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Illustrative Application Of The Nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology For Nonlinear Systems To The Nordheim–Fuchs Reactor Dynamics/Safety Model, Dan Gabriel Cacuci
Illustrative Application Of The Nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology For Nonlinear Systems To The Nordheim–Fuchs Reactor Dynamics/Safety Model, Dan Gabriel Cacuci
Faculty Publications
The application of the recently developed “nth-order comprehensive sensitivity analysis methodology for nonlinear systems” (abbreviated as “nth-CASAM-N”) has been previously illustrated on paradigm nonlinear space-dependent problems. To complement these illustrative applications, this work illustrates the application of the nth-CASAM-N to a paradigm nonlinear time-dependent model chosen from the field of reactor dynamics/safety, namely the well-known Nordheim–Fuchs model. This phenomenological model describes a short-time self-limiting power transient in a nuclear reactor system having a negative temperature coefficient in which a large amount of reactivity is suddenly inserted, either intentionally or by accident. This model is sufficiently complex to demonstrate all the …
Illustrative Application Of The Nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology For Nonlinear Systems To The Nordheim–Fuchs Reactor Dynamics/Safety Model, Dan Gabriel Cacuci
Illustrative Application Of The Nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology For Nonlinear Systems To The Nordheim–Fuchs Reactor Dynamics/Safety Model, Dan Gabriel Cacuci
Faculty Publications
The application of the recently developed “nth-order comprehensive sensitivity analysis methodology for nonlinear systems” (abbreviated as “nth-CASAM-N”) has been previously illustrated on paradigm nonlinear space-dependent problems. To complement these illustrative applications, this work illustrates the application of the nth-CASAM-N to a paradigm nonlinear time-dependent model chosen from the field of reactor dynamics/safety, namely the well-known Nordheim–Fuchs model. This phenomenological model describes a short-time self-limiting power transient in a nuclear reactor system having a negative temperature coefficient in which a large amount of reactivity is suddenly inserted, either intentionally or by accident. This model is sufficiently complex to demonstrate all the …
The NTh-Order Comprehensive Adjoint Sensitivity Analysis Methodology For Nonlinear Systems (Nth-Casam-N): Mathematical Framework, Dan Gabriel Cacuci
The NTh-Order Comprehensive Adjoint Sensitivity Analysis Methodology For Nonlinear Systems (Nth-Casam-N): Mathematical Framework, Dan Gabriel Cacuci
Faculty Publications
This work presents the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-CASAM-N), which enables the most efficient computation of exactly determined expressions of arbitrarily high-order sensitivities of generic nonlinear system responses with respect to model parameters, uncertain boundaries, and internal interfaces in the model’s phase space. The mathematical framework underlying the nth-CASAM-N is proven to be correct by using mathematical induction. The nth-CASAM-N is formulated in linearly increasing higher-dimensional Hilbert spaces—as opposed to exponentially increasing parameter-dimensional spaces—thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems.
Towards Overcoming The Curse Of Dimensionality: The Third-Order Adjoint Method For Sensitivity Analysis Of Response-Coupled Linear Forward/Adjoint Systems, Uncertainty Quantification And Predictive Modeling With Applications To Nuclear Energy Systems, Dan Gabriel Cacuci
Faculty Publications
This work presents the Third-Order Adjoint Sensitivity Analysis Methodology (3rd-ASAM) for response-coupled forward and adjoint linear systems. The 3rd-ASAM enables the efficient computation of the exact expressions of the 3rd-order functional derivatives (“sensitivities”) of a general system response, which depends on both the forward and adjoint state functions, with respect to all of the parameters underlying the respective forward and adjoint systems. Such responses are often encountered when representing mathematically detector responses and reaction rates in reactor physics problems. The 3rd-ASAM extends the 2nd-ASAM in the quest to overcome the “curse of dimensionality” in sensitivity analysis, uncertainty quantification and predictive …
Towards Overcoming The Curse Of Dimensionality: The Third-Order Adjoint Method For Sensitivity Analysis Of Response-Coupled Linear Forward/Adjoint Systems, With Applications To Uncertainty Quantification And Predictive Modeling, Dan Gabriel Cacuci
Faculty Publications
This work presents the Third-Order Adjoint Sensitivity Analysis Methodology (3rd-ASAM) for response-coupled forward and adjoint linear systems. The 3rd-ASAM enables the efficient computation of the exact expressions of the 3rd-order functional derivatives ("sensitivities") of a general system response, which depends on both the forward and adjoint state functions, with respect to all of the parameters underlying the respective forward and adjoint systems. Such responses are often encountered when representing mathematically detector responses and reaction rates in reactor physics problems. The 3rd-ASAM extends the 2nd-ASAM in the quest to overcome the "curse of dimensionality" in sensitivity analysis, uncertainty quantification and predictive …