4th-Order-SENS: A Software Module for Efficient and Exact 4th-Order Sensitivity Analysis of Neutron Transport

Fang, Ruixian; Cacuci, Dan G.

doi:10.1080/00295639.2023.2255725

Cited by 1 publication

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References 22 publications

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“…The influence of the size of the parameter variation will be illustrated below by considering the largest fourth-order mixed and, respectively, unmixed sensitivities, namely, (i) the largest fourth-order unmixed relative sensitivity S (4) = 2.720 × 10 6 for isotope #6 ( 1 H) of the PERP benchmark and (ii) the largest fourth-order mixed relative sensitivity S (4) σ 30 t,6 , σ 30 t,6 , σ 30 t,6 , σ 30 t,5 = 2.279 × 10 5 , for the leakage response with respect to the microscopic total cross-sections for group 30 of isotopes #5 ( 12 C) and #6 ( 1 H). The exact values for these sensitivities were computed [22] using the software package the "fourth-order SENS" [34], which computes the first-order through the fourth-order sensitivities of the PERP leakage response with respect to model parameters using the "Fourth-Order Comprehensive Adjoint Sensitivity Analysis Methodology" (fourth-CASAM). On the other hand, the finite difference formula that has been used for computing these sensitivities is reproduced below:…”

Section: Using Finite Differences: a Conceptually Simple But Computat...mentioning

confidence: 99%

Computation of High-Order Sensitivities of Model Responses to Model Parameters—I: Underlying Motivation and Current Methods

Cacuci

2023

Energies

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The mathematical/computational model of a physical system comprises parameters and independent and dependent variables. Since the physical system is seldom known precisely and since the model’s parameters stem from experimental procedures that are also subject to uncertainties, the results predicted by a computational model are imperfect. Quantifying the reliability and accuracy of results produced by a model (called “model responses”) requires the availability of sensitivities (i.e., functional partial derivatives) of model responses with respect to model parameters. This work reviews the basic motivations for computing high-order sensitivities and illustrates their importance by means of an OECD/NEA reactor physics benchmark, which is representative of a “large-scale system” involving many (21,976) uncertain parameters. The computation of higher-order sensitivities by conventional methods (finite differences and/or statistical procedures) is subject to the “curse of dimensionality”. Furthermore, as will be illustrated in this work, the accuracy of high-order sensitivities computed using such conventional methods cannot be a priori guaranteed. High-order sensitivities can be computed accurately and efficiently solely by applying the high-order adjoint sensitivity analysis methodology. The principles underlying this adjoint methodology are also reviewed in preparation for introducing, in the accompanying Part II, the “High-Order Function/Feature Adjoint Sensitivity Analysis Methodology” (nth-FASAM), which aims at most efficiently computing exact expressions of high-order sensitivities of model responses to functions (“features”) of model parameters.

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Section: Using Finite Differences: a Conceptually Simple But Computat...mentioning

confidence: 99%

Computation of High-Order Sensitivities of Model Responses to Model Parameters—I: Underlying Motivation and Current Methods

Cacuci

2023

Energies

View full text Add to dashboard Cite

show abstract

4th-Order-SENS: A Software Module for Efficient and Exact 4th-Order Sensitivity Analysis of Neutron Transport

Cited by 1 publication

References 22 publications

Computation of High-Order Sensitivities of Model Responses to Model Parameters—I: Underlying Motivation and Current Methods

Computation of High-Order Sensitivities of Model Responses to Model Parameters—I: Underlying Motivation and Current Methods

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