2026-09-19T04:05:47Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1124752022-01-13T07:53:53Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Qiqi Wang.
Ni, Angxiu
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics.
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
2017-12-05T19:14:28Z
2017-12-05T19:14:28Z
2017
2017
http://hdl.handle.net/1721.1/112475
1011356422
Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2017.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 61-63).
This thesis develops the Non-Intrusive Least Squares Shadowing (NILSS) method, which computes the sensitivity for long-time averaged objectives in chaotic dynamical systems. In NILSS, we represent a tangent solution by a linear combination of one inhomogeneous tangent solution and several homogeneous tangent solutions. Next, we solve a least squares problem using this representation; thus, the resulting solution can be used for computing sensitivities. NILSS is easy to implement with existing solvers. In addition, for chaotic systems with many degrees of freedom but few unstable modes, NILSS has a low computational cost. NILSS is applied to two chaotic PDE systems: the Lorenz 63 system and a CFD simulation of flow over a backward-facing step. In both cases, the sensitivities computed by NILSS reflect the trends in the long-time averaged objectives of dynamical systems.
by Angxiu Ni.
S.M.
63 pages
eng
Massachusetts Institute of Technology
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
Aeronautics and Astronautics.
Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS)
Thesis
application/pdf
Publication
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unknown
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<Abstract>This thesis develops the Non-Intrusive Least Squares Shadowing (NILSS) method, which computes the sensitivity for long-time averaged objectives in chaotic dynamical systems. In NILSS, we represent a tangent solution by a linear combination of one inhomogeneous tangent solution and several homogeneous tangent solutions. Next, we solve a least squares problem using this representation; thus, the resulting solution can be used for computing sensitivities. NILSS is easy to implement with existing solvers. In addition, for chaotic systems with many degrees of freedom but few unstable modes, NILSS has a low computational cost. NILSS is applied to two chaotic PDE systems: the Lorenz 63 system and a CFD simulation of flow over a backward-facing step. In both cases, the sensitivities computed by NILSS reflect the trends in the long-time averaged objectives of dynamical systems.</Abstract>
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