Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strategies for Reduced-Order Models for Predicting the Statistical
  Responses and Uncertainty Quantification in Complex Turbulent Dynamical
  Systems   Turbulent dynamical systems characterized by both a high-dimensional phase
space and a large number of instabilities are ubiquitous among many complex
systems in science and engineering. The existence of a strange attractor in the
turbulent systems containing a large number of positive Lyapunov exponents
results in a rapid growth of small uncertainties, requiring naturally a
probabilistic characterization for the evolution of the turbulent system.
Uncertainty quantification in turbulent dynamical systems is a grand challenge
where the goal is to obtain statistical estimates such as the change in mean
and variance for key physical quantities in their nonlinear responses to
changes in external forcing parameters or uncertain initial data. One central
issue in contemporary research is the development of a systematic methodology
that can recover the crucial features of the natural system in statistical
equilibrium (model fidelity) and improve the imperfect model prediction skill
in response to various external perturbations (model sensitivity). A general
mathematical framework to construct statistically accurate reduced-order models
that have skill in capturing the statistical variability in the principal
directions with largest energy of a general class of damped and forced complex
turbulent dynamical systems is discussed here. The methods are developed under
a universal class of turbulent dynamical systems with quadratic nonlinearity
that is representative in many applications in applied mathematics and
engineering. The validity of general framework of reduced-order models is
demonstrated on instructive stochastic triad models. Recent applications to
two-layer baroclinic turbulence in the atmosphere and ocean with combinations
of turbulent jets and vortices are also surveyed.

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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat