Model Order Reduction for Stochastic Dynamical Systems with Continuous Symmetries
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17m1126576.pdf
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Author(s)
Mowlavi, Saviz
Sapsis, Themistoklis P.
Date Issued
January 2018
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Citation
Mowlavi, Saviz, and Themistoklis P. Sapsis. “Model Order Reduction for Stochastic Dynamical Systems with Continuous Symmetries.” SIAM Journal on Scientific Computing 40, no. 3 (January 2018): A1669–A1695. © 2018 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
Stochastic dynamical systems with continuous symmetries arise commonly in nature and often give rise to coherent spatio-temporal patterns. However, because of their random locations, these patterns are not captured well by current order reduction techniques, and a large number of modes is typically necessary for an accurate solution. In this work, we introduce a new methodology for efficient order reduction of such systems by combining (i) the method of slices [C. W. Rowley and J. E. Marsden, Phys. D, 142 (2000), pp. 1-19; S. Froehlich and P. Cvitanovi\'c, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), pp. 2074-2084], a symmetry reduction tool, and (ii) any standard order reduction technique, resulting in efficient mixed symmetry-dimensionality reduction schemes. In particular, using the dynamically orthogonal (DO) equations [T. P. Sapsis and P. F. J. Lermusiaux, Phys. D, 238 (2009), pp. 2347-2360] in the second step, we obtain a novel nonlinear symmetry-reduced dynamically orthogonal (SDO) scheme. We demonstrate the performance of the SDO scheme on stochastic solutions of the one-dimensional Korteweg-de Vries and two-dimensional Navier-Stokes equations. Keywords: model order reduction, stochastic dynamical systems, symmetry reduction
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1137/17M1126576
