A coupling approach to rare event simulation via dynamic importance sampling
Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2017.
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| Other Authors: | |
| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2017
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| Online Access: | http://hdl.handle.net/1721.1/112384 |
| _version_ | 1826202226083758080 |
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| author | Zhang, Benjamin Jiahong |
| author2 | Youssef M. Marzouk. |
| author_facet | Youssef M. Marzouk. Zhang, Benjamin Jiahong |
| author_sort | Zhang, Benjamin Jiahong |
| collection | MIT |
| description | Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2017. |
| first_indexed | 2024-09-23T12:04:10Z |
| format | Thesis |
| id | mit-1721.1/112384 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T12:04:10Z |
| publishDate | 2017 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1123842019-04-12T22:52:20Z A coupling approach to rare event simulation via dynamic importance sampling Zhang, Benjamin Jiahong Youssef M. Marzouk. Massachusetts Institute of Technology. Department of Aeronautics and Astronautics. Massachusetts Institute of Technology. Department of Aeronautics and Astronautics. Aeronautics and Astronautics. Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2017. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Cataloged from student-submitted PDF version of thesis. Includes bibliographical references (pages 106-109). Rare event simulation involves using Monte Carlo methods to estimate probabilities of unlikely events and to understand the dynamics of a system conditioned on a rare event. An established class of algorithms based on large deviations theory and control theory constructs provably asymptotically efficient importance sampling estimators. Dynamic importance sampling is one these algorithms in which the choice of biasing distribution adapts in the course of a simulation according to the solution of an Isaacs partial differential equation or by solving a sequence of variational problems. However, obtaining the solution of either problem may be expensive, where the cost of solving these problems may be even more expensive than performing simple Monte Carlo exhaustively. Deterministic couplings induced by transport maps allows one to relate a complex probability distribution of interest to a simple reference distribution (e.g. a standard Gaussian) through a monotone, invertible function. This diverts the complexity of the distribution of interest into a transport map. We extend the notion of transport maps between probability distributions on Euclidean space to probability distributions on path space following a similar procedure to Itô's coupling. The contraction principle is a key concept from large deviations theory that allows one to relate large deviations principles of different systems through deterministic couplings. We convey that with the ability to computationally construct transport maps, we can leverage the contraction principle to reformulate the sequence of variational problems required to implement dynamic importance sampling and make computation more amenable. We apply this approach to simple rotorcraft models. We conclude by outlining future directions of research such as using the coupling interpretation to accelerate rare event simulation via particle splitting, using transport maps to learn large deviations principles, and accelerating inference of rare events. by Benjamin Jiahong Zhang. S.M. 2017-12-05T16:25:34Z 2017-12-05T16:25:34Z 2017 2017 Thesis http://hdl.handle.net/1721.1/112384 1011501785 eng MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission. http://dspace.mit.edu/handle/1721.1/7582 109 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Aeronautics and Astronautics. Zhang, Benjamin Jiahong A coupling approach to rare event simulation via dynamic importance sampling |
| title | A coupling approach to rare event simulation via dynamic importance sampling |
| title_full | A coupling approach to rare event simulation via dynamic importance sampling |
| title_fullStr | A coupling approach to rare event simulation via dynamic importance sampling |
| title_full_unstemmed | A coupling approach to rare event simulation via dynamic importance sampling |
| title_short | A coupling approach to rare event simulation via dynamic importance sampling |
| title_sort | coupling approach to rare event simulation via dynamic importance sampling |
| topic | Aeronautics and Astronautics. |
| url | http://hdl.handle.net/1721.1/112384 |
| work_keys_str_mv | AT zhangbenjaminjiahong acouplingapproachtorareeventsimulationviadynamicimportancesampling AT zhangbenjaminjiahong couplingapproachtorareeventsimulationviadynamicimportancesampling |