Illustrative Application of the 2<sup>nd</sup>-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Point-Detector Response

• 作者: Dan Gabriel Cacuci
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: Second-Order Adjoint Comprehensive Sensitivity Analysis Methodology (2^nd-CASAM) Evolution Benchmark Model Exact and Efficient Computation of First- and Second-Order Response Sensitivities
• 年，卷（期）: 2020,（3）
• 页码范围: 355-381
• 页数: 27页
• 分类号: O17

摘要

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.