A learning method for the approximation of discontinuous functions for stochastic simulations
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2013
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| Online Access: | http://hdl.handle.net/1721.1/76101 |
| _version_ | 1826191980233752576 |
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| author | Gorodetsky, Alex Arkady |
| author2 | Youssef Marzouk. |
| author_facet | Youssef Marzouk. Gorodetsky, Alex Arkady |
| author_sort | Gorodetsky, Alex Arkady |
| collection | MIT |
| description | Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012. |
| first_indexed | 2024-09-23T09:04:19Z |
| format | Thesis |
| id | mit-1721.1/76101 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T09:04:19Z |
| publishDate | 2013 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/761012019-04-10T20:32:31Z A learning method for the approximation of discontinuous functions for stochastic simulations Gorodetsky, Alex Arkady Youssef Marzouk. Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. Aeronautics and Astronautics. Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012. Cataloged from PDF version of thesis. Includes bibliographical references (p. 79-83). Surrogate models for computational simulations are inexpensive input-output approximations that allow expensive analyses, such as the forward propagation of uncertainty and Bayesian statistical inference, to be performed efficiently. When a simulation output does not depend smoothly on its inputs, however, most existing surrogate construction methodologies yield large errors and slow convergence rates. This thesis develops a new methodology for approximating simulation outputs that depend discontinuously on input parameters. Our approach focuses on piecewise smooth outputs and involves two stages: first, efficient detection and localization of discontinuities in high-dimensional parameter spaces using polynomial annihilation, support vector machine classification, and uncertainty sampling; second, approximation of the output on each region using Gaussian process regression. The discontinuity detection methodology is illustrated on examples of up to 11 dimensions, including algebraic models and ODE systems, demonstrating improved scaling and efficiency over other methods found in the literature. Finally, the complete surrogate construction approach is demonstrated on two physical models exhibiting canonical discontinuities: shock formation in Burgers' equation and autoignition in hydrogen-oxygen combustion. by Alex Arkady Gorodetsky. S.M. 2013-01-07T21:20:47Z 2013-01-07T21:20:47Z 2012 2012 Thesis http://hdl.handle.net/1721.1/76101 820461891 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 83 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Aeronautics and Astronautics. Gorodetsky, Alex Arkady A learning method for the approximation of discontinuous functions for stochastic simulations |
| title | A learning method for the approximation of discontinuous functions for stochastic simulations |
| title_full | A learning method for the approximation of discontinuous functions for stochastic simulations |
| title_fullStr | A learning method for the approximation of discontinuous functions for stochastic simulations |
| title_full_unstemmed | A learning method for the approximation of discontinuous functions for stochastic simulations |
| title_short | A learning method for the approximation of discontinuous functions for stochastic simulations |
| title_sort | learning method for the approximation of discontinuous functions for stochastic simulations |
| topic | Aeronautics and Astronautics. |
| url | http://hdl.handle.net/1721.1/76101 |
| work_keys_str_mv | AT gorodetskyalexarkady alearningmethodfortheapproximationofdiscontinuousfunctionsforstochasticsimulations AT gorodetskyalexarkady learningmethodfortheapproximationofdiscontinuousfunctionsforstochasticsimulations |