Illustrative Application of the 2<sup>nd</sup>-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Reaction-Rate 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: 382-397
• 页数: 16页
• 分类号: O17

摘要

This work continues the illustrative application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2^nd-CASAM) to a benchmark mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response considered in this work is a reaction-rate detector response, which provides the average interactions of particles with the respective detector or, alternatively, the time-average of the concentration of a mixture of substances in a medium. The definition of this model response includes both uncertain boundary points of the benchmark, thereby providing both direct and indirect contributions to the response sensitivities stemming from the boundaries. The exact expressions for the 1^st- and 2^nd-order response sensitivities to the boundary and model parameters obtained in this work can serve as stringent benchmarks for inter-comparing the performances of all (deterministic and statistical) sensitivity analysis methods.