Dynamic data-driven model reduction: adapting reduced models from incomplete data
This work presents a data-driven online adaptive model reduction approach for systems that undergo dynamic changes. Classical model reduction constructs a reduced model of a large-scale system in an offline phase and then keeps the reduced model unchanged during the evaluations in an online phase; h...
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| 格式: | Article |
| 語言: | English |
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Springer International Publishing
2016
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| 在線閱讀: | http://hdl.handle.net/1721.1/103331 https://orcid.org/0000-0002-5045-046X https://orcid.org/0000-0003-2156-9338 |
| _version_ | 1826217157660246016 |
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| author | Peherstorfer, Benjamin Willcox, Karen E. |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Peherstorfer, Benjamin Willcox, Karen E. |
| author_sort | Peherstorfer, Benjamin |
| collection | MIT |
| description | This work presents a data-driven online adaptive model reduction approach for systems that undergo dynamic changes. Classical model reduction constructs a reduced model of a large-scale system in an offline phase and then keeps the reduced model unchanged during the evaluations in an online phase; however, if the system changes online, the reduced model may fail to predict the behavior of the changed system. Rebuilding the reduced model from scratch is often too expensive in time-critical and real-time environments. We introduce a dynamic data-driven adaptation approach that adapts the reduced model from incomplete sensor data obtained from the system during the online computations. The updates to the reduced models are derived directly from the incomplete data, without recourse to the full model. Our adaptivity approach approximates the missing values in the incomplete sensor data with gappy proper orthogonal decomposition. These approximate data are then used to derive low-rank updates to the reduced basis and the reduced operators. In our numerical examples, incomplete data with 30–40 % known values are sufficient to recover the reduced model that would be obtained via rebuilding from scratch. |
| first_indexed | 2024-09-23T16:58:56Z |
| format | Article |
| id | mit-1721.1/103331 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:58:56Z |
| publishDate | 2016 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1033312022-09-29T22:52:27Z Dynamic data-driven model reduction: adapting reduced models from incomplete data Peherstorfer, Benjamin Willcox, Karen E. Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Peherstorfer, Benjamin Willcox, Karen E. This work presents a data-driven online adaptive model reduction approach for systems that undergo dynamic changes. Classical model reduction constructs a reduced model of a large-scale system in an offline phase and then keeps the reduced model unchanged during the evaluations in an online phase; however, if the system changes online, the reduced model may fail to predict the behavior of the changed system. Rebuilding the reduced model from scratch is often too expensive in time-critical and real-time environments. We introduce a dynamic data-driven adaptation approach that adapts the reduced model from incomplete sensor data obtained from the system during the online computations. The updates to the reduced models are derived directly from the incomplete data, without recourse to the full model. Our adaptivity approach approximates the missing values in the incomplete sensor data with gappy proper orthogonal decomposition. These approximate data are then used to derive low-rank updates to the reduced basis and the reduced operators. In our numerical examples, incomplete data with 30–40 % known values are sufficient to recover the reduced model that would be obtained via rebuilding from scratch. United States. Air Force Office of Scientific Research (AFOSR MURI on multi-information sources of multi-physics systems, Award Number FA9550-15-1-0038) United States. Dept. of Energy (Applied Mathematics Program, Award DE-FG02 08ER2585) United States. Dept. of Energy (Applied Mathematics Program, Award DE-SC0009297) 2016-06-24T18:14:50Z 2016-06-24T18:14:50Z 2016-03 2015-11 2016-05-23T09:38:26Z Article http://purl.org/eprint/type/JournalArticle 2213-7467 http://hdl.handle.net/1721.1/103331 Peherstorfer, Benjamin, and Karen Willcox. "Dynamic data-driven model reduction: adapting reduced models from incomplete data." Advanced Modeling and Simulation in Engineering Sciences. 2016 Mar 21;3(1):11 https://orcid.org/0000-0002-5045-046X https://orcid.org/0000-0003-2156-9338 en http://dx.doi.org/10.1186/s40323-016-0064-x Advanced Modeling and Simulation in Engineering Sciences Creative Commons Attribution http://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer International Publishing Springer International Publishing |
| spellingShingle | Peherstorfer, Benjamin Willcox, Karen E. Dynamic data-driven model reduction: adapting reduced models from incomplete data |
| title | Dynamic data-driven model reduction: adapting reduced models from incomplete data |
| title_full | Dynamic data-driven model reduction: adapting reduced models from incomplete data |
| title_fullStr | Dynamic data-driven model reduction: adapting reduced models from incomplete data |
| title_full_unstemmed | Dynamic data-driven model reduction: adapting reduced models from incomplete data |
| title_short | Dynamic data-driven model reduction: adapting reduced models from incomplete data |
| title_sort | dynamic data driven model reduction adapting reduced models from incomplete data |
| url | http://hdl.handle.net/1721.1/103331 https://orcid.org/0000-0002-5045-046X https://orcid.org/0000-0003-2156-9338 |
| work_keys_str_mv | AT peherstorferbenjamin dynamicdatadrivenmodelreductionadaptingreducedmodelsfromincompletedata AT willcoxkarene dynamicdatadrivenmodelreductionadaptingreducedmodelsfromincompletedata |