Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robust Approximation of the Stochastic Koopman Operator   We analyze the performance of Dynamic Mode Decomposition (DMD)-based
approximations of the stochastic Koopman operator for random dynamical systems
where either the dynamics or observables are affected by noise. For many DMD
algorithms, the presence of noise can introduce a bias in the DMD operator,
leading to poor approximations of the dynamics. In particular, methods using
time delayed observables, such as Hankel DMD, are biased when the dynamics are
random. We introduce a new, robust DMD algorithm that can approximate the
stochastic Koopman operator despite the presence of noise. We then demonstrate
how this algorithm can be applied to time delayed observables, which allows us
to generate a Krylov subspace from a single observable. This allows us to
compute a realization of the stochastic Koopman operator using a single
observable measured over a single trajectory. We test the performance of the
algorithms over several examples.

31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int