The n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (n<sup>th</sup>-CASAM-N): Mathematical Framework
This work presents the n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (n<sup>th</sup>-CASAM-N), which enables the most efficient computation of exactly determined expressions of arbitrarily high-order sensitivities of generic...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Journal of Nuclear Engineering |
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| Online Access: | https://www.mdpi.com/2673-4362/3/3/10 |
| _version_ | 1797486269443342336 |
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| author | Dan Gabriel Cacuci |
| author_facet | Dan Gabriel Cacuci |
| author_sort | Dan Gabriel Cacuci |
| collection | DOAJ |
| description | This work presents the n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (n<sup>th</sup>-CASAM-N), which enables the most efficient computation of exactly determined expressions of arbitrarily high-order sensitivities of generic nonlinear system responses with respect to model parameters, uncertain boundaries, and internal interfaces in the model’s phase space. The mathematical framework underlying the n<sup>th</sup>-CASAM-N is proven to be correct by using mathematical induction. The n<sup>th</sup>-CASAM-N is formulated in linearly increasing higher-dimensional Hilbert spaces—as opposed to exponentially increasing parameter-dimensional spaces—thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems. |
| first_indexed | 2024-03-09T23:30:50Z |
| format | Article |
| id | doaj.art-0abf06aa0b7349d7ba824e7c5a517f29 |
| institution | Directory Open Access Journal |
| issn | 2673-4362 |
| language | English |
| last_indexed | 2024-03-09T23:30:50Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Journal of Nuclear Engineering |
| spelling | doaj.art-0abf06aa0b7349d7ba824e7c5a517f292023-11-23T17:08:39ZengMDPI AGJournal of Nuclear Engineering2673-43622022-06-013316319010.3390/jne3030010The n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (n<sup>th</sup>-CASAM-N): Mathematical FrameworkDan Gabriel Cacuci0Center for Nuclear Science and Energy, University of South Carolina, Columbia, SC 29208, USAThis work presents the n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (n<sup>th</sup>-CASAM-N), which enables the most efficient computation of exactly determined expressions of arbitrarily high-order sensitivities of generic nonlinear system responses with respect to model parameters, uncertain boundaries, and internal interfaces in the model’s phase space. The mathematical framework underlying the n<sup>th</sup>-CASAM-N is proven to be correct by using mathematical induction. The n<sup>th</sup>-CASAM-N is formulated in linearly increasing higher-dimensional Hilbert spaces—as opposed to exponentially increasing parameter-dimensional spaces—thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems.https://www.mdpi.com/2673-4362/3/3/10large-scale nonlinear modelshigh-order sensitivitiesadjoint operatorscurse of dimensionality |
| spellingShingle | Dan Gabriel Cacuci The n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (n<sup>th</sup>-CASAM-N): Mathematical Framework Journal of Nuclear Engineering large-scale nonlinear models high-order sensitivities adjoint operators curse of dimensionality |
| title | The n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (n<sup>th</sup>-CASAM-N): Mathematical Framework |
| title_full | The n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (n<sup>th</sup>-CASAM-N): Mathematical Framework |
| title_fullStr | The n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (n<sup>th</sup>-CASAM-N): Mathematical Framework |
| title_full_unstemmed | The n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (n<sup>th</sup>-CASAM-N): Mathematical Framework |
| title_short | The n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (n<sup>th</sup>-CASAM-N): Mathematical Framework |
| title_sort | n sup th sup order comprehensive adjoint sensitivity analysis methodology for nonlinear systems n sup th sup casam n mathematical framework |
| topic | large-scale nonlinear models high-order sensitivities adjoint operators curse of dimensionality |
| url | https://www.mdpi.com/2673-4362/3/3/10 |
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