Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1137/16M1059308 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
nonlinear dynamical systems,proper orthogonal decomposition,dynamic mode decomposition,data-driven modeling,reduced order modeling,dimensionality reduction | Dynamic mode decomposition,Mathematical optimization,Nonlinear system,Matrix decomposition,Surrogate model,Order reduction,Periodic graph (geometry),Nonlinear model,Mathematics,Speedup | Journal |
Volume | Issue | ISSN |
39 | 5 | 1064-8275 |
Citations | PageRank | References |
6 | 0.47 | 8 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alessandro Alla | 1 | 13 | 4.40 |
| J. Nathan Kutz | 2 | 225 | 47.13 |