Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition   Spectral decomposition of the Koopman operator is attracting attention as a
tool for the analysis of nonlinear dynamical systems. Dynamic mode
decomposition is a popular numerical algorithm for Koopman spectral analysis;
however, we often need to prepare nonlinear observables manually according to
the underlying dynamics, which is not always possible since we may not have any
a priori knowledge about them. In this paper, we propose a fully data-driven
method for Koopman spectral analysis based on the principle of learning Koopman
invariant subspaces from observed data. To this end, we propose minimization of
the residual sum of squares of linear least-squares regression to estimate a
set of functions that transforms data into a form in which the linear
regression fits well. We introduce an implementation with neural networks and
evaluate performance empirically using nonlinear dynamical systems and
applications.

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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom