Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extended Dynamic Mode Decomposition for Inhomogeneous Problems   Dynamic mode decomposition (DMD) is a powerful data-driven technique for
construction of reduced-order models of complex dynamical systems. Multiple
numerical tests have demonstrated the accuracy and efficiency of DMD, but
mostly for systems described by partial differential equations (PDEs) with
homogeneous boundary conditions. We propose an extended dynamic mode
decomposition (xDMD) approach to cope with the potential unknown sources/sinks
in PDEs. Motivated by similar ideas in deep neural networks, we equipped our
xDMD with two new features. First, it has a bias term, which accounts for
inhomogeneity of PDEs and/or boundary conditions. Second, instead of learning a
flow map, xDMD learns the residual increment by subtracting the identity
operator. Our theoretical error analysis demonstrates the improved accuracy of
xDMD relative to standard DMD. Several numerical examples are presented to
illustrate this result.

31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph