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NONLINEAR MODEL ORDER REDUCTION VIA DYNAMIC MODE DECOMPOSITION
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DOI：10.1137/16M1059308.png)
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摘要
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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.
Keyword:
nonlinear dynamical systems
proper orthogonal decomposition
dynamic mode decomposition
data-driven modeling
reduced order modeling
dimensionality reduction
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