Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

The Second-Order Features Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (2nd-FASAM-L): Mathematical Framework and Illustrative Application to an Energy System

Version 1 : Received: 1 April 2024 / Approved: 1 April 2024 / Online: 5 April 2024 (11:01:27 CEST)

A peer-reviewed article of this Preprint also exists.

Cacuci, D.G. The Second-Order Features Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (2nd-FASAM-L): Mathematical Framework and Illustrative Application to an Energy System. Energies 2024, 17, 2263. Cacuci, D.G. The Second-Order Features Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (2nd-FASAM-L): Mathematical Framework and Illustrative Application to an Energy System. Energies 2024, 17, 2263.

Abstract

This work presents the mathematical framework of the Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (abbreviated as “2nd-CASAM-L”), which enables the most efficient computation of exactly obtained mathematical expressions of first- and second-order sensitivities of a generic system response with respect to functions (“features”) of model parameters. Subsequently, the first- and second-order sensitivities with respect to the model’s uncertain parameters, boundaries, and internal interfaces are obtained analytically and exactly, without needing large-scale computations. Within the 2nd-FASAM-L methodology, the number of large-scale computations is proportional to the number of model features (defined as functions of model parameters), as opposed to being proportional to the number of model parameters, which are considerably more than the number of features, being incomparably more efficient and more accurate than any other methods (statistical, finite differences, etc.) for computing exact expressions of response sensitivities (of any order) with respect to the model’s features and/or primary uncertain parameters, boundaries, and internal interfaces. The application of the 2nd-CASAM-L methodology is illustrated using a simplified energy-dependent neutron transport model of fundamental significance in nuclear reactor physics.

Keywords

exact computation of first- and second-order sensitivities of model responses to features of model parameters; first- and second-level adjoint sensitivity systems; neutron slowing down and transport

Subject

Physical Sciences, Mathematical Physics

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