of the parameters underlying the respective forward/adjoint systems. Volume 2 of this book presents the application of the nth-CASAM-L to perform a fourth-order sensitivity and uncertainty analysis of an OECD/NEA reactor physics benchmark which is representative of a large-scale model comprises many (21,976) uncertain parameters, thereby amply illustrating the unique potential of the nth-CASAM-L to enable the exact and efficient computation of chosen high-order response sensitivities to model parameters. Volume 3 of this book presents the "nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems" (abbreviation: nth-CASAM-N) for the practical, efficient, and exact computation of arbitrarily-high order sensitivities of responses to model parameters for systems that are also nonlinear in their underlying state functions. Such computations are not feasible with any other methodology. The application of the nth-CASAM-L and the nth-CASAM-N overcomes the so-called "curse of dimensionality" in sensitivity and uncertainty analysis, thus revolutionizing all of the fields of activities which require accurate computation of response sensitivities. Since this monograph includes many illustrative, fully worked-out, paradigm problems, it can serve as a textbook or as supplementary reading for graduate courses in academic departments in the natural sciences and engineering.

How long is The Nth-order Comprehensive Adjoint Sensitivity Analysis Methodology?

The Nth-order Comprehensive Adjoint Sensitivity Analysis Methodology by Dan Gabriel Cacuci is 0 pages long, and a total of 0 words.

This makes it 0% the length of the average book. It also has 0% more words than the average book.

How Long Does it Take to Read The Nth-order Comprehensive Adjoint Sensitivity Analysis Methodology Aloud?

The average oral reading speed is 183 words per minute. This means it takes to read The Nth-order Comprehensive Adjoint Sensitivity Analysis Methodology aloud.

What Reading Level is The Nth-order Comprehensive Adjoint Sensitivity Analysis Methodology?

The Nth-order Comprehensive Adjoint Sensitivity Analysis Methodology is suitable for students ages 2 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy The Nth-order Comprehensive Adjoint Sensitivity Analysis Methodology?

The Nth-order Comprehensive Adjoint Sensitivity Analysis Methodology by Dan Gabriel Cacuci is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

To buy The Nth-order Comprehensive Adjoint Sensitivity Analysis Methodology by Dan Gabriel Cacuci on Amazon click the button below.

Buy The Nth-order Comprehensive Adjoint Sensitivity Analysis Methodology on Amazon