Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Discrete Empirical Interpolation Method for Interpretable Immersion
  and Embedding of Nonlinear Manifolds   Manifold learning techniques seek to discover structure-preserving mappings
of high-dimensional data into low-dimensional spaces.
  While the new sets of coordinates specified by these mappings can closely
parameterize the data, they are generally complicated nonlinear functions of
the original variables. This makes them difficult to interpret physically.
  Furthermore, in data-driven model reduction applications the governing
equations may have structure that is destroyed by nonlinear mapping into
coordinates on an inertial manifold, creating a computational bottleneck for
simulations.
  Instead, we propose to identify a small collection of the original variables
which are capable of uniquely determining all others either locally via
immersion or globally via embedding of the underlying manifold.
  When the data lies on a low-dimensional subspace the existing discrete
empirical interpolation method (DEIM) accomplishes this with recent variants
employing greedy algorithms based on pivoted QR (PQR) factorizations.
  However, low-dimensional manifolds coming from a variety of applications,
particularly from advection-dominated PDEs, do not lie in or near any
low-dimensional subspace.
  Our proposed approach extends DEIM to data lying near nonlinear manifolds by
applying a similar pivoted QR procedure simultaneously on collections of
patches making up locally linear approximations of the manifold, resulting in a
novel simultaneously pivoted QR (SimPQR) algorithm.
  The immersion provided by SimPQR can be extended to an embedding by applying
SimPQR a second time to a modified collection of vectors.
  The SimPQR method for computing these `nonlinear DEIM' (NLDEIM) coordinates
is successfully applied to real-world data lying near an inertial manifold in a
cylinder wake flow as well as data coming from a viscous Burgers equation with
different initial conditions.

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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int