Illustrative Application of the 2<sup>nd</sup>-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Point-Detector Response
- 1 Center for Nuclear Science and Energy, Department of Mechanical Engineering, University of South Carolina, Columbia SC, USA
Abstract
This work illustrates the application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2 nd -CASAM) to a mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response is the value of the model’s state function (particle concentration or particle flux) at a point in phase-space, which would simulate a pointwise measurement of the respective state function. This paradigm model admits exact closed-form expressions for all of the 1 st - and 2 nd -order response sensitivities to the model’s uncertain parameters and domain boundaries. These closed-form expressions can be used to verify the numerical results of production and/or commercial software, e.g., particle transport codes. Furthermore, this paradigm model comprises many uncertain parameters which have relative sensitivities of identical magnitudes. Therefore, this paradigm model could serve as a stringent benchmark for inter-comparing the performances of all deterministic and statistical sensitivity analysis methods, including the 2 nd -CASAM.
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