A Gaussian Mixture Model Smoother for Continuous Nonlinear Stochastic Dynamical Systems: Theory and Scheme
Retrospective inference through Bayesian smoothing is indispensable in geophysics, with crucial applications in ocean and numerical weather estimation, climate dynamics, and Earth system modeling. However, dealing with the high-dimensionality and nonlinearity of geophysical processes remains a major...
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| Format: | Article |
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American Meteorological Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/114992 https://orcid.org/0000-0002-1869-3883 |
| _version_ | 1826201569879654400 |
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| author | Lolla, Tapovan Lermusiaux, Pierre |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Lolla, Tapovan Lermusiaux, Pierre |
| author_sort | Lolla, Tapovan |
| collection | MIT |
| description | Retrospective inference through Bayesian smoothing is indispensable in geophysics, with crucial applications in ocean and numerical weather estimation, climate dynamics, and Earth system modeling. However, dealing with the high-dimensionality and nonlinearity of geophysical processes remains a major challenge in the development of Bayesian smoothers. Addressing this issue, a novel subspace smoothing methodology for high-dimensional stochastic fields governed by general nonlinear dynamics is obtained. Building on recent Bayesian filters and classic Kalman smoothers, the fundamental equations and forward-backward algorithms of new Gaussian Mixture Model (GMM) smoothers are derived, for both the full state space and dynamic subspace. For the latter, the stochastic Dynamically Orthogonal (DO) field equations and their time-evolving stochastic subspace are employed to predict the prior subspace probabilities. Bayesian inference, both forward and backward in time, is then analytically carried out in the dominant stochastic subspace, after fitting semiparametric GMMs to joint subspace realizations. The theoretical properties, varied forms, and computational costs of the new GMM smoother equations are presented and discussed. |
| first_indexed | 2024-09-23T11:53:30Z |
| format | Article |
| id | mit-1721.1/114992 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T11:53:30Z |
| publishDate | 2018 |
| publisher | American Meteorological Society |
| record_format | dspace |
| spelling | mit-1721.1/1149922022-10-01T06:46:08Z A Gaussian Mixture Model Smoother for Continuous Nonlinear Stochastic Dynamical Systems: Theory and Scheme Lolla, Tapovan Lermusiaux, Pierre Massachusetts Institute of Technology. Department of Mechanical Engineering Lolla, Tapovan Lermusiaux, Pierre Retrospective inference through Bayesian smoothing is indispensable in geophysics, with crucial applications in ocean and numerical weather estimation, climate dynamics, and Earth system modeling. However, dealing with the high-dimensionality and nonlinearity of geophysical processes remains a major challenge in the development of Bayesian smoothers. Addressing this issue, a novel subspace smoothing methodology for high-dimensional stochastic fields governed by general nonlinear dynamics is obtained. Building on recent Bayesian filters and classic Kalman smoothers, the fundamental equations and forward-backward algorithms of new Gaussian Mixture Model (GMM) smoothers are derived, for both the full state space and dynamic subspace. For the latter, the stochastic Dynamically Orthogonal (DO) field equations and their time-evolving stochastic subspace are employed to predict the prior subspace probabilities. Bayesian inference, both forward and backward in time, is then analytically carried out in the dominant stochastic subspace, after fitting semiparametric GMMs to joint subspace realizations. The theoretical properties, varied forms, and computational costs of the new GMM smoother equations are presented and discussed. United States. Office of Naval Research (N00014-09-1- 0676) United States. Office of Naval Research (N00014-14-1- 0476) United States. Office of Naval Research (N00014-13-1-0518) United States. Office of Naval Research ( N00014-14-1-0725) 2018-04-27T15:46:48Z 2018-04-27T15:46:48Z 2017-07 2016-12 2018-02-23T19:48:13Z Article http://purl.org/eprint/type/JournalArticle 0027-0644 1520-0493 http://hdl.handle.net/1721.1/114992 Lolla, Tapovan, and Pierre F. J. Lermusiaux. “A Gaussian Mixture Model Smoother for Continuous Nonlinear Stochastic Dynamical Systems: Theory and Scheme.” Monthly Weather Review 145, 7 (July 2017): 2743–2761 © 2017 American Meteorological Society https://orcid.org/0000-0002-1869-3883 http://dx.doi.org/10.1175/MWR-D-16-0064.1 Monthly Weather Review 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. application/pdf American Meteorological Society American Meteorological Society |
| spellingShingle | Lolla, Tapovan Lermusiaux, Pierre A Gaussian Mixture Model Smoother for Continuous Nonlinear Stochastic Dynamical Systems: Theory and Scheme |
| title | A Gaussian Mixture Model Smoother for Continuous Nonlinear Stochastic Dynamical Systems: Theory and Scheme |
| title_full | A Gaussian Mixture Model Smoother for Continuous Nonlinear Stochastic Dynamical Systems: Theory and Scheme |
| title_fullStr | A Gaussian Mixture Model Smoother for Continuous Nonlinear Stochastic Dynamical Systems: Theory and Scheme |
| title_full_unstemmed | A Gaussian Mixture Model Smoother for Continuous Nonlinear Stochastic Dynamical Systems: Theory and Scheme |
| title_short | A Gaussian Mixture Model Smoother for Continuous Nonlinear Stochastic Dynamical Systems: Theory and Scheme |
| title_sort | gaussian mixture model smoother for continuous nonlinear stochastic dynamical systems theory and scheme |
| url | http://hdl.handle.net/1721.1/114992 https://orcid.org/0000-0002-1869-3883 |
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