Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning Bounded Koopman Observables: Results on Stability, Continuity,
  and Controllability   The Koopman operator is an useful analytical tool for studying dynamical
systems -- both controlled and uncontrolled. For example, Koopman
eigenfunctions can provide non-local stability information about the underlying
dynamical system. Koopman representations of nonlinear systems are commonly
calculated using machine learning methods, which seek to represent the Koopman
eigenfunctions as a linear combinations of nonlinear state measurements. As
such, it is important to understand whether, in principle, these eigenfunctions
can be successfully obtained using machine learning and what eigenfunctions
calculated in this way can tell us about the underlying system. To that end,
this paper presents an analysis of continuity, stability and control
limitations associated with Koopman eigenfunctions under minimal assumptions
and provides a discussion that relates these properties to the ability to
calculate Koopman representations with machine learning.

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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin