Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks
We introduce a data-driven forecasting method for high-dimensional chaotic systems using long shortterm memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set...
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| Format: | Article |
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The Royal Society
2019
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| Online Access: | http://hdl.handle.net/1721.1/120011 https://orcid.org/0000-0001-7264-3628 https://orcid.org/0000-0003-0302-0691 |
| _version_ | 1826206726389497856 |
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| author | Vlachas, Pantelis R. Byeon, Wonmin 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 R. Byeon, Wonmin Koumoutsakos, Petros Wan, Zhong Yi Sapsis, Themistoklis P. |
| author_sort | Vlachas, Pantelis R. |
| collection | MIT |
| description | We introduce a data-driven forecasting method for high-dimensional chaotic systems using long shortterm memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPS) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPS in short-Term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks. |
| first_indexed | 2024-09-23T13:37:17Z |
| format | Article |
| id | mit-1721.1/120011 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T13:37:17Z |
| publishDate | 2019 |
| publisher | The Royal Society |
| record_format | dspace |
| spelling | mit-1721.1/1200112024-06-28T14:42:14Z Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks Vlachas, Pantelis R. Byeon, Wonmin Koumoutsakos, Petros Wan, Zhong Yi Sapsis, Themistoklis P. Massachusetts Institute of Technology. Department of Mechanical Engineering Wan, Zhong Yi Sapsis, Themistoklis P. We introduce a data-driven forecasting method for high-dimensional chaotic systems using long shortterm memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPS) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPS in short-Term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks. United States. Air Force. Office of Scientific Research (Grant FA9550-16-1-0231) United States. Office of Naval Research (Grant N00014-15-1-2381) United States. Army Research Office (Grant 66710-EG-YIP) 2019-01-11T20:36:26Z 2019-01-11T20:36:26Z 2018-05 2018-12-18T16:13:28Z Article http://purl.org/eprint/type/JournalArticle 1364-5021 1471-2946 http://hdl.handle.net/1721.1/120011 Vlachas, Pantelis R., Wonmin Byeon, Zhong Y. Wan, Themistoklis P. Sapsis, and Petros Koumoutsakos. “Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 474, no. 2213 (May 2018): 20170844. © 2018 The Authors https://orcid.org/0000-0001-7264-3628 https://orcid.org/0000-0003-0302-0691 http://dx.doi.org/10.1098/RSPA.2017.0844 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf The Royal Society arXiv |
| spellingShingle | Vlachas, Pantelis R. Byeon, Wonmin Koumoutsakos, Petros Wan, Zhong Yi Sapsis, Themistoklis P. Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks |
| title | Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks |
| title_full | Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks |
| title_fullStr | Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks |
| title_full_unstemmed | Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks |
| title_short | Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks |
| title_sort | data driven forecasting of high dimensional chaotic systems with long short term memory networks |
| url | http://hdl.handle.net/1721.1/120011 https://orcid.org/0000-0001-7264-3628 https://orcid.org/0000-0003-0302-0691 |
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