Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational Multi-scale Super-resolution : A data-driven approach for
  reconstruction and predictive modeling of unresolved physics   The variational multiscale (VMS) formulation formally segregates the
evolution of the coarse-scales from the fine-scales. VMS modeling requires the
approximation of the impact of the fine scales in terms of the coarse scales.
In linear problems, our formulation reduces the problem of learning the
sub-scales to learning the projected element Green's function basis
coefficients. For the purpose of this approximation, a special neural-network
structure - the variational super-resolution N-N (VSRNN) - is proposed. The
VSRNN constructs a super-resolved model of the unresolved scales as a sum of
the products of individual functions of coarse scales and physics-informed
parameters. Combined with a set of locally non-dimensional features obtained by
normalizing the input coarse-scale and output sub-scale basis coefficients, the
VSRNN provides a general framework for the discovery of closures for both the
continuous and the discontinuous Galerkin discretizations. By training this
model on a sequence of $L_2-$projected data and using the subscale to compute
the continuous Galerkin subgrid terms, and the super-resolved state to compute
the discontinuous Galerkin fluxes, we improve the optimality and the accuracy
of these methods for the convection-diffusion problem, linear advection and
turbulent channel flow. Finally, we demonstrate that - in the investigated
examples - the present model allows generalization to out-of-sample initial
conditions and Reynolds numbers. Perspectives are provided on data-driven
closure modeling, limitations of the present approach, and opportunities for
improvement.

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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
32
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: math-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: chem-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: hep-lat