Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Model Reduction via Dynamic Mode Decomposition   This work proposes a new framework of model reduction for parametric complex
systems. The framework employs a popular model reduction technique dynamic mode
decomposition (DMD), which is capable of combining data-driven learning and
physics ingredients based on the Koopman operator theory. In the offline step
of the proposed framework, DMD constructs a low-rank linear surrogate model for
the high dimensional quantities of interest (QoIs) derived from the (nonlinear)
complex high fidelity models (HFMs) of unknown forms. Then in the online step,
the resulting local reduced order bases (ROBs) and parametric reduced order
models (PROMs) at the training parameter sample points are interpolated to
construct a new PROM with the corresponding ROB for a new set of target/test
parameter values. The interpolations need to be done on the appropriate
manifolds within consistent sets of generalized coordinates. The proposed
framework is illustrated by numerical examples for both linear and nonlinear
problems. In particular, its advantages in computational costs and accuracy are
demonstrated by the comparisons with projection-based proper orthogonal
decomposition (POD)-PROM and Kriging.

22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom