Data-assisted reduced-order modeling of extreme events in complex dynamical systems
This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The prediction of extreme events, from avalanches and droughts t...
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| Format: | Article |
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Public Library of Science (PLoS)
2019
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| Online Access: | http://hdl.handle.net/1721.1/120303 https://orcid.org/0000-0001-7264-3628 https://orcid.org/0000-0003-0302-0691 |
| _version_ | 1811096107677122560 |
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| author | Vlachas, Pantelis Koumoutsakos, Petros Wan, Zhong Yi Sapsis, Themistoklis P. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Vlachas, Pantelis Koumoutsakos, Petros Wan, Zhong Yi Sapsis, Themistoklis P. |
| author_sort | Vlachas, Pantelis |
| collection | MIT |
| description | This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The prediction of extreme events, from avalanches and droughts to tsunamis and epidemics, depends on the formulation and analysis of relevant, complex dynamical systems. Such dynamical systems are characterized by high intrinsic dimensionality with extreme events having the form of rare transitions that are several standard deviations away from the mean. Such systems are not amenable to classical order-reduction methods through projection of the governing equations due to the large intrinsic dimensionality of the underlying attractor as well as the complexity of the transient events. Alternatively, data-driven techniques aim to quantify the dynamics of specific, critical modes by utilizing data-streams and by expanding the dimensionality of the reduced-order model using delayed coordinates. In turn, these methods have major limitations in regions of the phase space with sparse data, which is the case for extreme events. In this work, we develop a novel hybrid framework that complements an imperfect reduced order model, with data-streams that are integrated though a recurrent neural network (RNN) architecture. The reduced order model has the form of projected equations into a low-dimensional subspace that still contains important dynamical information about the system and it is expanded by a long short-term memory (LSTM) regularization. The LSTM-RNN is trained by analyzing the mismatch between the imperfect model and the data-streams, projected to the reduced-order space. The data-driven model assists the imperfect model in regions where data is available, while for locations where data is sparse the imperfect model still provides a baseline for the prediction of the system state. We assess the developed framework on two challenging prototype systems exhibiting extreme events. We show that the blended approach has improved performance compared with methods that use either data streams or the imperfect model alone. Notably the improvement is more significant in regions associated with extreme events, where data is sparse. |
| first_indexed | 2024-09-23T16:38:03Z |
| format | Article |
| id | mit-1721.1/120303 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T16:38:03Z |
| publishDate | 2019 |
| publisher | Public Library of Science (PLoS) |
| record_format | dspace |
| spelling | mit-1721.1/1203032022-10-03T07:18:11Z Data-assisted reduced-order modeling of extreme events in complex dynamical systems Vlachas, Pantelis Koumoutsakos, Petros Wan, Zhong Yi Sapsis, Themistoklis P. Massachusetts Institute of Technology. Department of Mechanical Engineering Wan, Zhong Yi Sapsis, Themistoklis P. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The prediction of extreme events, from avalanches and droughts to tsunamis and epidemics, depends on the formulation and analysis of relevant, complex dynamical systems. Such dynamical systems are characterized by high intrinsic dimensionality with extreme events having the form of rare transitions that are several standard deviations away from the mean. Such systems are not amenable to classical order-reduction methods through projection of the governing equations due to the large intrinsic dimensionality of the underlying attractor as well as the complexity of the transient events. Alternatively, data-driven techniques aim to quantify the dynamics of specific, critical modes by utilizing data-streams and by expanding the dimensionality of the reduced-order model using delayed coordinates. In turn, these methods have major limitations in regions of the phase space with sparse data, which is the case for extreme events. In this work, we develop a novel hybrid framework that complements an imperfect reduced order model, with data-streams that are integrated though a recurrent neural network (RNN) architecture. The reduced order model has the form of projected equations into a low-dimensional subspace that still contains important dynamical information about the system and it is expanded by a long short-term memory (LSTM) regularization. The LSTM-RNN is trained by analyzing the mismatch between the imperfect model and the data-streams, projected to the reduced-order space. The data-driven model assists the imperfect model in regions where data is available, while for locations where data is sparse the imperfect model still provides a baseline for the prediction of the system state. We assess the developed framework on two challenging prototype systems exhibiting extreme events. We show that the blended approach has improved performance compared with methods that use either data streams or the imperfect model alone. Notably the improvement is more significant in regions associated with extreme events, where data is sparse. United States. Air Force. Office of Scientific Research (Grant FA9550-16-1-0231) United States. Army Research Office (Grant W911NF-17-1-0306) United States. Office of Naval Research (Grant N00014-17-1-2676) 2019-02-08T19:52:15Z 2019-02-08T19:52:15Z 2018-05 2018-03 2018-12-18T16:07:15Z Article http://purl.org/eprint/type/JournalArticle 1932-6203 http://hdl.handle.net/1721.1/120303 Wan, Zhong Yi, Pantelis Vlachas, Petros Koumoutsakos, and Themistoklis Sapsis. “Data-Assisted Reduced-Order Modeling of Extreme Events in Complex Dynamical Systems.” Edited by Daniel Durstewitz. PLOS ONE 13, no. 5 (May 24, 2018): e0197704. © 2018 Wan et al. https://orcid.org/0000-0001-7264-3628 https://orcid.org/0000-0003-0302-0691 http://dx.doi.org/10.1371/JOURNAL.PONE.0197704 PLOS ONE Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by/4.0/ application/pdf Public Library of Science (PLoS) PLoS |
| spellingShingle | Vlachas, Pantelis Koumoutsakos, Petros Wan, Zhong Yi Sapsis, Themistoklis P. Data-assisted reduced-order modeling of extreme events in complex dynamical systems |
| title | Data-assisted reduced-order modeling of extreme events in complex dynamical systems |
| title_full | Data-assisted reduced-order modeling of extreme events in complex dynamical systems |
| title_fullStr | Data-assisted reduced-order modeling of extreme events in complex dynamical systems |
| title_full_unstemmed | Data-assisted reduced-order modeling of extreme events in complex dynamical systems |
| title_short | Data-assisted reduced-order modeling of extreme events in complex dynamical systems |
| title_sort | data assisted reduced order modeling of extreme events in complex dynamical systems |
| url | http://hdl.handle.net/1721.1/120303 https://orcid.org/0000-0001-7264-3628 https://orcid.org/0000-0003-0302-0691 |
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