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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 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 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. This Volume Two, the second of three, presents the large-scale application of C-ASAM to compute exactly the first-, second-, third-, and fourth-order sensitivities of the Polyethylene-Reflected Plutonium (PERP) OECD/NEO international benchmark which is modeled mathematically by the Boltzmann particle transport equation. It follows from the description of the C-ASAM framework applied to linear systems in Volume One where the PERP benchmark's response of interest is the leakage of particles through its outer boundary. The benchmark represents the largest sensitivity analysis endeavor ever carried out in the field of reactor physics and the numerical results shown in this book prove, for the first time ever, that many of the second-order sensitivities are much larger than the corresponding first-order ones. Currently, the nth-CASAM is the only known methodology which enables such large-scale computations of the exact expressions and values of the nth-order response sensitivities.

Statistical science --- Mathematics --- Mathematical physics --- Nuclear physics --- Relation between energy and economics --- Applied physical engineering --- Engineering sciences. Technology --- Planning (firm) --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- energiebeheer (technologie) --- energiemanagement (economie) --- ICT (informatie- en communicatietechnieken) --- energiebeleid --- energie-economie --- economie --- mathematische modellen --- statistiek --- mineralen (chemie) --- mijnbouw --- wiskunde --- ingenieurswetenschappen --- fysica --- atoomfysica --- statistisch onderzoek --- Large scale systems. --- Linear systems. --- Sensitivity theory (Mathematics)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Mathematical physics. --- Computer simulation. --- Mathematical models. --- Statistics. --- Energy policy. --- Energy and state. --- Engineering mathematics. --- Engineering—Data processing. --- Nuclear physics. --- Computational Physics and Simulations. --- Mathematical Modeling and Industrial Mathematics. --- Statistical Theory and Methods. --- Energy Policy, Economics and Management. --- Mathematical and Computational Engineering Applications. --- Nuclear Physics. --- Atomic nuclei --- Atoms, Nuclei of --- Nucleus of the atom --- Physics --- Engineering --- Engineering analysis --- Mathematical analysis --- Energy and state --- Power resources --- State and energy --- Industrial policy --- Energy conservation --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Models, Mathematical --- Simulation methods --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Model-integrated computing --- Physical mathematics --- Government policy --- Large scale systems. --- Nonlinear systems. --- Sensitivity theory (Mathematics) --- Sensitivity (Mathematics) --- System sensitivity theory (Mathematics) --- Control theory --- Systems, Nonlinear --- System theory --- Systems, Large scale --- Engineering systems --- System analysis