Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems
Drawing upon the bursting mechanism in slow-fast systems, we propose indicators for the prediction of such rare extreme events which do not require a priori known slow and fast coordinates. The indicators are associated with functionals defined in terms of optimally time-dependent (OTD) modes. One s...
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| Format: | Article |
| Language: | English |
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American Physical Society
2016
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| Online Access: | http://hdl.handle.net/1721.1/105430 https://orcid.org/0000-0003-0302-0691 |
| _version_ | 1826205657704955904 |
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| author | Farazmand, Mohammad M Sapsis, Themistoklis P. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Farazmand, Mohammad M Sapsis, Themistoklis P. |
| author_sort | Farazmand, Mohammad M |
| collection | MIT |
| description | Drawing upon the bursting mechanism in slow-fast systems, we propose indicators for the prediction of such rare extreme events which do not require a priori known slow and fast coordinates. The indicators are associated with functionals defined in terms of optimally time-dependent (OTD) modes. One such functional has the form of the largest eigenvalue of the symmetric part of the linearized dynamics reduced to these modes. In contrast to other choices of subspaces, the proposed modes are flow invariant and therefore a projection onto them is dynamically meaningful. We illustrate the application of these indicators on three examples: a prototype low-dimensional model, a body-forced turbulent fluid flow, and a unidirectional model of nonlinear water waves. We use Bayesian statistics to quantify the predictive power of the proposed indicators. |
| first_indexed | 2024-09-23T13:16:33Z |
| format | Article |
| id | mit-1721.1/105430 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:16:33Z |
| publishDate | 2016 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1054302022-10-01T14:12:31Z Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems Farazmand, Mohammad M Sapsis, Themistoklis P. Massachusetts Institute of Technology. Department of Mechanical Engineering Farazmand, Mohammad M Sapsis, Themistoklis P. Drawing upon the bursting mechanism in slow-fast systems, we propose indicators for the prediction of such rare extreme events which do not require a priori known slow and fast coordinates. The indicators are associated with functionals defined in terms of optimally time-dependent (OTD) modes. One such functional has the form of the largest eigenvalue of the symmetric part of the linearized dynamics reduced to these modes. In contrast to other choices of subspaces, the proposed modes are flow invariant and therefore a projection onto them is dynamically meaningful. We illustrate the application of these indicators on three examples: a prototype low-dimensional model, a body-forced turbulent fluid flow, and a unidirectional model of nonlinear water waves. We use Bayesian statistics to quantify the predictive power of the proposed indicators. 2016-11-22T20:15:13Z 2016-11-22T20:15:13Z 2016-09 2016-07 2016-09-14T22:00:18Z Article http://purl.org/eprint/type/JournalArticle 2470-0045 2470-0053 http://hdl.handle.net/1721.1/105430 Farazmand, Mohammad, and Themistoklis P. Sapsis. “Dynamical Indicators for the Prediction of Bursting Phenomena in High-Dimensional Systems.” Physical Review E 94.3 (2016): n. pag. © 2016 American Physical Society https://orcid.org/0000-0003-0302-0691 en http://dx.doi.org/10.1103/PhysRevE.94.032212 Physical Review E Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Farazmand, Mohammad M Sapsis, Themistoklis P. Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems |
| title | Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems |
| title_full | Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems |
| title_fullStr | Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems |
| title_full_unstemmed | Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems |
| title_short | Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems |
| title_sort | dynamical indicators for the prediction of bursting phenomena in high dimensional systems |
| url | http://hdl.handle.net/1721.1/105430 https://orcid.org/0000-0003-0302-0691 |
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