Sensitivity Theory for General Systems of Nonlinear Equations

Cacuci, Dan Gabriel; Weber, C.F.; Oblow, E.M.; Marable, J.H.

doi:10.13182/nse75-88

Cited by 147 publications

(147 citation statements)

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“…Structural identifiability was introduced by Bellman and Astrom (1970) as a tool in biological modeling to assess the internal structure of a system from input-output measurements (Cobelli and Romanin-Jacur, 1976;Cobelli and DiStefano, 1980). The adjoint method has been demonstrated by several investigators in the fields of climatological modeling, reactor thermal hydraulics, and reactor safety (Koda et al 1979;Cacuci et al, 1980;Hall et al, 1982). In this approach, 'exact' (Downing et al 1985) sensitivities are calculated as defined by partial derivatives.…”

Section: Introductionmentioning

confidence: 99%

A review of techniques for parameter sensitivity analysis of environmental models

Hamby

1994

Environ Monit Assess

1,562

852

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Abstract. Mathematical models are utilized to approximate various highly complex engineering, physical, environmental, social, and economic phenomena. Model parameters exerting the most influence on model results are identified through a 'sensitivity analysis'. A comprehensive review is presented of more than a dozen sensitivity analysis methods. This review is intended for those not intimately familiar with statistics or the techniques utilized for sensitivity analysis of computer models. The most fundamental of sensitivity techniques utilizes partial differentiation whereas the simplest approach requires varying parameter values one-at-a-time. Correlation analysis is used to determine relationships between independent and dependent variables. Regression analysis provides the most comprehensive sensitivity measure and is commonly utilized to build response surfaces that approximate complex models.

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Section: Introductionmentioning

confidence: 99%

A review of techniques for parameter sensitivity analysis of environmental models

Hamby

1994

Environ Monit Assess

1,562

852

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“…However, these early adjoint methods were applicable solely to linear problems, since nonlinear operators do not admit "adjoints", as is universally known. Cacuci and co-workers (Cacuci et al 1980a;Cacuci et al 1980b) initiated the application of adjoint methods for computing sensitivities of simple responses in simple nonlinear problems. In a remarkable breakthrough, Cacuci (Cacuci 1981a;Cacuci 1981b;Cacuci 1988) developed in 1981 a mathematically-rigorous "adjoint sensitivity analysis" theory applicable to completely general nonlinear systems.…”

Section: Results and Discussion: Design For Responsementioning

confidence: 99%

Validated predictive computational methods for surface charge in heterogeneous functional materials: HeteroFoaM™

Reifsnider

Cacuci

Baker

et al. 2015

Mech Adv Mater Mod Process

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Background: Essentially all heterogeneous materials are dielectric, i.e., they are imperfect conductors that generally display internal charge displacements that create dissipation and local charge accumulation at interfaces. Over the last few years, the authors have focused on the development of an understanding of such behaviour in heterogeneous functional materials for energy conversion and storage, called HeteroFoaM (www.HeteroFoaM.com). Using paradigm problems, this work will indicate major directions for developing generally applicable methods for the multiphysics, multi-scale design of heterogeneous functional materials. Methods: The present paper outlines the foundation for developing validated predictive computational methods that can be used in the design of multi-phase heterogeneous functional materials, or HeteroFoaM, as a genre of materials. Such methods will be capable of designing not only the constituent materials and their interactions, but also the morphology of the shape, size, surfaces and interfaces that define the heterogeneity and the resulting functional response of the material system. Results: Relationships to applications which drive this development are identified. A paradigm problem based on dielectric response is formulated and discussed in context.

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“…With 7 parameters this yields (3)^=2,187 different sensitivity calculations that can be made simply by substitution into Equation (12) to obtain the approximate fractional change in the response. The exact change in R would require that the primal cork and bottle problem be solved 2,187 times.…”

Section: Computed Changes In Output Responsementioning

confidence: 99%

Uncertainty analysis

Thomas¹

1982

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Sensitivity Theory for General Systems of Nonlinear Equations

Cited by 147 publications

References 0 publications

A review of techniques for parameter sensitivity analysis of environmental models

A review of techniques for parameter sensitivity analysis of environmental models

Validated predictive computational methods for surface charge in heterogeneous functional materials: HeteroFoaM™

Uncertainty analysis

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