期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 39, 期 5, 页码 B778-B796出版社
SIAM PUBLICATIONS
DOI: 10.1137/16M1059308
关键词
nonlinear dynamical systems; proper orthogonal decomposition; dynamic mode decomposition; data-driven modeling; reduced order modeling; dimensionality reduction
资金
- U.S. Department of Energy [DE-SC0009324]
- Air Force Office of Scientific Research [FA9550-15-1-0385]
- U.S. Department of Energy (DOE) [DE-SC0009324] Funding Source: U.S. Department of Energy (DOE)
We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed dynamic mode decomposition (DMD), an equation-free method, to approximate the nonlinear term. DMD is a spatio-temporal matrix decomposition of a data matrix that correlates spatial features while simultaneously associating the activity with periodic temporal behavior. With this decomposition, one can obtain a fully reduced dimensional surrogate model and avoid the evaluation of the nonlinear term in the online stage. This allows for a reduction in the computational cost and, at the same time, accurate approximations of the problem. We present a suite of numerical tests to illustrate our approach and to show the effectiveness of the method in comparison to existing approaches.
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