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Computer programs --- Automatic differentiation. --- Sensitivity theory (Mathematics) --- Logiciels --- Théorie de la sensibilité (Mathématiques)

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Differentiable dynamical systems --- Sensitivity theory (Mathematics) --- State-space methods --- Dynamique différentiable --- Théorie de la sensibilité (Mathématiques) --- Espace d'état, méthodes de l'

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Evolutionary computation. --- Architecture --- Sensitivity theory (Mathematics) --- Structural optimization. --- Réseaux neuronaux à structure évolutive --- Théorie de la sensibilité (Mathématiques) --- Optimisation des structures --- Technological innovations. --- Computer-aided design. --- Innovations --- Conception assistée par ordinateur --- Sasaki, Mutsuro --- Réseaux neuronaux à structure évolutive --- Théorie de la sensibilité (Mathématiques) --- Conception assistée par ordinateur

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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?" (v) 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"; (viii) 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 system's uncertain boundaries and internal interfaces in phase-space. The model's responses can be either scalar-valued functionals of the model's 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.

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 --- Sensitivity theory (Mathematics) --- Linear systems --- Mathematical models.

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Artificial neural networks are used to model systems that receive inputs and produce outputs. The relationships between the inputs and outputs and the representation parameters are critical issues in the design of related engineering systems, and sensitivity analysis concerns methods for analyzing these relationships. Perturbations of neural networks are caused by machine imprecision, and they can be simulated by embedding disturbances in the original inputs or connection weights, allowing us to study the characteristics of a function under small perturbations of its parameters. This is the first book to present a systematic description of sensitivity analysis methods for artificial neural networks. It covers sensitivity analysis of multilayer perceptron neural networks and radial basis function neural networks, two widely used models in the machine learning field. The authors examine the applications of such analysis in tasks such as feature selection, sample reduction, and network optimization. The book will be useful for engineers applying neural network sensitivity analysis to solve practical problems, and for researchers interested in foundational problems in neural networks.

Neural networks (Computer science). --- Sensitivity theory (Mathematics). --- Neural networks (Computer science) --- Sensitivity theory (Mathematics) --- Mechanical Engineering --- Engineering & Applied Sciences --- Computer Science --- Mechanical Engineering - General --- Information Technology --- Artificial Intelligence --- Neural circuitry. --- Circuitry, Neural --- Circuits, Neural --- Nerve net --- Nerve network --- Neural circuits --- Neurocircuitry --- Neuronal circuitry --- Artificial neural networks --- Nets, Neural (Computer science) --- Networks, Neural (Computer science) --- Neural nets (Computer science) --- Computer science. --- Artificial intelligence. --- Computer simulation. --- Pattern recognition. --- Statistical physics. --- Dynamical systems. --- Engineering design. --- Control engineering. --- Robotics. --- Mechatronics. --- Computer Science. --- Artificial Intelligence (incl. Robotics). --- Control, Robotics, Mechatronics. --- Statistical Physics, Dynamical Systems and Complexity. --- Pattern Recognition. --- Simulation and Modeling. --- Engineering Design. --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automation --- Machine theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Programmable controllers --- Design, Engineering --- Engineering --- Industrial design --- Strains and stresses --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Mathematical statistics --- Design perception --- Pattern recognition --- Form perception --- Perception --- Figure-ground perception --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Self-organizing systems --- Fifth generation computers --- Neural computers --- Informatics --- Science --- Design --- Statistical methods --- Electrophysiology --- Nervous system --- Neural networks (Neurobiology) --- Reflexes --- Artificial intelligence --- Natural computation --- Soft computing --- Optical pattern recognition. --- Artificial Intelligence. --- Complex Systems. --- Optical data processing --- Pattern perception --- Perceptrons --- Visual discrimination --- Automation. --- System theory. --- Pattern recognition systems. --- Control, Robotics, Automation. --- Automated Pattern Recognition. --- Computer Modelling. --- Pattern classification systems --- Pattern recognition computers --- Computer vision --- Systems, Theory of --- Systems science --- Automatic factories --- Automatic production --- Computer control --- Engineering cybernetics --- Factories --- Industrial engineering --- Mechanization --- Assembly-line methods --- Automatic control --- Automatic machinery --- CAD/CAM systems --- Robotics --- Philosophy